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**International
Conference on Theoretical Physics 2011**

**Moscow, Russia**

20-23 **of June
2011**

**Moscow State Open
University**

**The****
****entropy****
****gain****
****and****
****the****
****Choi****-****Jamiolkowski****
****correspondence****
****for****
****infinite****-****dimensional****
****quantum****
****evolutions**

S. Holevo

Steklov Mathematical Institute, Russia

holevo@mi.ras.ru

In the first part of the talk we discuss the entropy gain for infinite-dimensional quantum evolutions. We show that unlike finite-dimensional case where the minimal entropy gain is always nonpositive, there are many channels with positive minimal entropy gain. We present the new lower bound and compute the minimal entropy gain for a broad class of Bosonic Gaussian channels by proving that the infimum is attained on the Gaussian states. The second part of the talk is devoted to the Choi-Jamiolkowski correspondence between channels and states in the infinite-dimensional case in the form close to one used in quantum information theory. In particular, we obtain explicit expression for the Choi-Jamiolkowski operator defining a general nondegenerate Bosonic Gaussian evolution and compute its norm.

**On****
****Superstitions****
****and****
****Errors****
****in****
****Understanding****
****the****
****Relativity****
****Theory**

Nikolai V. Mitskievich

Universidad de Guadalajara, Mexico

nmitskie@gmail.com

In this lecture, with strictly given proofs, we show that several basic axioms, including those used in generally accepted foundations of Special and General Relativity theory, do merely represent regrettable misunderstandings whose elimination by no means does falsify these theories, but it helps to understand more profoundly their contents and opens new horizons for the development of Theoretical Physics. This situation is illustrated by two examples which are accepted to be obvious truths from which were admittedly deduced both Special, as well as General Relativity Theories: in the first case it is shown that the so-called Galileo transformations have in fact the same contents as the Lorentz transformations, and in the second case that the Principle of Equivalence of Inertial and Gravitating Masses is not fulfilled in General Relativity Theory trivially yielding an unavoidable relativistic generalization of this Equivalence Principle which radically differs from the generally accepted formulation of this Principle, not reducing to addition of small corrections to this old and primitive formulation.

**Quantum****
****Effects****
****in****
****Photosynthesis****
****and**

**Entropy
Decreasing**

Igor V. Volovich

Steklov Mathematical Institute

Russian Academy of Sciences

Gubkin St. 8, 119991, Moscow, Russia

email:volovich@mi.ras.ru

Photosynthesis changes the energy from the sun into chemical energy and is vital for life on Earth. Study of photosynthesis is of a fundamental importance not only for pure science but also for applications. If researchers could learn how to move energy with such precision and efficiency over comparable distance as Nature does in photosynthesis, then enormous leaps in the development of cheap organic solar cell technology would ensue.

Previously the role of quantum effects in the photosynthesis at the room temperature was ruled out because of the quantum decoherence. However, a remarkable recent experiment (Scholes et al.) has shown that quantum mechanics might be involved in the process of photosynthesis in some marine algae even at the room temperature, see [1] for a discussion.

In this talk, based on [2], it will be suggested that the phenomenon of the enhancement of the transport of excitons in photosynthesis might be related with the decreasing (not increasing!) of entropy for the solutions of the master equation for some the complete positive trace-preserving noisy quantum channels. A constructive role of noise in quantum computations was mentioned earlier and a new paradigm for quantum computations which goes beyond the quantum Turing machine was suggested, see [1]. Note also that it was found by Caruso et al that the quantum capacity for a quantum channel in the quantum network dynamics can be enhanced by introducing dephasing noise.

References

[1] M. Ohya and I. Volovich, Mathematical Foundations of Quantum Information

and Computation and Its Applications to Nano- and Bio-systems, Springer, 2011.

[2] S. Iriyama, M. Ohya, K. Sato and I. Volovich, Photosynthetic anthenna and

entropy decreasing, TUS preprint, 2010 (to be published).

**The mechanism of
tunneling and formation of bound pairs of electrons**

Martin Rivas

University of the Basque Country, Spain

martin.rivas@ehu.es

The classical description of elementary spinning particles shows that the center of mass and center of charge of an elementary particle are different points. This separation is half Compton's wave length and because of this the interaction of two electrons with their spins parallel can produce a bound pair provided the internal phase is opposite and the relative velocity of their centers of mass is below a certain limit. It is also this separation which justifies that an electron under a potential barrier can cross it with an energy below the top of the potential provided the spin is properly oriented and the barrier has a narrow range. This can justify the spin polarized tunneling effect.

References

M. Rivas Kinematical Theory of spinning particles, Classical and quantum mechanical formalism of elementary particles, Fundamental Theories of Physics Series, Vol 116, Kluwer Academic Publishers and Springer

author web-page:http://tp.lc.ehu.es/martin.htm

**Soliton
Configurations in Generalized Mie Electrodynamics**

Yu.P. Rybakov

Peoples’ Friendship University

Department of Theoretical Physics

E-mail: soliton4@mail.ru

We consider the generalization of the G. Mie electrodynamics including 8-spinor field source and higher degrees of the Mie invariant. Peculiar topological properties of 8-spinors are distinguished and expressed via the existence of the remarkable 8-squares F. Brioschi identity permitting to obtain the natural 8-spinor unification of the Skyrme baryons model and the Faddeev leptons model, these particles being considered as the topological solitons. We construct the two types of the soliton-like configurations admitted by the model: charged static ones and luxons, i.e. neutral photon-like solitons.

**Non-classical
soliton structures in dynamics**

M. A. Aguero

Department of Physics, Faculty of Science, Universidad Autonoma del Estado de Mexico, 50000 Toluca, Mexico,

maagueorg@uaemex.mx

We have analyzed the improved Dauxoi-Peyrard-Bishop model that takes into consideration the inclusion of nonlinear interaction between adjacent pair of bases. The study of displacements along the Hydrogen bonds of DNA shows the appearance of nonlinear structures named crowdons, cuspons and peakons. These solutions exist in certain domain of the main parametric space of the model that determines a priori the velocity of the traveling structures. Nevertheless these structures would allow us to catch some peculiarities of the denaturation process. The crowdon perturbations should be considered the natural counterparts that cure the appearance of denaturation.

**Are electrons
pointlike or extended?**

Alexander Burinskii, Moscow,

NSI Russian Academy of Sciences

bur@ibrae.ac.ru

We give a brief review of the old and recent models of the extended electron, in particular the toroidal ringlike (stringlike) models considered from diverse posits of view by many authors (Parson (1916), A.Compton (1919-21), H. Hoenl 1938 and many others). After the great success of QED, and experiments on the deep inelastic scattering, these old models were considered as obsolete. Meanwhile, the QED does not take into account gravity, and moreover, there is great problem with its consistence with gravity. On the other hand, there are many evidences that black holes are akin to elementary particles (G. `t Hooft, A.Sen, F.Wilczek), and the Kerr-Newman solution has given new evidences in support of the old stringlike extended model of the electron. After Carter’s observation (1968) that the KN solution has g=2 as that of the Dirac electron there appears new activity on the model of spinning electron consistent with gravity. Singular ring of the KN solution takes the form of the lightlike circular string of the Compton size [1]. The KN model of an extended electron was started by W.Israel (1969), and from diverse point of view was considered by author in [2] as a model of a `microgeon with spin’. C.Lopez (1984) developed the Israel model (there were also the works by Arcos and Pereira (2004), T. Nieuwenhuizen (2006), Dymnikova (2006), and others, some of the refs. are given in [3].) In the paper [3] we showed that the regularization of the KN solution by the Higgs field leads to a model of the extended spinning electron consistent with gravitaty, and again there appeared a circular string of the Compton size on the border of the KN source, reproducing the old toroidal ring models. We show now that the lowest excitation of the KN soliton creates a singular node, which may be exhibited as a pointlike structure of the consistent with gravity extended KN electron.

References

[1] A. Burinskii, "Some Properties of the Kerr Solution to Low-energy String Theory," Phys. Rev. D 52 (1995) 5826 [arXiv:hep-th/9504139].

[2] A.Ya. Burinskii, «Микрогеон со спином». ЖЭТФ, т.66 (1974) 406-411; translation in: Sov. Phys. JETP, 39 (1974) 193.

[3] A. Burinskii, “Regularized Kerr-Newman Solution as a Gravitating Soliton"J. Phys. A: Math. Theor. 43 (2010) 392001, [arXiv: 1003.2928].

**Mimicking the
probability distribution of a two-dimensional Grover walk with a
single-qubit coin**

Carlo Di Franco

Physics Department, University College Cork, Ireland

cdifranco@caesar.ucc.ie

The two-dimensional Grover quantum walk has raised the interests of the scientific community, as it can be used in order to implement the two-dimensional Grover search algorithm [1]. During this talk, I will demonstrate that the non-localized case of the spatial density probability of the Grover walk can be obtained using only a two-dimensional coin space and a quantum walk in alternate directions [2]. To prove formally this equivalence, I will illustrate how the coefficients of the Grover walk in the non-localized case can be mapped to the coefficients of the alternate walk state for a particular instance of the coin initial conditions.

One of the key properties of quantum walks is their ability to evolve disentangled states into entangled ones and to efficiently generate entanglement in experimentally feasible systems [3]. Controlled entanglement generation has currently a place at the forefront of research, as it is a fundamental resource in quantum computation and cryptography and therefore a pre-requisite for the construction of reliable devices for quantum information processing [4]. I will present an analysis of the behavior of the coin-position as well as the x-y spatial entanglement in the proposed scheme with respect to the Grover one. I will show that this experimentally simpler scheme allows to entangle the two orthogonal directions of the walk more efficiently.

Finally, I will discuss a possible physical implementation of the proposed walk, along the lines of a recent experimental realization of a linear quantum walk of a single neutral atom in a spin-dependent one-dimensional optical lattice [5].

References

[1] N. Shenvi, J. Kempe, and K. B. Whaley, Phys. Rev. A 67, 052307 (2003); A. Ambainis, J. Kempe, and A. Rivosh, in Proc. 16th ACM-SIAM SODA, Vancouver (SIAM, Philadelphia, USA, 2005), p. 1099; A. Tulsi, Phys. Rev. A 78, 012310 (2008).

[2] C. Di Franco, M. McGettrick, Th. Busch, arXiv:1010.2470 (2010), accepted to be published on Phys. Rev. Lett.

[3] S. E. Venegas-Andraca and S. Bose, arXiv:0901.3946 (2009); S. K. Goya and C. M. Chandrashekar, J. Phys. A 43, 235303 (2010).

[4] R. Horodecki, P. Horodecki, M. Horodecki and K. Horodecki, Rev. Mod. Phys. 81, 865 (2009).

[5] M. Karski, L. Forster, J.-M. Choi, A. Steffen, W. Alt, D. Meschede and A. Widera, Science 325, 174 (2009).

**Densyty Matrices
of the nuclear Shall Model**

Deveikis

Vytautas Magnus University, Lithuania

a.deveikis@if.vdu.lt

The initio no-core nuclear shell-model approach is based on calculation of wave functions for description of many particle systems [1]. However it is well known that long series expansion of exact wave function in shell model ones is plagued with a number of serious convergence problems. In the light of ever-increasing model space size, the more promising approach for calculation of identical particle systems may be based on translationally invariant density matrices instead of wave functions. The approach based on density matrices may considerably reduce the size of calculations and memory demand. Moreover the translationally invariant density matrices may be calculated in antisymmetric but not translationally basis, so the sophisticated calculation of translationally invariant coefficients of fractional parentage may be completely avoided.

The
presented
two-particle
translationally
invariant
density
matrices
are
defined
as
two-particle
density
matrices
integrated
over
centre-of-mass
position
vector
of
two
last
particles
and
complemented
with
isospin
variables
[2]. The
procedures
for
calculation
of
two-particle
translationally
invariant
density
matrices
were
developed
and
implemented
in
computer
code.
The
theoretical
formulation
have
been
illustrated
by
calculation
of
translationally
invariant
density
matrices
for
E_{x}=0,1,2,3,4
excitations
in
the
case
of
A=6
and
JT=21
nucleus.

References

[1] Navr/SPAN> P., Quaglioni S., Stetcu I., Barrett B.R. Recent developments in no-core shell-model calculations // J. Phys. G: Nucl. Part. Phys. 2009. V.36, 083101, P. 1–54.

[2] Deveikis A., Kamuntavicius G.P. Intrinsic density matrices of the nuclear shell model // Lithuanian J. Phys. 1996. V.36, No. 2, P. 83–95.

**Darboux****
****Transformations****
****for****
****Generalized****
****Schr"odingerEquations**

A.A. Suzko and E.P. Velicheva (JINR)

suzko@jinr.ru

The generalized Darboux transformations are constructed for Schr"odinger equations with a position-dependent effective mass and with linearly energy-dependent potentials.

The point canonical method and the intertwining relation technique are used to obtain a family of exact solutions for this type of equations. Some examples are given for different forms of mass functions.

**The Smooth Skew
Product in the Plane with Ramified Continuum as the Global Chaotic
Attractor Containing Nonchaotic Invariant Subsets**

L,S. Efremova

Nizhny Novgorod State University, Russia

lefunn@gmail.com

Using the notions of the NT>-function and of functions suitable for the NT>-function [1], we construct the example of the C^1-smooth skew product in the closed unit square with the one-dimensional ramified continuum as the global attractor such that the following properties are valid:

(1) the set of ramification points of the global attractor has continuum cardinality, and the order of any ramification point equals 3;

(2) the cardinality of the set of points of local connectedness of , just as the cardinality of the set of points which are not points of local connectedness of , equals continuum;

(3) although the topological entropy of the map on is positive (in this sense is a chaotic attractor), nevertheless contains invariant (under some iterations of the map) closed intervals with nonchaotic behavior of trajectories, where the topological entropy of the map equals zero [2], [3].

This research was supported in the part by the Federal Target Program "Scientific and Scientific-Pedagogical Personnel of Innovative Russia" (2009 -- 2011) of the Federal Education Agency (Project No. NK -13/9).

References

1. Efremova L. S., Space of C^1-smooth skew products of maps of an interval, Theor. and Math. Physics 164 (2010), no. 3, 1208--1214.

2. Efremova L. S, Example of the smooth skew product in the plane with the one-dimensional ramified continuum as the global attractor, ESAIM: PROCEEDINGS (2011).

3. Efremova L. S., Differential properties and attracting sets of a simplest skew product of interval maps, Sbornik: Mathematics 201 (2010), no. 6, 873-907.

**Quantum Mechanics
as Asymptotics of Classical Diffusion Processes for Waves in the
Phase Space**

E.M. Beniaminov

Moscow State Gumenitary University

ebeniamin@yandex.ru

We consider the process of diffusion scattering of a wave function given on the phase space. In this process the heat diffusion is considered only along momenta. We write down the modified Kramers equation describing this situation. In this model, the usual quantum description arises as asymptotics of this process for large values of resistance of the medium per unit of mass of particle.It is shown that in this case the process passes several stages. During the first short stage, the wave function goes to one of ``stationary'' values. At the second long stage, the wave function varies in the subspace of``stationary'' states according to the Schrodinger equation. Further, dissipation of the process leads to decoherence, and any superposition of states goes to one of eigenstates of the Hamilton operator. At the last stage, the mixed state of heat equilibrium (the Gibbs state) arises due to the heat influence of the medium and the random transitions among the eigenstates of the Hamilton operator. Besides that, it is shown that, on the contrary, if the resistance of the medium per unit of mass of particleis small, then in the considered model, the density of distribution of probability satisfies the standard Liouville equation, as in classical statistical mechanics.

**The dynamics of
binary alternatives for a discrete pregeometry**

Alexey L. Krugly

Scientific Research Institute for System Analysis of the Russian Academy of Science

akrugly@mail.ru

An example of a discrete pregeometry on a microscopic scale is introduced. The model is a directed dyadic acyclic graph. This is the particular case of a causal set. The causal set is a locally finite partially ordered set. The dynamics of this model is a stochastic sequential growth dynamics. New vertexes are added one by one. The probability of this addition of a new vertex depends on the structure of existed graph. The particular case of the dynamics is considered. This dynamics is based on binary alternatives. Each directed path is considered as a sequence of outcomes of binary alternatives. The probabilities of a stochastic sequential growth have quadratic dependence on these paths. There is a matrix form of the dynamics. A matrix of amplitudes of causal connection is introduced for the description of binary alternatives. We have linear equations for the matrix of amplitudes during sequential growth of a graph. These equations are represented by evolution operators. The probabilities of a stochastic sequential growth have quadratic dependence on the matrix of amplitudes.

**Integral charge
quark super symmetry**

U.
V. S. SESHAVATHARAM^{1}
& Prof. S. LAKSHMINARAYANA^{2}

^{1}DIP
QA Engineer, Lanco Industries Ltd, Srikalahasti-517641, A.P, India.

^{2}Department
Of Nuclear Physics, Andhra University,

Visakhapatnam-530003, AP, India.

‘Quark flavor’ is a property of ‘strong interaction charge’ and nowhere connected with ‘fermions’ or ‘bosons’. There exists nature friendly ‘integral charge quark flavors’. If a ‘charged quark flavor’ rests in a ‘fermionic container’ it is a ‘quark fermion’. Similarly if a ‘charged quark flavor’ rests in a ‘bosonic container’ it is a ‘quark boson’. Strong interaction charge contains ‘multiple flavors’ and can be called as the ‘hybrid charge quark’. No 3 quark fermions couples together to form a baryon and no 2 quark fermions couples together to form a meson. In super symmetry, quark fermion and quark boson mass ratio is Si = 2.262218404 but not unity. Quark fermions convert into quark baryons and effective quark fermions convert into effective quark baryons. Similarly quark bosons convert into quark mesons. Effective quark baryons generates charged and unstable multi flavor baryons and light quark bosons couples with these charged baryons and generates doublets or triplets. Any two oppositely charged quark mesons generates neutral and unstable mesons.

T.F. Kamalov

Physics Department, Moscow State Open University

TimKamalov@gmail.com

The problem of axiomatization of physics formulated by Hilbert as early as 1900 and known as the Sixth Problem of Hilbert is nowadays even more topical than at the moment of its formulation. Axiomatic inconsistency of classic, quantum, and geometrized relativistic physics of the general relativistic theory does not in the least fade away, but on the contrary, becomes more pronounced each year. This naturally evokes the following questions: 1. Is it possible, without drastically changing the mathematics apparatus, to set up the axiomatics of physics so as to transform physics, being presently a multitude of unmatched theories with inconsistent axiomatics, into an integrated science? 2. Is it possible, maybe through expanding their scopes, to generalize of transform the existing axiomatics into an integral system of axioms in such a manner that existing axiomatics of inconsistent theories would follow there from as a particular case?

**Dark energy:
Astronomical aspects**

A.D. Chernin

Sternberg Astronomical Institute, Moscow University, Russia

Dark energy is the mysterious form of cosmic energy that produces antigravity and accelerates the global expansion of the universe. It was first discovered in observations of the Hubble expansion flow with the use of type Ia supernovae at horizon-size distances of more than 1000 megaparsec (Mpc) (1 Mpc is equal to 3.26 million light-years). These and other studies, especially the observations of the cosmic microwave background (CMB) anisotropy, indicate that the global dark energy density is (0.75±0.05)x10PAN>^2PAN> kilograms per cubic meter (kg/m^3). It contributes nearly 3/4 the total energy of the universe. According to the simplest, straightforward and quite likely interpretation, dark energy is described by the Einstein cosmological constant. If this is so, dark energy is the energy of the cosmic vacuum with the equation of state . Here , are the dark energy density and pressure which are both constant in time and uniform in space (the speed of light c=1). The interpretation implies that although dark energy betrayed it existence through its effect on the universe as a whole, it exists everywhere in space with the same density and pressure. We have found dynamical effects of dark energy in our closest galactic neighborhood using systematic observations of distances and motions of galaxies in the Local Group and in the flow around it carried out with the Hubble Space Telescope.

**Kerr-Schild Way
to Quantum Gravity**

Alexander Burinskii

Moscow, NSI, Russian Academy of Sciences

Controversies between quantum theory and gravity are well known. It is expected that resolution of these controversies could bring to solution of the one of the principal problems of the modern theoretical physics – the unified theory of quantum gravity. The black holes (BH) are the most convenient objects for studying this inconsistency. One of the sources of the inconsistency is related with general covariance of General Relativity which conflicts with the Fourier transform. In this respect the Kerr-Schild (KS) form of the BH solutions represents exclusive interest. Being based on a congruence of twistor null lines in Minkowski space-time, the KS geometry is strongly linked to the Minkowski background [1], and the coordinate freedom of General Relativity turns out to be maximally suppressed in the KS representation. It allows one to use a special “twistor version” of the Fourier transform [2] in the curved KS space-time, which is necessary for Quantum treatments. In the work [3,4] we described a class of the exact Kerr-Schild (KS) solutions for electromagnetic (EM) excitations of the Kerr-Newman (KN) black hole and their back-reaction on the metric and horizon. It has been shown that there are no smooth harmonic excitations on the KS background, and the typical EM excitations of the KS geometry take the form singular beams which have very strong back-reaction on metric and the BH horizon. There were also obtained the fluctuating beamlike solutions, which deform the BH horizon topologically. The fluctuating KS geometry leads to a fluctuating horizon, which allows matter to escape the BH. The obtained KS geometry of fluctuating beams differs drastically from the usual smooth stationary gravity and was classified as a pre-quantum geometry [4]. Now we can specify the transfer to the usual classical gravity. It was shown in [4,5] that the beamlike solutions are determined by twistorial structure of the Kerr-Schild (KS) geometry which is built of a time-oriented congruence of the lightlike geodesics, forming a time-oriented vacuum (ket) state |in >. The congruences are determined by the Kerr Theorem via a special generating function F(T) of the projective twistor variables T=(Y, AN>-Yv, u+Y AN>*), and for the idealized KN background function F is quadratic in Y. We notice that any process of the measurement of a physical observable ‘G’ breaks this idealization, since the measurer breaks topology of the initial KN space-time. In accordance with the Kerr theorem [6], the measurer creates extra sheets of the space-time with an extra twistor structure which has an opposite-oriented congruence (directed from the measurer to BH) and may be identified with the dual (bra-) vacuum state <out| . The measurement is related with formation of an amplitude of probability < out| G |in > and involves the dual (bra-) state < out| which is complex conjugate to state |in > and described by a reverse time-evolution. Therefore, the obtained classical Kerr-Schild geometry of fluctuating twistor beams may be associated with a ket |in > pre-quantum vacuum state, while the transfer to the classical level of the real physical observables is related with an interplay with the dual (bra-) vacuum state <out| , in accordance with the known principles of quantum theory.

References

[1] G.C. Debney, R.P. Kerr and A. Schild, J. Math. Phys., 10, 1842 (1969).

[2] E. Witten, Comm. Math. Phys. 252, 189 (2004).

[3] A. Burinskii, First Award of GRF 2009, Gen. Rel. Grav. 41, 2281 (2009).

[4] A. Burinskii, J. Phys.: Conf. Ser. 222, 012044 (2010), arXiv:1001.0332[hep-th].

[5] A. Burinskii, Theor. Math. Phys. 163 (3), 782-787, (2010), arXiv:1001.0332.

[6] A. Burinskii, Grav. Cosmol. 11, 301 (2005);

**On Quantization
in Gravity Theory**

M.L. Fil’chenkov, Yu.P. Laptev

Institute of Gravitation and Cosmology,

Peoples’ Friendship University of Russia

fmichael@mail.ru

Gravity theory is shown to be consistent with quantum theory. Gravitation is considered within the framework of General Relativity as well as Newtonian theory. Quantum theory is presented on the level of quantum mechanics and quantum field theory. Quantization is performed following perturbation theory for weak gravitational fields and by nonperturbative methods for strong ones.

It is widely believed that quantum gravity does not exist at all, which is correct if by this an impossibility is meant of constructing the theory by perturbative methods at high energies, because the gravitational field is not normalizable in this case. Since in the theories for other fields only perturbative methods are used, there arises an illusion about impossibility of quantizing the gravitational field, in principle.

We consider the levels of quantization as follows:

Quantization in a given gravitational field or a given Riemannian space-time including quantum mechanics and quantum field theory.

Quantization of a curved space-time or a gravitational field including perturbative approaches, e.g. quantization of a weak gravitational field and superstring theory, as well as nonperturbative ones, e.g. quantum geometrodynamics and loop quantum gravity.

In the framework of field-theoretic and geometric approaches a set of problems has been considered. Although a unified approach is not found, nevertheless it is possible to obtain some results for spherically symmetric and cosmological models being of interest for relativistic astrophysics and cosmology.

**Dirac****'****s****
****scalar****
****field****
****as****
****the****
****metric****
****tensor****
****component****
****and****
****the****
****cosmological****
****constant****
****problem**

O.
V.
Babourova^{1},
B.
N.
Frolov^{2}

Moscow State Pedagogical University

Department of Physics and Computer Technologies

In the Poincare-Weyl gauge theory of gravitation developed by the authors [1], additional scalar (Dirac) field appears as an essential geometrical component of the metric tensor, and the spacetime has the geometrical structure of Weyl-Cartan space.

The Lagrange density of the theory can be found in [2]. It includes Lagrangians quadratic in torsion and nonmetricity, and also a proper Lagrangian of , in which an effective cosmological constant determined by describes the energy of physical vacuum (the dark energy). It is accepted in modern cosmology that the dark energy (described by the cosmological constant) is of dominant importance in dynamics of the universe.

The major unsolved problem of modern fundamental physics is very large difference of around 120 orders of magnitude between a very small value of Einstein's cosmological constant, which can be estimated on the basis of modern observations in cosmology, and theoretical calculation in quantum field theory of quantum fluctuation contributions to the vacuum energy [3].

In homogeneous and isotropic spacetime for the spatially flat FRW metric and for the inflation stage (when the densities of ordinary matter and dark matter are very small), the field equations have the consequences

(1)

where the coefficients are calculated via the coupling constants of . In this case the theory becomes similar to the generalized Brans–Dicke theory with Dirac scalar field. Then the field equations lead to the system of equations, which has two families of solutions for the definite values of the couple constants of the .

The first one has exponential form and has been realized at the beginning of the universe evolution, when the effective cosmological constant has been very large:

, , . (1a)

The second family of the solutions can be realized at the last period of inflation:

, , . (2)

where is an arbitrary constant of integration, and a power can be chosen to fulfill physical requirements. This ‘power law’ inflation is more suitable for the last stage of inflation, because of the problem of the smooth transition from the inflation stage to the Friedman stage of universe evolution.

Thus the exponential solution (1) can explain the exponential decrease in time at very early universe of the dark energy (the energy of physical vacuum), describing by the effective cosmological constant. This solves the problem of cosmological constant.

This research work has been performed in the framework of the Federal Purposeful Program “Research and Pedagogical Personnel of Innovative Russia” for 2009-2013.

References

1. Babourova O. V., Frolov B. N., Zhukovsky V. Ch. Phys. Rev. D . 2006. V. 74. P. 064012-1-12 (gr-qc/0508088, 2005).

2. Babourova O. V., Frolov B. N., Kostkin R. S. Dirac's scalar field as an effective component of the dark energy and an evolution of the cosmological ‘constant’. 2011. e-Print: gr-qc/1102.2901.

3. Weinberg S. Rev. Mod. Phys. 1989. V. 61. No 1. P. 1-23.

**Self-coordinated
system of equations for interacting **

**electromagnetic****
****and****
****quadratic****
****bispinor****
****fields**

Vladimir V. Kassandrov

Institute of Gravitation and Cosmology,

Peoples’ Friendship University of Russia, Moscow

Nina V. Markova

Department of Mathematics,

Peoples’ Friendship University of Russia, Moscow

In
Ref.[1]
we
had
shown
that
*any**
**solution*
to
free
Dirac
equation
can
be
obtained
via
differentiation
from
a
*doublet*
of
scalar
fields
both
obeying
free
Klein-Gordon
equation.
This
is
possible
owing
to
the
known
factorization
property
of
free
Dirac
equation.
As
a
consequence,
one
can
obtain
then
a
whole
hierarchy
of
solutions
to
both
Dirac
and
Klein-Gordon
equations.
Besides,
we
had
demonstrated
that
canonical
spinor
transformations
(and
even
more
general
ones!)
follow
as
a
result
of
combination
of
Lorentz
transformations
for
Dirac
operator
and
internal
symmetry
transformation
intermixing
the
components
of
the
scalar
field
doublet.

Unfortunately,
the
procedure
cannot
be
explicitly
generalized
to
the
case
of
scalar-spinor
fields
interacting
with
electromagnetic
or
gravitational
ones.
This
is
obviously
related
to
the
loss
of
factorization
property
of
the
Klein-Gordon
operator
in
these
cases.
However,
many
interesting
consequences
of
the
above
construction
can
be
preserved
by
consideration
of
the
*quadric**
**Dirac**
**equation**
*(QDE)
instead
of
ordinary
linear
Dirac
equation
(LDE)
itself.
In
the
case
of
a
bispinor
field
interacting,
say,
with
an
electromagnetic
one,
the
QDE
operator
is
well
known
to
factorize
into
a
product
of
two
canonical
(i.e.
with
)
Dirac
equations.
Moreover,
in
the
case
of
a
*fixed**
**external**
4-**potential*
the
above
scheme
reproduces
the
results
of
orthodox
relativistic
quantum
mechanics,
e.g.
in
the
problem
of
*hydrogen**
**atom**
**spectrum**
*etc*.*
(for
this,
see
below,
Eq.
(5)).

On
the
other
hand,
the
interchange
of
LDE
and
QDE
leads
to
a
quite
new
theory
in
the
general
case
of
self-consistently
interacting
electromagnetic
and
bispinor
fields.
In
the
case
of
LDE
one
deals
in
fact
with
a
classical
analogue
of
the
canonical
system
of
equations
(for
corresponding
field
operators)
accepted
in
*quantum**
**electrodynamics**.*
Alternatively,
in
the
case
of
QDE
one
comes
to
a
principally
novel
system
which
can
be
set
by
the
following
Lagrangian:

, (1)

where
is
the
electromagnetic
field
strength
tensor,
the
set
of
four
Dirac
matrices,
and
the
last
*Pauli**
**interaction*
term
is
necessary
to
guarantee
the
factorization
property.
System
of
field
Eqs.
corresponding
to
(1) takes
the
form:

(2a)

(2b)

and one more equation for the Dirac-conjugated bispinor . Now it is a simple exercise to convince oneself that Eq.(2a) may be equivalently represented as

(3)

i.e. in an ordinary factorized form. Then for a newly defined bispinor field

(4)

the canonical Dirac linear equation will be fulfilled,

(5)

Let
us
now
notice
some
peculiarities
of
the
above
self-coordinated
system
of
Eqs.
(2a,2b).
In
the
first
place,
one
has
to
distinguish
therein
the
*Dirac**
**current*
4-vector
associated
usually
with
positive
definite
probability
density
of
a
Dirac
particle
from
the
*electromagnetic**
**current*
4-vector
defined
by
Maxwell
Eqs.(2b).
First
one
is
obviously
conserved
if
it
is
defined
via
the
auxiliary
bispinor
(4); second
is
conserved
as
a
result
of
Maxwell
Eqs.(2b)
themselves.
Thus
one
has
more
conserved
quantities
in
the
framework
of
the
presented
model
than
in
the
canonical
case.
Moreover,
if
one
would
attempt
to
substitute
the
*quantum**
**electrodynamics**
(**operator**)
**system*
for
that
given
by
Eqs.(2a),(2b),
he
is
not
obliged
to
introduce
*two*
independent
bispinor
fields
– for
electrons
and
positrons,
respectively,
but
could
hope
to
describe
both
particles
by
only
one
bispinor
field
satisfying
the
QDE
and
system
(2a,2b)
as
a
whole!
This
opportunity
is
just
related
to
indefinite
sign
of
the
*charge**
**density*
in
the
r.h.s.
of
Eq.(2b).

We,
however,
are
interested
in
a
purely
*classical*
consideration
of
particle-like
(``soliton-like’’)
solutions
to
self-coordinated
system
of
Eqs.(2a,2b).
It
is
noteworthy
to
mention
that
such
solutions
have
been
studied
for
the
case
of
the
canonical
Dirac-Maxwell
system
for
minimally
interacting
fields
in
Refs.2-4
and
others.
Despite
some
interesting
*exact*
results,
e.g.
the
obtained
general
relationship
between
admissible
spin
and
charge
of
such
soliton-like
formations
(Ref.2),
conclusive
status
of
the
Dirac-Maxwell
system
of
Eqs.
can
be
considered
as
rather
low.
Indeed,
the
main
difficulty
for
exact
examination
of
such
a
model
was
the
impossibility
of
separation
of
variables
and
isolation
of
individual
spherical
harmonics.
As
to
(numerically)
obtained
properties
of
the
Maxwell-Dirac
solitons,
all
found
representatives
of
these
possess
*negative**
**proper**
**energy*
(as
it
was
obtained
previously
in
the
model
of
interacting
scalar
and
electromagnetic
fields,
Ref.
5).

For the model based on the QDE, the energy of solitons is not positively defined too. Nonetheless, a special investigation is needed to determine the true sign of the solitons’ rest energy. Search of solitons for the self-coordinated system of Eqs. (2a),(2b) is currently in process. Some preliminary results will be presented at the report.

References

1. Kassandrov
V.V.
// *Gravit**.
**and**
**Cosmol*,
**14**,
No.1,
2008, p.53.

2. Kassandrov
V.V.,
Terletskii
Ya.P.
// In:
*Problems**
**in**
**Quantum**
**Physics**,
*M.,
Peoples’
Friend.
Univ.
Press,
1977, p.
39 (in
Russian).
*
*

3. Kassandrov
V.V.
// Vestnik
Peoples’
Friend.
Univ.
Russia,
Fizika,
**3(1)**,
1995, p.168
(in
Russian).

4. Wakano
M.
// *Prog**.
**Theor**.
**Phys**.*,
**35**,
1966, p.
1117.

5. Rosen
N.
// *Phys**.
**Rev**.*,
**55**,
1939, p.94;

Menius
A.C.,
Rosen
N.
// *Phys**.
**Rev**.*,
**62**,
1942, p.
436.

**Ricci scalar
describes both particle and field densities**

I.E. Bulyzhenkov

_{Lebedev Physics
Institute RAS}

ibw@sci.lebedev.ru

Ricci scalar density can be used for geometrization of the extended radial particle together with geometrization of its radial field. The right hand side of the 1915 Einstein equation can be dropped for such continuous matter. Static metric solutions for nonempty (material) space are free from Schwarzschild singularities. General Relativity can be developed as a selfcontained theory by accepting quantitative equivalence of mass-energy densities associated with the inertial particle and with its gravitational field.

**A new model of
the Eath athmosphere with strong electric fields described by means
of the Yang-Mills theory**

A.S. Rabinowitch, S.Yu. Abakumov

Moscow State University of Instrument Construction and Information Sciences

20 Stromynka str., Moscow 107996, Russia

rabial@mail.ru, ab_sergei@mail.ru

We study a model of the Earth atmosphere in which the influence of strong electric fields is taken into account. The model is a generalization of the standard one and can be described by the following equation of equilibrium of the atmosphere:

, (1)

where is the atmospheric pressure for a certain latitude and longitude, is a distance from the Earth center, is the Earth radius, is the atmospheric mass density, is the free fall acceleration at the Earth surface, is the Earth electric field and is the density of the atmospheric electric charge.

Eq. (1) without the electric field term corresponds to the standard atmospheric model. As follows from computations, this model is applicable for altitudes not more than 150 km. For higher altitudes its predictions substantially differ from experimental data. This shows the importance of the electric field term in Eq. (1). In order to describe strong electric fields in the atmosphere, we use a nonlinear generalization of the classical theory of electricity proposed in Refs. [1 – 3] which is based on the Yang-Mills equations with SU(2) symmetry.

To determine values of the parameters of the suggested model and then to compute solutions of Eq. (1) and compare them with experimental data, we use the empirical model MSIS-E-90 [4] based on data derived from spacecrafts.

Applying our model, we have computed the distributions of the atmospheric mass density and pressure for different geographic coordinates, dates and day times. The computations show that the obtained numerical results are in a good agreement with experimental data. This can be regarded as a serious argument in favor of our model.

References

1. Rabinowitch A.S. Bulletin of PFUR, ser. Phys., 2005, No. 13, pp. 68-77.

2. Rabinowitch A.S. Russ. J. Math. Phys., 2008, Vol. 15, No. 3, pp. 389-394.

3. Rabinowitch A.S. Nonlinear Physical Fields and Anomalous Phenomena. New York, Nova

Science Publishers, 2009.

4. http://omniweb.gsfc.nasa.gov/vitmo/ .

**Physics of
rotating and expanding black hole universe**

U. V. S. SESHAVATHARAM

DIP QA Engineer, Lanco Industries Ltd, Srikalahasti-517641, A.P, India.

Throughout
its
journey,
universe
follows
strong
gravity.
Planck
particle
can
be
considered
as
the
baby
universe.
A
simple
derivation
is
given
for
rotating
black
hole’s
temperature.
When
the
rotation
speed
approaches
‘light
speed’,
temperature
approaches
Hawking’s
Black
hole
temperature.
Appling
this
idea
to
the
cosmic
black
hole,
it
is
noticed
that,
there
is
‘no
cosmic
temperature’
if
there
is
‘no
cosmic
rotation’.
Starting
from
the
Planck
scale,
it
is
assumed
that-
“universe
is
a
‘rotating
and
expanding’
black
hole”.
Another
key
assumption
is
that,
“at
any
time,
cosmic
black
hole
rotates
with
light
speed
”. For
this
cosmic
sphere
as
a
whole,
while
in
light
speed
rotation,
‘rate
of
decrease’
in
temperature
or
‘rate
of
increase’
in
cosmic
red
shift
is
a
measure
of
‘rate
of
cosmic
expansion”.
Measured
isotropic
CMBR
temperature
2.725^{0}
Kelvin
indicates
that,
at
present
“rate
of
decrease”
in
temperature
is
practically
‘zero’
and
‘rate
of
expansion’
is
practically
‘zero’.
If
present
CMBR
temperature
is
2.725 degree
Kelvin,
present
value
of
obtained
angular
velocity
is
2.17 x
10^{-18}
rad/sec
= 67 Km/sec/Mpc.
Present
‘cosmic
mass
density’
and
‘cosmic
time’
are
fitted
with
the
natural
logarithm
of
ratio
of
cosmic
volume
and
planck
particle’s
volume.

**Investigation of
closed orbits of nucleons and antinucleons moving in nonlinear fields**

A.S. Rabinowitch, M.A. Kramskoy

Moscow State University of Instrument Construction and Information Sciences

20 Stromynka str., Moscow 107996, Russia

rabial@mail.ru, k.m.a@rambler.ru

We study movements of nucleons and antinucleons round nuclei under the action of their nuclear and electric fields. As is known, the classical Yukawa theory cannot describe nonlinear properties of nuclear forces [1]. That is why we use its nonlinear generalization proposed in Refs. [2 – 4]. In this nonlinear theory the relativistic movement of a hadron is described by the following equation:

, (1)

where , is the nuclear potential, is the electromagnetic strengths, is the proton mass at rest, are the mass at rest and electric charge of the moving hadron, respectively, are its space-time coordinates of the Minkowski geometry, and .

We solve Eqs. (1) for moving nucleons and antinucleons round nuclei using the polar coordinates. Then these equations can be reduced to a system of two nonlinear differential equations of the second order for the radial coordinate and polar angle of a particle. Numerical computations for the system of equations are performed. They show that protons and neutrons can move in closed orbits round only light nuclei. At the same time antiprotons can move in closed orbits round also medium and heavy nuclei. Besides, such orbits can be sufficiently remote from nuclei. Then the annihilation is impossible and quasi-nuclei with rotating antiprotons can appear. The conditions of forming closed orbits and quasi-nuclei are investigated in both cases of non-relativistic and relativistic antiprotons.

References

Ericson T., Weise W. Pions and Nuclei. Oxford, Clarendon Press, 1988.

Rabinowitch A.S. Int. J. Theor. Phys., 1994, Vol. 33, No 10, pp. 2049-2056.

Rabinowitch A.S. Int. J. Theor. Phys., 1997, Vol. 36, No 2, pp. 533-544.

Rabinowitch A.S. Nonlinear Physical Fields and Anomalous Phenomena. New York,

Nova Science Publishers, 2009.

**Avogadro's Strong
Nuclear Gravity, Super Symmetry and grand unification**

U.
V. S. SESHAVATHARAM^{1}
& Prof. S. LAKSHMINARAYANA^{2}

^{1}DIP
QA Engineer, Lanco Industries Ltd, Srikalahasti-517641, A.P, India.

Email: seshavatharam.uvs@gmail.com

^{2}Department
Of Nuclear Physics, Andhra University,

Visakhapatnam-530003, AP, India.

It
is
suggested
that
‘strong
nuclear
gravitational
constant’
is
(Avogadro
number)^{2}
times
the
‘classical
gravitational
constant’
.
It
can
be
suggested
that
is
a
consequence
of
the
existence
of
.
plays
a
vital
role
in
the
construction
of
atom,
elementary
particles
and
the
charged
nuclear
space-time
curvature.
Based
on
‘strong
nuclear
gravity’
and
‘super
symmetry’
it
is
noticed
that
is
a
secondary
physical
constant.
Previously
proposed
2 strong
interaction
fermion
rest
masses
revised
to
105.3226825 MeV
and
11460.81321 MeV.
Super
symmetric
fermion-boson
mass
ratio
is
revised
to
2.262218404. Nuclear
charge
radius
is
fitted.
Charged
lepton
rest
masses
fitted
accurately
and
4^{th}
heavy
lepton
is
predicted
at
42262 MeV.
Up
and
down
quark
mass
ratio
is
equal
to
.
Quark
masses,
nucleons
rest
masses
and
nuclear
binding
energy
constants
are
fitted
accurately.
QCD
scale,
strong
coupling
constant
and
Fermi's
weak
coupling
constant
are
fitted.
It
can
be
suggested
that
top
quark
boson
and
electroweak
boson
both
are
same.
boson
constitutes
2 oppositely
charged
bosons.
Finally
it
can
be
suggested
that
nuclear
and
particle
physics
can
be
studied
in
the
view
of
`Avogadro’s
strong
nuclear
gravity
and
super
symmetry.

**Thermal noise and
coating optimization in multilayer dielectric mirrors**

Nikita Kondratiev

MSU

noxobar@mail.ru

Optical multilayer coatings of high-reflective mirrors significantly determine properties of Fabry Perot resonators. Thermal (Brownian) noise in these coatings produce excess phase noise which can seriously degrade the sensitivity of high-precision measurements using these cavities. In particular it is one of the main limiting factors at the current stage in laser gravitational-wave detectors (for example project LIGO). We present a method to calculate this effect accurately and analyze different strategies to diminish it by optimizing the coating.

Traditionally the effect of the Brownian noise is calculated as if the beam is reflected from the very surface of the mirror's coating. However, the beam penetrates the coating and Brownian expansion of the layers leads to dephasing of interference in the coating and consequently to additional change in reflected amplitude and phase. Fluctuations in the thickness of a layer change the strain in the medium and hence, due to photoelastic effect, change the refractive index of this layer. This additional effect should also be considered. It is possible to reduce the noise by changing the total number and thicknesses of high and low refractive layers preserving the reflectivity. We show how an optimized coating may be constructed analytically rather than numerically as before. We also check the possibility to use internal resonant layers, optimized cap layer and double mirrors to decrease the thermal noise.

**Neutrino
Telescopes in ocean and in Antarctica**

Vladimir A. Zhukov

Institute for Nuclear Research, RAS

_vlzhukov@mail.ru

Significant progress was made in the field of neutrino physics in the last 30 years. Solved the problem of solar neutrinos, neutrino oscillations are found and registered neutrinos from supernova. There is a serious development of neutrino astronomy. Stage of prototype testing of deep neutrino telescope is completed. Methods of deployment at sea neutrino telescopes worked on pilot arrays in the Mediterranean (NESTOR,ANTARES), in Baikal (NT200) and in Antarctica (AMANDA). Construction of large-scale neutrino telescope with a working volume of 1 cubic km in the Mediterranean launched. Telescope of this size (ICE CUBE) has already been built in the ice of Antarctica. Upper limit in the flux of cosmic high energy neutrinos received.

**Axially-Symmetric
and Closed-String in the Skyrme Gauge Model**

Yu. P. Rybakov, E. Benavente Ramirez

Department of Theoretical Physics,

Peoples Friendship University of Russia,

6, Miklukho- Maklaya str., Moscow, 117198, Russia

The structure of axially-symmetric fields in the gauge Skyrme SU(2) model is studied. The Hamiltonian and the topological charge are constructed for the corresponding invariant class. The internal discrete group of the model is found, thus impliying essential simplification of the energy functional.Within the scope of the Skyrme SU(2) gauge model we consider closed chiral strings (vortices), яthe closure radius being supposed large with respect to the characteristic transversal scale determined by the model parameters. In this approximation the chiral and gauge fields inside the vortex, as well as its energy, can be estimated as functions of the topological charge Q.

**Pairwise****
****Interaction****
****Potential****
****Parameters****
****of****
****Alkali****
****Halide****
****Crystals****
****I****-****Static****
****Crystal****
****Method**

S.
Sh.
Soulayman*,
J.
Attiyah^{**
}
and
A.
Molhem**
, S.
Yunusova
***

*) Higher Institute of Applied Sciences and Technology, Department of Applied Physics, Damascus, P. O. Box 31983, Syria

**) Al-Baath University, Faculty of Sciences, Department of Physics,

Homs, P.O.Box77, Syria

***) Department of Theoretical Physics, Peoples` Friendship University of Russia

6, Miklukho-Maklaya str., Moscow, 117198, Russia

ssoulayman@hiast.edu.sy

In this work a methodology suitable for determination the parameters of the potential of pairwise interactions in the alkali halide crystals is presented. The method of static crystal was applied for several known forms of the potential. Different types of functions viz. Pauling, Born-Mayer-Huggins, Varshni-Shukla and Woodcock have been used for the Born repulsive part of energy. The Van der Waals energy due to the dipole-dipole and dipole-quadruple interactions are also considered. A comparison between the obtained results and those available in literature values is carried out.

**Supersymmetry in
Quantum Optics**

V.A. Andreev

P.N. Lebedev Physical Institute, Moscow, Russia

The realization of Witten’s quantum mechanics superssymmetrical cheme in quantum optics is constructed. We consider the two-level systems interacting with one or two bosonic modes. They are described by the Jaynes-Cummings Hamiltonian and its generalizations. It is shown that some of such Hamiltonians form superssymmetrical pairs and can be considered as components of one superssymmetrical Hamiltonian.

**Quantum
description of complex systems and physical constructivism**

Y.Ozhigov

MSU of M.V.Lomonosov, Russia

The core of quantum informatics is the theory and experiments on QuantumComputer. This still hypothetic device bears the outstanding role for theoretical physics, because it represents the most general model of a complex system on the quantum level that could include the more profound understanding of the life. We are standing at the beginning of new discipline: quantum physics of complex systems, in which it will be possible to understand how living things behave. But to analyze this topic we first of all must develop the new mathematical apparatus, because the traditional formalism of quantum mechanics fits only for the simple quantum effects like interference of one - two quantum particles. The only possibility to build this new apparatus is to use constructive mathematics that means to rest on algorithms instead of abstract algebra. We show how to include decoherence in the constructive model of quantum computer and how to represent the real evolutions in Hilbert space without addressing to hypothetic scalable quantum computer in sense of Deutsch and Di Vincenzo. We describe how computer programs look, which model quantum systems with many particles if to account as complex quantum entanglement as the limited classical memory can contain. Constructive rebuilding of quantum theory resolves some old problems, like the absence of "hidden variables" turning it to the exact theorem; it also puts in some order our representation of "quantum" and "classical" worlds that makes possible to focus on the practically important work - building of computer programs simulating real world on the quantum level.

**Electron Trapping in
Weakly Coupled Concentric Quantum Rings**

I. Filikhin, S.G. Matinyan, J. Nimmo, and B. Vlahovic

North Carolina Central University, Durham, NC, USA

We
are
investigating
electron
wave
function
localization
in
double
concentric
quantum
rings
(DCQR)[1]
when
a
perpendicular
magnetic
field
is
applied.
In
weakly
coupled
double
quantum
ring,
a
possible
situation
occurs
when
the
single
electron
energy
levels
associated
with
different
rings
may
cross.
Degeneracy
is
avoided
by
anti-crossing
of
corresponding
levels
of
DCQR.
We
show
that
in
this
DCQR
the
electron
spatial
transition
between
the
rings
occurs
due
to
the
electron
level
anti-crossing
(see,
for
instant,
[2]). The
anti-crossing
of
the
levels
with
different
radial
quantum
numbers
provides
conditions
for
the
electron
tunneling
between
rings.
DCQRs
are
composed
of
GaAs
in
an
Al_{0.70}Ga_{0.30}As
substrate
[1]. To
study
electronic
structure
of
DCQR,
the
single
sub-band
effective
mass
approach
was
used
with
energy
dependence
of
the
electron
effective
mass
[3]. Results
of
numerical
simulation
for
the
electron
transition
are
presented
for
the
DCQR
with
the
geometry
parameters
corresponding
to
experimentally
fabricated
DCQR
in
[1]. Estimation
for
energy
gap
between
anti-crossing
levels
is
performed
to
show
the
energy
gap
dependence
on
distance
between
rings
and
radial
quantum
numbers
of
the
states.
The
last
defines
spreading
of
the
electron
wave
function
in
DCQR.
The
adequacy
of
the
model
is
confirmed
by
comparing
obtained
results
with
PL
data.
Effect
of
the
trapping
of
an
electron
in
the
inner
QR
of
the
DCQR
(or
QD
inside
QR)
may
be
interesting
from
the
point
of
view
of
quantum
computing.

This work is supported by the NSF (HRD-0833184) and NASA (NNX09AV07A).

References

[1] T. Mano at al. Nano Letters 5, 425, 2005; T. Kuroda et al. Phys. Rev. B 72, 205301, 2005.

[2] V. Arsoski, M. Tadic and F.M. Peeters, Acta Physica Polonica, 117, 733, 2010.

[3] I. Filikhin, V. M. Suslov and B. Vlahovic, Phys. Rev. B 73, 205332, 2006.

**Novel Quantum
Approach to the Heisenberg Uncertainty Principle**

Itzhak
Orion
Ph.D.
and
Michael
Laitman
Ph.D.^{*}

Ben-Gurion University of the Negev, POB 653, Beer-Sheva,84105 ISRAEL

* Ashlag Research Institute, POB 1552, Ramat-Gan 52115 ISRAEL

Quantum physics perception deals with three basic principles: particle-wave duality, the Heisenberg uncertainty and the wave function interpretation.

We present here a new approach for the uncertainty principle as an outcome of a different quantization order level. Particles and waves are represented the same in quantum physics. Therefore, the particle has to possess wave properties, which leads to the uncertainty problem. In our previous published paper, about particle-wave duality, we proposed that wave properties can be observed only if a bunch of particles are in a state of EoF (Equivalence of Form). Only under this condition the particles would be connected as a group (Kevutsa) holding wave properties.

The uncertainty principle is based on wave-package qualities, where frequency differences between the wave-envelope and its position is produced by a constant.

We claim in this paper that the particle is actualized out of the waves in a wave's dispersion process that gives the particle its’ properties from the wave- package for a certain energy (similar to photons). Other states, or other particles, are possible to be actualized due to the other information structures folded in the wave-package. The appearance of state levels in the atom follows an internal order (like quantum numbers in a range). In atomic or nuclear systems, the propagation operator is extracting the informatics of the wave-package that put into reality a process of photon absorption, from a previous state toward a new state population.

Behind the apparent uncertainty, there is organized information to be potentially expressed, as a particle or a state, with a probable intensity to be realized, while the whole picture of the quantum states for a system is complete.

We propose a new name to this approach: Informational Quantization.

**Causality and
probability in quantum mechanics**

D.A. Slavnov

MSU

slavnov@goa.bog.msu.ru

We discuss the causality problem in quantum theory. We show that there exists a formulation of quantum theory that, on one hand, preserves the mathematical apparatus of the standard quantum mechanics and, on the other hand, ensures the satisfaction of the causality condition for each individual event including the measurement procedure.

Accuracy features for quantum tomography

Yu. I. Bogdanov, I.D. Bukeev

Institute of Physics and Technology, Russian Academy of Sciences,

A throughout study of statistical characteristics of fidelity in different protocols of quantum tomography is given. We consider the protocols based on geometry of platonic solids and semiregular polyhedrons such as fullerene. Characteristics of fidelity in different protocols are compared to the theoretical level of the minimum possible level of fidelity loss. Tomography of pure and mixed states in Hilbert spaces of different dimension is studied.

Platonic solids are used to provide the most symmetrical and uniform distribution of quantum states on the Bloch sphere. States, which set projection quantum measurements, are defined by vectors directed from the center of Bloch sphere to corresponding centers of solid's faces. Therefore the number of solid's faces determines the number of quantum measurement protocol's rows and this number is respectively: 4 for tetrahedron, 6 for cube, 8 for octahedron, 12 for dodecahedron and 20 for icosahedron. Since these five described solids cover the whole set of platonic solids, search for quantum measurement protocols which possess high symmetry and number of rows more than 20 makes us to refer to semiregular polyhedrons which are called Archimedean polyhedrons. As examples of such polyhedrons were chosen fullerene (truncated icosahedron), which determines the quantum protocol with 32 measurements, and polyhedron dual to fullerene (Pentakis dodecahedron), which defines the quantum protocol with 60 rows (according to the number of it's faces or, what is actually the same, to the number of fullerene's vertices).

Fidelity
comparison
of
considered
protocols
with
maximum
available
fidelity
shows
that
as
the
number
of
regular
and
semiregular
polyhedrons'
faces
increases
considered
fidelity
rapidly
converges
to
the
theoretical
limit
(in
addition
an
uniformity
of
fidelity
distribution
on
Bloch
sphere
increases
fast).
In
this
work
is
shown
that
accuracy
of
suggested
protocols
is
much
higher
in
comparison
with

an
accuracy,
which
provide
protocols
not
possessing
high
symmetry.

Considered method is generalized on the case of multi-qubit state tomography and accepts the reconstruction of not only pure states but mixed states of arbitrary rank, too.

Developed method is addressed to increase the fidelity and efficiency of quantum tomography procedures. Results of this work could be used for control of states procedures' debugging in quantum cryptography and for the realization of quantum computer's logic gates.

**Semiconductor
quantum ring in strong lateral electrostatic fields**

V.A.Harutyunyan

State Engineering University of Armenia, Gyumri Branch, 2 M.Mkrtchyan St., 3103 Gyumri, Republic of Armenia

volhar@mail.ru

During two last decades electronic and optical properties of low-dimensional semiconductor structures have been studied both experimentally and theoretically. Along with long-known systems like quantum wells (quntum films), quantum wires, quantum dots and superlattices, the novel confined structures called quntum rings (QR’s) attract much attention [1].

In this report the specificity of single-particle states of charge carriers in semiconductor quantum ring in the presence of strong lateral homogeneous electrostatic field is examined theoretically.The finiteness of the ring thickness in both radial and perpendicular to the radial plane direction is taken into account. The explicit forms of wave functions and of energy spectrum of charge carriers in a quantum ring in the presence of strong uniform field are obtained.

It is shown, that a strong external field creates a new deep potential well; because of this, along with the quantum confinement in the radial direction, the charge carriers in the QR are additionally localized also along their angular motion. Instead of the rotation in the QR circle the particle under action of a strong external field vibrates now in a narrow angular cone of the azimuth variable. The localization cones of opposite charges are disposed at opposite edges of the QR’s diameter directed along the external homogeneous field.

As an example of application of these results we will consider the optical transitions in QR in the presence of external strong electrostatic field. Relevant characteristics for interband and intersubband electro-optical transitions in the ring are calculated analytically in this report. Particularly, it is shown that absorption intensities and threshold frequencies of electro-optical transitions depend explicitly on geometrical sizes of sample, on intensities of external fields and on effective masses of charge carriers. These theoretical results can be effectively used for the experimental observation of optical transitions in quantum ring, and for the controlled variation of electro-optical parameters of the sample.

References

1. T. Chacraborty, Adv. In Sol. St. Phys. 43, 71 (2003); T.Chacraborty and P.Pietilainen, Phys.

Rev. 50, 8460 (1994); B.Szafran, Phys. Rev. B77, 205313 (2008).

**Information****
****Transfer****
****Constraints****
****in****
****Quantum****
****Measurements**

S.Mayburov

Lebedev Institute of Physics

Moscow, Russia, RU – 117924

Any measurement process includes the transfer of information from the measured object S to the information system O, which stores and processes it; thus, any measuring system (MS) can be regarded as the information channel. It was found earlier that due to the severe constraints induced by Heisenberg commutation relations, the capacity of quantum channels channels is relatively small [1], so the resulting information losses in MS can be significant and influence the measurement outcome [1]. Here the influence of such constraints on the measurement outcomes will be studied for simple MS model [2].

To check their effect, we considered the model measurement of dichotomic S observable AN> performed by MS, which includes the detector D and O, both of them are regarded as the quantum objects [1]. The measurement of two S ensembles is considered; EPAN> includes the pure states which are the superposition of AN> eigenstates with amplitudes , another ensemble EPAN> is the probabilistic mixture of such eigenstates with the same AN>. First, we analyze the information transfer during S, D and D, O interactions, neglecting D, O decoherence by their environement.

In this case Heisenberg constraints The comparison of final MS states for such ensembles demonstrates that the information about the purity of incoming S ensemble isn't transferred to O; for ensembles it is described by the expectation value of S observable AN>conjugated to AN>. As the result, O can't discriminate the pure and mixed S ensembles with the same AN> [3]. Apllying the quantum formalism of system self-descripiton [4], it is shown that such losses induce the appearance of randomness in the measurement of S pure ensemble EPAN>, so that in the individual events O would detect