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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

  1. S. Holevo

  2. Steklov Mathematical Institute, Russia


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


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


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.


[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


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.


  1. 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

  2. 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,


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


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.


[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


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].


[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

  1. Deveikis

Vytautas Magnus University, Lithuania


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 Ex=0,1,2,3,4 excitations in the case of A=6 and JT=21 nucleus.


[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)


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


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).


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


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


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


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


2Department 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.

Axiomatization of Mechanics

T.F. Kamalov

Physics Department, Moscow State Open University


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 physicsthe 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 specialtwistor versionof 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 Gbreaks 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.


[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


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:

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

  2. 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. Babourova1, B. N. Frolov2

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


where the coefficients are calculated via the coupling constants of . In this case the theory becomes similar to the generalized BransDicke 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. Thispower lawinflation 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 ProgramResearch and Pedagogical Personnel of Innovative Russiafor 2009-2013.


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 cosmologicalconstant’. 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:



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


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


the canonical Dirac linear equation will be fulfilled,


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 fieldsfor 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.


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., PeoplesFriend. Univ. Press, 1977, p. 39 (in Russian).

3. Kassandrov V.V. // Vestnik PeoplesFriend. 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


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.


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


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 holes temperature. When the rotation speed approacheslight speed’, temperature approaches Hawkings Black hole temperature. Appling this idea to the cosmic black hole, it is noticed that, there isno cosmic temperatureif there isno cosmic rotation’. Starting from the Planck scale, it is assumed that- “universe is arotating and expandingblack 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 decreasein temperature orrate of increasein cosmic red shift is a measure ofrate of cosmic expansion”. Measured isotropic CMBR temperature 2.7250 Kelvin indicates that, at presentrate of decreasein temperature is practicallyzeroandrate of expansionis practicallyzero’. 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. Presentcosmic mass densityandcosmic timeare fitted with the natural logarithm of ratio of cosmic volume and planck particles 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.


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

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

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

  4. 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


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

Email: seshavatharam.uvs@gmail.com

2Department Of Nuclear Physics, Andhra University,

Visakhapatnam-530003, AP, India.


It is suggested thatstrong nuclear gravitational constant is (Avogadro number)2 times theclassical 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 onstrong nuclear gravityandsuper symmetryit 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 4th 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 `Avogadros strong nuclear gravity and super symmetry.

Thermal noise and coating optimization in multilayer dielectric mirrors

Nikita Kondratiev



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


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


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


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 Al0.70Ga0.30As 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).


[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 itsproperties 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



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


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


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.


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


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