Stochastic linear maps and transition probability

Some aspects of the transition probability P(, ) between states , on unital ^*-algebras are discussed. It is shown that P increases under the action of any stochastic linear map T, i.e., P(T, T)P(, ). Some properties of P are derived in starting from a recently-proved characterization of the quantity in question.     

Collisionless kinetic equations for massive particles with spins 1/2 and 0 in gravitational and electromagnetic fields

We define a covariant and gauge-invariant generalization of the Wigner functions of particles with spins 1/2 and 0. The collisionless kinetic equations are obtained for these particles in external gravitational and electromagnetic fields in the quasiclassical approximation; also obtained are the momentum representations of the energy-momentum tensor, current, and spin tensor, taking into account the effects of the spin's interaction with the gravitational field an electromagnetic field. The following notation is used: e and m are the charge and mass of the particles; is Planck's constant; (x) are the covariant-fixed Dirac matrices; ^,=(1/4)[, ]: a(^b)=(1/2) (a b +ab ); [A, B]=A·B – B·A; A,B=A·B+B·A; g(x)=det(g (x));R = –...; the speed of light c=1.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 47–53, September, 1990.The author wishes the thank Yu. G. Ignat'ev and members of the seminar in General Relativistic Statistics and Cosmology of the Kazan' Pedagogical Institute for useful discussions.     

Surviving extrema for the action on the twisted SU(∞) one point lattice

We give a simplified construction of twist eating configurations, based on a theorem due to Frobenius. These configurations are defined through the equation:U U U ⁺ U ⁺ =exp(2in /N) withU SU(N), =1 tod andn an antisymmetric matrix with integer entries. In the (Twisted)-Eguchi-Kawai model they yield extrema some of which survive forN. Comparison is made with the Monte Carlo data of the internal energy in the small coupling region.     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

Goldstone theorem for bose systems

In three or more dimensions (3) it is proved that if the correlations decay faster than |x|^-(-20) then gauge symmetry breaking is excluded. In one and two dimensions (=1 or 2) the gauge symmetry is always preserved.     

Singularity theorems and the [General Relativity + additional matter fields] formulation of metric theories of gravitation

By using the [General Relativity + additional matter fields] formulation (which depends on a redefined metrich ) of metric theories of gravitation, the study of singularities characterized by incomplete nonspacelike geodesics is simplified, but may be used only if (at least) the non-spacelike geodesics of the original metricg are conserved under the transformation betweeng and the new metrich . In order that every class of geodesies of a diagonal Bianchi I metric correspond to the same class of geodesies of a diagonal metrich , it is necessary that the transformation between these two metrics be a constant (positive) conformal transformation. We analyse the implications of the previous results for the singularitiesg when the latter is a solution of theories with a quadratic or polynomial Lagrangian.     

High-frequency expansion of relativistic classical plasma dielectric tensor

A high-frequency sum-rule expansion is derived for the transverse elements of the relativistic classical plasma dielectric tensor in an isotropic system. The relativistic results are different from the nonrelativistic ones by a factor of ^–1(1 – ²/3c ²) for ₂ (k) and longitudinal plasmon and transverse photon frequencies, and by ^–2(1–2 ²/3c ²) for ₂ (k).     

Poincaré Algebra and Space-Time Critical Dimensions for Paraspinnings Strings

In this paper, we paraquantize the spinning string theory in the Neveu-Shwarz model. Unlike the Ardalan and Mansouri work [Phys. Rev. D, Vol. 9, (1974) 3341], the paraquantum system is such that both the center of mass variables and the excitation modes of the string verify paracommutation relations. The commutators of the Poincaré algebra are satisfied, except the [p ,p ] one, since one can only write [p ,p ]= 0, for Q1. Because of the relation [x ,x ] =,0 and with the sole use of the trilinear relations, we find existence possibilities of spinning strings defined in a noncommutative space-time at space-time dimensions other than D=10.     

Manifestation of Extracoordination in the Resonance Raman Spectra of Water‐Soluble Cation Co‐Porphyrins

Resonance Raman spectra (RRS) of Co(II) and Co(III)5,10,15,20tetrakis(4Nmethylpyridinium)porphyrin ((Co^II(TmpyP4), and Co^III(TMPyP4)) in aqueous solutions at different pH as well as in organic solvents (methanol, ethanol, DMSO, DMF) are obtained. The increased sensitivity of the oscillation frequencies ₂, ₄, ₈, and ₆ — the markers of the oxidation state of a metal — to the nature of an axial ligand has been revealed. For Co^III(TmpyP4), the shifts of the indicated frequencies in extracoordination have turned out to be twofold larger than those for Co^II(TmpyP4). The spectral effects observed are related to different electron influence of the extraligands on the system of the porphyrin ring. In the case of Co(III)porphyrin, interaction of the d orbitals of the metal and the e _g ^*orbitals of the macrocycle is more efficient since its ionic radius is smaller than for the Co(II)complex. For Co^III(TmpyP4), a linear correlation between the oscillation frequencies ₂, ₄, ₈, and ₆ and the experimental Gutmann parameters characterizing the electronacceptor properties of solvents is found.     

Error performance analysis for an optical heterodyne FSK communication system with a limiter-discriminator-integrator detector

The error probability for a coherent optical heterodyne FSK system with a limiter-discriminator-integrator (LDI) detector is analysed. The analysis includes laser quantum phase noise, the correlated receiver additive white Gaussian noise (AWGN), Gaussian narrow-band IF filtering and intersymbol interference (ISI) caused by it. It is shown that, for 1 dBEb/N ₀penalty at bit error rate (BER) 10^–9, (i) the normalized IF beat spectral linewidth T0.35% for frequency deviation ratioh=0.5(MSK), and T0.5% forh=0.7 (the receiver is insensitive to laser quantum phase noise ath=1.0, if ISI is not included.); (ii) if ISI is incorporated, T0.15% forh=0.5, T0.5% forh=0.7, both with 3dB bandwidth-bit period product (3.0>BT1.5), and T0.5% forh=1.0 with BT1.0 ifT0.35% when ISI exists,h=0.7 is optimum;h=1.0 otherwise.     

An approximation method to solve Einstein's field equations on a curved background metric

An approximation method is developed to calculate the gravitational field of a matter sourceT moving on a curved background metric that is an exact solution of the field equations and deviates only weakly from flat space-time. The fieldh of the sourceT is supposed to be much smaller than the curved part of the background, so that in the series expansion ofh each order can be expanded in powers of the background.     

Self-affine fractal clusters: Conceptual questions and numerical results for directed percolation

In this paper we address the question of the existence of a well defined, non-trivial fractal dimensionD of self-affine clusters. In spite of the obvious relevance of such clusters to a wide range of phenomena, this problem is still open since thedifferent published predictions forD have not been tested yet. An interesting aspect of the problem is that a nontrivial global dimension for clusters is in contrast with the trivial global dimension of self-affine functions. As a much studied example of self-affine structures, we investigate the infinite directed percolation cluster at the threshold. We measuredD ind=2 dimensions by the box counting method. Using a correction to scaling analysis, we obtainedD=1.765(10). This result does not agree with any of the proposed relations, but it favorsD=1+(1- )/ , where and are the correlation length exponents and is a Fisher exponent in the cluster scaling.     

Diffusion in a one-dimensional gas of hard point particles

We simulate the classical diffusion of a particle of massM in an infinite one-dimensional system of hard point particles of massm in equilibrium. Each computer run corresponds to about 10⁸ collisions of the diffusive particle. We find that (t) 1/t fort large enough, and a crossover from an M m regime where=2 to=3 forM=m. The diffusion constant has a sharp maximum atM=m. We study moments x(t)² and x(t)⁴, and examine the behavior ofq ² (t)=x(t)⁴/3x(t)²². We find thatq(t)1 (consistent with a normal distribution) in theM limit (for all timest) and in the t limit for allM. On sabbatical leave from IVIC-Instituto Venezolano de Investigaciones Cientificas.     

True self-avoiding walk on critical percolation clusters and lattice animal

The statistics of true-self-avoiding walk model on two dimensional critical percolation clusters and lattice animals are studied using real-space renormalization group method. The correlation length exponents 's are found to be _TSAW ^pc 0.576 and _TSAW ^LA 0.623 respectively for the critical percolation clusters and lattice animals.     

Infrared absorption by free polarons

Expressions are obtained for the coefficient of absorption of a weak electromagnetic wave by free carriers in polar semiconductors with interaction of polarons with acoustic and optical phonons. The appearance in the absorption coefficient of Feynman variational parameters leads, in general, to a change in the frequency dependence. The results are applicable for the frequency range (), where () is the mean reciprocal relaxation time.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 76–80, July, 1980.     

Correlated majority model

We extend the bichromatic majority model by including (one-dimensional isotropic) correlations and numerically discuss, through Monte Carlo simulations, the simple, 1/3, and 2/3 majority rules. We calculate, as functions of the concentration and correlation degree, the mean finite cluster size, and the order parameterm as well as their respective critical exponents and. We find1 regardless of the correlation degree or the type of majority. Also, a supplementary divergence of is observed at the>0 borderline.     

MSA for segregating liquid mixtures: Crossover from mean-spherical to mean-field exponents

The critical exponents , , and of a binary mixture of equal-sized hard spheres with repulsive Yukawa interactions for unlike-atom pairs and attractive Yukawa interactions for like-atom pairs are calculated from analytical solutions in the mean spherical approximation. For strong to moderate screening we find the expected mean spherical values of the critical exponents; for weak screening the system shows a mean field behaviour. For an intermediate range of the potential, the system displays a crossover from mean-field behaviour to mean-spherical behaviour in the immediate vicinity of the critical point. The domain over which the mean-spherical exponents describe the critical behaviour shrinks as the range of the interatomic potential increases.     

Double-Beta Decay in Deformed Nuclei

A brief review of theoretical results for the double-beta decay and the double-electron capture in heavy deformed nuclei is presented. The half life of ¹⁶⁰Gd is evaluated using an extended version of the pseudo SU(3) model. While the 2 mode is forbidden when the most probable occupations are considered, states with different occupation numbers can be mixed through the pairing interaction. The amount of this mixing is calculated using perturbation theory. The possibility of observing the decay in ¹⁶⁰Gd is discussed for both the 2 and 0 modes.     

Nonsymmetric Kaluza-Klein and Jordan-Thiry theory in a general non-Abelian case

This paper is devoted to an (n+4)-dimensional unification of NGT (nonsymmetric gravitation theory) and Yang-Mills theory in a Jordan-Thiry manner. We find interference effects between gravitational and Yang-Mills fields which appear to be due to the skew-symmetric part of the metric on the (n+4)-dimensional manifold (nonsymmetrically metrized principal fiber bundle). Our unification, called the nonsymmetric-non-Abelian Jordan-Thiry theory, becomes classical if the skew-symmetric part of the metric is zero. We find the Yang-Mills field Lagrangian up to the second order of approximation inh =g – . We also deal with the Lagrangian for the scalar field (connected to the gravitational constant). We consider the spin content of the theory and a relationship between the cosmological constant and the coupling constant between the skewon field and the gauge field in the first order of approximation. We show how to derive a dielectric model of a confinement from interference effects in these theories. We underline some similarities between the nonsymmetric Jordan-Thiry Lagrangian in the flat space limit and the soliton bag model Lagrangian.     

Instability of two counter-streaming gyrating beams of electrons

The linear theory of the two-beam instability of weak gyrating beams is investigated. Maximum growth rates of instabilities, instability limits and frequencies of unstable waves are numerically determined. The aperiodic instability withk _{z z0}= _c( _z0 is the velocity of the beam along the magnetic field, _c is the cyclotron frequency andk _z is the longitudinal wave number) and the instability with= _c/2 and withk _{z z0}= _c/2 possess greatest growth rates. Dependence of growth rates on longitudinal and transversal components of the wave vector is investigated in detail.