Nonequilibrium statistical thermodynamics of channeled particles: Resonance transitions and dechanneling

An elementary act of dechanneling includes diffusion of particles in the space of transverse energies and a resonance transition that occurs after a particle reaches the channeling-regime potential level. The dechanneling rate coefficient is defined using equations of nonequilibrium statistical thermodynamics. Physical quantities including the resonance transition matrix element, single-phonon and electron scattering relaxation rates, and the transverse quasi-temperature function related to the difference between the thermodynamic parameters of fast particles and the thermostat determining the dechanneling rate coefficient are expressed in terms of the basic parameters of the theory. Translated from Teoreticheskaya i Matematicheskaya Fizika. Vol. 116, No. 1, pp. 146–160, July, 1998.     

Nonequilibrium statistical thermodynamics of channeled particles: Thermal particles

The rate of atomic particles escaping a potential minimum as a result of interactions with the lattice thermal vibrations and the electron gas is investigated using nonequlibrium statistical thermodynamic methods. The physical properties of the theory are analyzed. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 116, No. 3, pp. 442–455, September, 1998.     

Nonequilibrium statistical thermodynamics of cascade processes in solids: the quasi temperature of cascade particles

Displacement cascades in solids are investigated in the framework of nonequilibrium statistical thermodynamics. The quasi temperature of a subsystem of cascade particles in metals and semiconductors is derived using the energy balance equation for a cascade process.     

Nonequilibrium statistical thermodynamics of channeled particles. The transverse quasitemperature

Fast charged particles moving in a crystal in the channeling regime are treated as an independent thermodynamic subsystem for which energy acnd momentum balance equations are derived in the comoving coordinate system. It is shown that the solution of these equations gives an expression for the transverse quasitemperature of the channeled particles in terms of the fundamental parameters of the nicroscopic theory. If the electron scattering is quasielastic, then at a penetration depth of the order of the coherence length the system as a whole remains in strong disequilibrium despite the attainment of internal equilibrium in the subsystem of the particles. There is a large difference between the thermodynamic parameters of the channeled particles and of the thermal reservoir.A. A. Baikov Institute of Metallurgy, Russian Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 1, pp. 106–118, January, 1995.     

Nonequilibrium statistical thermodynamics of positronium atoms moving in solids

We calculate the quasitemperature of positronium atoms moving in a solid in the framework of nonequilibrium statistical thermodynamics. We represent the quasitemperature in the form of the renormalized temperature of the thermostat. The renormalization results from taking the positronium formation rate, the kinetic effects of interaction, and the dynamical effects of collisions into account. We obtain an expression for the thermalization time of positronium atoms.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 142, No. 1, pp. 112–126, January, 2005.     

Nonequilibrium statistical thermodynamics of displacement cascade thermalization in a solid

A. A. Baikov Institute of Metallurgy, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 87, No. 2, pp. 283–292, May, 1991.     

Diffusion approximation of branching migration processes

We study the behavior of a Galton-Watson process with homogeneous migration component stopped at zero (i.e., the state zero is absorbing). Assuming that the process is initiated at time zero by a large number of particles, we find a diffusion approximation for this process in the case where the average number of offspring per individual is close to one. Supported by the Russian Foundation for Fundamental Research (grant Nos. 96-01-00338 and 96-15-96092) and INTAS-RFBR (grant No. 95-0099). Proceedings of the Seminar on Stability Problems for Stochastic Models, Hajdúszoboszló, Hungary, 1997, Part III.     

Critical decomposable Bellman-Harris processes with two types of particles

Translated from Matematicheskie Zametki, Vol. 43, No. 2, pp. 276–282, February, 1988.     

Diffusion with interactions between two types of particles and Pressureless gas equations

We construct two d-dimensional independent diffusions $\text{X}{}_{\mathrm{t}}{}^{\mathrm{a}}\text{=a+∫}{}_0{}^{\mathrm{t}}\text{u(X}{}_{\mathrm{s}}{}^{\mathrm{a}}\text{,s)}\text{d}\text{s+νB}{}_{\mathrm{t}}{}^{\mathrm{a}}\text{,}\text{X}{}_{\mathrm{t}}{}^{\mathrm{b}}\text{=b+∫}{}_0{}^{\mathrm{t}}\text{u(X}{}_{\mathrm{s}}{}^{\mathrm{b}}\text{,s)}\text{d}\text{s+νB}{}_{\mathrm{t}}{}^{\mathrm{b}}$, with the same viscosity ν≠0 and the same drift u(x,t)=(pρ_t^a(x)v₁+(1?p)ρ_t^b(x)v₂)/(pρ_t^a(x)+(1?p)ρ_t^b(x)), where ρ_t^a,ρ_t^b are respectively the density of X_t^a and X_t^b. Here $\text{a,b,v}{}_1\text{,v}{}_2\text{∈}\text{R}{}^{\mathrm{d}}$ and p∈(0,1) are given. We show that $\text{(ρ}{}_{\mathrm{t}}\text{(x)=pρ}{}_{\mathrm{t}}{}^{\mathrm{a}}\text{(x)+(1?p)ρ}{}_{\mathrm{t}}{}^{\mathrm{b}}\text{(x),u(x,t):}\text{t?0,}\text{x∈}\text{R}{}^{\mathrm{d}}\text{)}$ is the unique weak solution of the following pressureless gas system

such that $\text{ρ}{}_{\mathrm{t}}\text{(x)}\text{d}\text{x→pδ}{}_{\mathrm{a}}\text{+(1?p)δ}{}_{\mathrm{b}}\text{,}\text{u(x,t)ρ}{}_{\mathrm{t}}\text{(x)}\text{d}\text{x→pv}{}_1\text{δ}{}_{\mathrm{a}}\text{+(1?p)v}{}_2\text{δ}{}_{\mathrm{b}}$ as t→0+. To cite this article: A. Dermoune, S. Filali, C. R. Acad. Sci. Paris, Ser. I 337 (2003).     

Non-extensive thermodynamics and stationary processes of localization

We focus our attention on dynamical processes characterized by an entropic index Q<1. According to the probabilistic arguments of Tsallis, C and Bukman, DJ [Phys Rev E 1996;54:R2197] these processes are subdiffusional in nature. The non-extensive generalization of the Kolmogorov–Sinai (KS) entropy yielding the same entropic index implies the stationary condition. We note, on the other hand, that enforcing the stationary property on subdiffusion has the effect of producing a localization process occurring within a finite time scale. We thus conclude that the stationary dynamic processes with Q<1 must undergo a localization process occurring at a finite time. We check the validity of this conclusion by means of a numerical treatment of the dynamics of the logistic map at the critical point.     

A quantum generalization of equilibrium statistical thermodynamics: Effective macroparameters

We propose a generalization of statistical thermodynamics in which quantum effects are taken into account on the macrolevel without explicitly using the operator formalism while traditional relations between the macroparameters are preserved. In a generalized thermostat model, thermal equilibrium is characterized by an effective temperature bounded from below. We introduce fundamental theoretical macroparameters: the effective entropy and the effective action. Because the effective entropy is nonzero at low temperatures, we can write the third law of thermodynamics in the form postulated by Nernst. The effective action at any temperature coincides with the product of standard deviations of the coordinate and momentum in the Heisenberg uncertainty relation and is therefore bounded from below. We establish that the ratio of the effective action to the effective entropy in the low-temperature limit is determined by a holistic stochastic-action constant depending on the Planck and Boltzmann constants. We show that the same results can be obtained in the framework of a modified version of thermofield dynamics in which the quantum oscillator is described by a temperature-dependent complex macroscopic wave function. We study the discrepancy between the behavior of the action-to-entropy ratio in the low-temperature limit in our proposed theory and that in quantum equilibrium statistical mechanics, which can be verified experimentally. __________ Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 154, No. 1, pp. 183–196, January, 2008.     

Strong approximation of semimartingales and statistical processes

Summary As an application of general convergence results for semimartingales, exposed in their book Limit Theorems for Stochastic Processes, Jacod and Shiryaev obtained a fundamental result on the convergence of likelihood ratio processes to a Gaussian limit. We strengthen this result in a quantitative sense and show that versions of the likelihood ratio processes can be defined on the space of the limiting experiment such that we get pathwise almost sure approximations with respect to the uniform metric. The approximations are considered under both sequences of measures, the hypothesisP ⁿ and the alternative . A consequence is e.g. an estimate for the speed of convergence in the Prohorov metric. New approximation techniques for stochastic processes are developed.This article was processed by the author using the L^AT_EX style filepljourIm from Springer-Verlag.     

On the uniqueness problem of two dimensional diffusion processes occurring in population genetics

Summary We shall investigate two dimensional diffusion processes occurring in population genetics. In order to construct such processes, we shall consider a martingale problem and discuss its uniqueness problem. Though the standard methods are not applicable in our case, we obtain the uniqueness in a fairly general case.