Nucleation with allowance for fluctuation effects

A theory of homogeneous nucleation is developed on the basis of the concept of a hypersurface formed by a set of slowly varying order parameters in the space of all order parameters with respect to which a transition of the system from one phase state to another can take place. An equation that determines this hypersurface with allowance for fluctuation effects is obtained. The energy of formation of a nucleating center of critical size is estimated in the effective-field approximation for a system of gas—liquid type.State Technical University, Novosibirsk. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 100, No. 2, pp. 312–318, August, 1994.     

Solution of Kirkwood-Salsburg equations for a one-dimensional lattice gas

Expressions are obtained for the lowest correlation functions directly from the Kirkwood-Salsburg equations for an infinite system of particles on a one-dimensional lattice with two-body nearest-neighbor interaction in certain external fields. The problem of finding the external field that makes the density oscillation near the wall uniform is considered.State University, Tyumen'. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 102, No. 3, pp. 463–469, March, 1995.     

Global smooth solutions for a one-dimensional nonisentropic hydrodynamic model with non-constant lattice temperature

In this paper, a one-dimensional nonisentropic hydrodynamic model for semiconductors with non-constant lattice temperature is studied. The model is self-consistent in the sense that the electric field, which forms a forcing term in the momentum equation, is determined by the coupled Poisson equation. The existence and uniqueness of the corresponding stationary solutions are investigated carefully under proper conditions. Then, global existence of the smooth solutions for the Cauchy problem with initial data, which are perturbations of stationary solutions, is established. It is shown that these smooth solutions tend to the stationary solutions exponentially fast as t → ∞.      

Quasiclassical approximation for models of spin-spin interaction on a one-dimensional lattice

The one-dimensional anisotropic Heisenberg model in an external field is considered. For the corresponding energy operator with parameter, the quasiclassical (h0) spectral series are constructed using the method of the canonical operator. In the integrable case (in the absence of the external field) the results obtained coincide with the exact ones.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 133, pp. 63–76, 1984.     

Invariant measures of one-dimensional dynamical systems of anharmonic oscillators

Institute of Information Transmission Problems, USSR Academy of Sciences. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 76, No. 2, pp. 261–271, August, 1988.     

Nonequilibrium fluctuations for a tagged particle in mean-zero one-dimensional zero-range processes

We prove a non-equilibrium functional central limit theorem for the position of a tagged particle in mean-zero one-dimensional zero-range process. The asymptotic behavior of the tagged particle is described by a stochastic differential equation governed by the solution of the hydrodynamic equation.     

Nonequilibrium stationary states of noninteracting electrons in a one-dimensional lattice

Nonequilibrium stationary states of a one-dimensional quantum conductor placed between two reservoirs are investigated. Applying the theory of C^*-algebra, as t→+∞, any state including the degrees of freedom of reservoirs is shown to weakly evolve to a quasifree stationary state with nonvanishing currents. The stationary state exhibits transports which are consistent with nonequilibrium thermodynamics and, in this sense, it has broken time symmetry. Particularly, the electric and energy currents are shown to be expressed by two-probe Landauer-type formulas and they reduce to the results by Sivan–Imry and Bagwell–Orlando in appropriate regimes. As a consequence of the time reversal symmetry, there exists another stationary state with anti-thermodynamical transports, which is the t→−∞ limit of the initial state. The consistency between the dynamical reversibility and the irreversibility of the evolution of states is discussed as well.     

Periodic orbits of a one-dimensional inelastic particle system

The dynamical behavior of a one-dimensional inelastic particle system with two particles of different masses traveling between two walls is investigated. Energy is added at only one of the walls, which is oscillating, while the other wall is stationary. We show that if the particle nearer to the stationary wall is slightly lighter than the other particle and collisions between particles tend to the elastic limit, there are an infinite number of stable orbits. We also show that the widely studied situation of equal masses is an extremely special case, in which all the orbits are degenerate and collapse to a single trivial orbit in which one of the particles is trapped against the stationary wall. To cite this article: J.J. Wylie, Q. Zhang, C. R. Acad. Sci. Paris, Ser. I 339 (2004).     

Continuous orbit transitions in a one-dimensional inelastic particle system

Continuous transitions between different periodic orbits in a one-dimensional inelastic particle system with two particles are investigated. We explain why continuous transitions that occur when adding or subtracting a single collision are, generically, of co-dimension 2. However, we show that there are an infinite set of degenerate transitions of co-dimension 1. We provide an analysis that gives a simple criteria to classify which transitions are degenerated purely from the discrete set of collisions that occur in the orbits.     

Analytic properties of Gibbs states for a class of one-dimensional lattice quantum systems

Analyticity of the free energy and Gibbs state with respect to the parameter >0 (the inverse temperature) is established for a certain class of one-dimensional lattice quantum bosonic systems with long-range potential. The method of proof is a modification for the quantum case of the well-known method of cluster expansions.Moscow State University. Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 94, No. 1, pp. 98–121, January, 1993.