arXiv subjects

Yuri Kozitsky

Publications and source records attributed to Yuri Kozitsky.

59 records · Page 4Linked to original sources

arXiv2006

A Phase Transition in a Quantum Crystal with Asymmetric Potentials

A translation invariant system of interacting quantum anharmonic oscillators indexed by the elements of a simple cubic lattice $\mathbb{Z}^d$ is considered. The anharmonic potential is of general type, which in particular means that it might have no symmetry. For this system, we prove that the global polarization (obtained in the thermodynamic limit) gets discontinuous at a certain value of the external field provided $d\geq 3$, and the particle mass as well as the interaction intensity are big enough. The proof is based on the representation of local Gibbs states in terms of path measures and thereby on the use of the infrared estimates and the Garsia-Rodemich-Rumsey inequality.

math-ph↗

arXiv2005

Euclidean Gibbs Measures of Quantum Anharmonic Crystals

A lattice system of interacting temperature loops, which is used in the Euclidean approach to describe equilibrium thermodynamic properties of an infinite system of interacting quantum particles performing anharmonic oscillations (quantum anharmonic crystal), is considered. For this system, it is proven that: (a) the set of tempered Gibbs measures is non-void and weakly compact; (b) every Gibbs measure obeys an exponential integrability estimate, the same for all such measures; (c) every Gibbs measure has a Lebowitz-Presutti type support; (d) the set of all Gibbs measures is a singleton at high temperatures. In the case of attractive interaction and one-dimensional oscillations we prove that at low temperatures the system undergoes a phase transition. The uniqueness of Gibbs measures due to strong quantum effects (strong diffusivity) and at a nonzero external field are also proven in this case. Thereby, a complete description of the properties of the set of all Gibbs measures has been done, which essentially extends and refines the results obtained so far for models of this type.

math-ph↗

arXiv1999

A Nonlinear Dynamical System on the Set of Laguerre Entire Functions

A nonlinear modification of a parabolic Cauchy problem for entire functions of a single complex variable is considered. The modification means that the time half-line is divided onto the intervals of equal length and on each such interval the evolution is to be described by the mentioned equation but at the endpoints the function is changed in a nonlinear way. If the initial function is chosen in the set of Laguerre entire functions, then the solution of the problem remains in this set. The Laguerre entire functions are obtained as uniform limits on compact subsets of the complex plane of the polynomials having real nonpositive zeros only. It is shown that the asymptotic properties of the solution change considerably when interval length reaches a threshold value. Certain applications, including limit theorems for weakly and strongly dependent random vectors, are given.

math.DS↗

arXiv1998

Classical Limits of Euclidean Gibbs States for Quantum Lattice Models

Models of quantum and classical particles on the d-dimensional cubic lattice with pair interparticle interactions are considered. The classical model is obtained from the corresponding quantum one when the reduced physical mass of the particle tends to infinity. For these models, it is proposed to define the convergence of the Euclidean Gibbs states, when the reduced mass tends to infinity, by the weak convergence of the corresponding Gibbs specifications, determined by conditional Gibbs measures. In fact it is proved that all conditional Gibbs measures of the quantum model weakly converge to the conditional Gibbs measures of the classical model. A similar convergence of the periodic Gibbs measures and, as a result, of the order parameters, for such models with the pair interactions possessing the translation invariance, has also been proven.

math-ph↗

arXiv1998

Laguerre Entire Functions and Related Locally Convex Spaces

A scale of the Frechet spaces of exponential type entire functions of one complex variable is considered. Certain special properties of subsets of these spaces consisting of Laguerre entire functions, which are obtained as uniform limits on compact subsets of the complex plane of polynomials with real nonpositive zeros only, are described. A class of infinite order differential operators which act between these Frechet spaces is inrtoduced and studied. In particular, it is shown that this class preserves the set of Laguerre entire functions. The results obtained are then used to obtain and to study the solutions of a certain initial value problem.

math.CV↗