EUCLIDEAN GIBBS STATES OF QUANTUM LATTICE SYSTEMS

Author:

ALBEVERIO S.123,KONDRATIEV YU.456,KOZITSKY YU.7,RÖCKNER M.4

Affiliation:

1. Abteilung für Stochastik, Universität Bonn, D 53115 Bonn, Germany

2. SFB 256; BiBoS Research Center, Bielefeld, Germany

3. CERFIM, Locarno and USI, Switzerland

4. Fakultät für Mathematik, Universität Bielefeld, D 33615 Bielefeld, Germany

5. SFB 256; BiBoS Research Center, Bielefeld, Germany

6. Institute of Mathematics, Kiev, Ukraine

7. Instytut Matematyki, Uniwersytet Marii Curie-Skłodowskiej, PL 20-031 Lublin, Poland

Abstract

An approach to the description of the Gibbs states of lattice models of interacting quantum anharmonic oscillators, based on integration in infinite dimensional spaces, is described in a systematic way. Its main feature is the representation of the local Gibbs states by means of certain probability measures (local Euclidean Gibbs measures). This makes it possible to employ the machinery of conditional probability distributions, known in classical statistical physics, and to define the Gibbs state of the whole system as a solution of the equilibrium (Dobrushin–Lanford–Ruelle) equation. With the help of this representation the Gibbs states are extended to a certain class of unbounded multiplication operators, which includes the order parameter and the fluctuation operators describing the long range ordering and the critical point respectively. It is shown that the local Gibbs states converge, when the mass of the particle tends to infinity, to the states of the corresponding classical model. A lattice approximation technique, which allows one to prove for the local Gibbs states analogs of known correlation inequalities, is developed. As a result, certain new inequalities are derived. By means of them, a number of statements describing physical properties of the model are proved. Among them are: the existence of the long-range order for low temperatures and large values of the particle mass; the suppression of the critical point behavior for small values of the mass and for all temperatures; the uniqueness of the Euclidean Gibbs states for all temperatures and for the values of the mass less than a certain threshold value, dependent on the temperature.

Publisher

World Scientific Pub Co Pte Lt

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Cited by 20 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Sergio’s Work in Statistical Mechanics: From Quantum Particles to Geometric Stochastic Analysis;Quantum and Stochastic Mathematical Physics;2023

2. Decay of correlations in N-vector ferromagnetic quantum models with long-range interactions;Journal of Statistical Mechanics: Theory and Experiment;2014-10-01

3. PHASE TRANSITIONS AND QUANTUM EFFECTS IN ANHARMONIC CRYSTALS;International Journal of Modern Physics B;2012-04-30

4. The Statistical Mechanics of Quantum Lattice Systems;EMS TRACTS MATH;2009-07-08

5. PHASE TRANSITIONS AND QUANTUM STABILIZATION IN QUANTUM ANHARMONIC CRYSTALS;Reviews in Mathematical Physics;2008-06

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3