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2015 Fiscal Year Final Research Report

An approach to Bose-Einstein condensation in terms of operator valued random variables

Research Project

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Project/Area Number 24540168
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeMulti-year Fund
Section一般
Research Field Basic analysis
Research InstitutionKanazawa University

Principal Investigator

Tamura Hiroshi  金沢大学, 機械工学系, 教授 (80188440)

Research Collaborator Zagrebnov Valentin A.  Institut de Mathematiques de Marseille
Project Period (FY) 2012-04-01 – 2016-03-31
Keywords量子力学系 / 反復摂動 / 調和振動子 / 密度行列 / 開放系の発展方程式 / 非平衡定常状態 / 部分系の時間発展
Outline of Final Research Achievements

An exactly soluble dynamical system generated by repeated harmonic perturbations of the one-mode quantum oscillator is proposed and examined.
For the case of isolated system, although the dynamics is given by Hamiltonian, it shows relaxation to the steady state in the large-time limit. The relaxation is accompanied by the entropy production. A universality of the dynamics in a certain short-interaction-time limit is also obtained.
To study the case of the dissipative system, unbounded Kossakowski-Lindblad-Davies generators are considered. The existence of uniquely determined minimal trace-preserving strongly continuous dynamical semigroups on the space of density matrices are proved. The corresponding dual W*-dynamical system is shown to be unital quasi-free and completely positive automorphisms of the CCR-algebra. The long-time asymptotic behaviour of various subsystems of the model are treated in the framework of the W*-dynamical system approach.

Free Research Field

数理物理学

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Published: 2017-05-10  

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