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

2015 Fiscal Year Final Research Report

• Project/Area Number: 24540168
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Basic analysis
• Research Institution: Kanazawa 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