An approach to Bose-Einstein condensation in terms of operator valued random variables
| Project/Area Number |
24540168
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Multi-year Fund |
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| Section | 一般 |
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| Research Field |
Basic analysis
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| Research Institution | Kanazawa University |
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Principal Investigator |
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| Research Collaborator |
Zagrebnov Valentin A. Institut de Mathematiques de Marseille
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| Project Period (FY) |
2012-04-01 – 2016-03-31
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| Project Status |
Completed (Fiscal Year 2015)
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| Budget Amount *help |
¥4,810,000 (Direct Cost: ¥3,700,000、Indirect Cost: ¥1,110,000)
Fiscal Year 2015: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2014: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2013: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
Fiscal Year 2012: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
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| 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 / 開放系の統計力学 / 国際研究者交流 / フランス / 数理物理学 / 関数解析 / 量子統計力学 / ボーズ・アインシュタイン凝縮 |
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| 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.
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Report
(5 results)
Research Products
(12 results)
