Research of quantum statistical mechanics in terms of random fields

随机场方面的量子统计力学研究

• 批准号: 20540162
• 负责人: TAMURA Hiroshi
• 金额: $ 2.83万
• 依托单位: Kanazawa University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 2008
• 资助国家: 日本
• 起止时间: 2008 至 2011
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-20540162/
• 关键词: 関数解析; 統計力学; 確率場; Bose-Einstein凝縮; 関数解析学; 量子統計力学

Various physically interesting systems of boson gas are investigated by means of the Random(Point) Fields.For a model of a mean-field interacting boson gas trapped by a weak harmonic potential, it is shown that in the Weak Harmonic Trap limit there are two phases which are different from each other in the local density : finite in one phase and divergent in another phase. The mechanism of the divergence is considered in the different scale using random field, which makes the role of BEC clear.For the perfect Bose-gas trapped in extremely anisotropic boxes, quasi BEC states as well as usual BEC occur. We investigated particle distribution in these cases.Limit theorems on the particle distribution, including the large deviation principle, are also established for the ideal boson gas in BEC.

通过随机（点）场研究了玻色子气体的各种物理有趣系统。对于被弱谐波势捕获的平均场相互作用玻色子气体模型，表明在弱谐波陷阱极限中有两个局域密度彼此不同的相：一相有限，另一相发散。利用随机场在不同尺度上考虑了发散的机制，这使得BEC的作用变得清晰。对于被困在极端各向异性盒子中的完美玻色气体，会出现准BEC态和通常的BEC态。我们研究了这些情况下的粒子分布。对于BEC中的理想玻色子气体，还建立了粒子分布的极限定理，包括大偏差原理。

项目成果

The Bose-Einstein Condensations and the Random Point Fields

玻色-爱因斯坦凝聚和随机点场

• 发表时间: 2008
• 作者: Tamura; H.
• 通讯作者: H.

The Bose-EinsteinCondensations and the Random Point Fields

玻色-爱因斯坦凝聚和随机点场

• 发表时间: 2008
• 作者: Tamura; H.
• 通讯作者: H.

Boson gas mean field models trapped by weak harmonic potentials in mesoscopic scaling

介观尺度中弱谐波势所捕获的玻色子气体平均场模型

• 发表时间: 2009
• 作者: 田村博志

Bose Gases in Scaled Harmonic Traps in terms of Random Point Fields

随机点场的缩放谐波陷阱中的玻色气体

• 发表时间: 2009
• 作者: Tamura; H.
• 通讯作者: H.

Mean field interacting boson random point fields in weak harmonic traps

弱谐波陷阱中平均场相互作用玻色子随机点场

• 发表时间: 2009
• 作者: Tamura; H.; Zagrebnov; V. A.
• 通讯作者: V. A.