有限玻色系统的临界行为研究

The present project is aimed to study the critical behavior of finite Bose systems within a microcanonical-ensemeble treatment. Different ensembles give rise to different resutls for finite systems which are far away from the thermodynamic limit. The thermodynamical quantities are continuously smooth in the grand-canonical and canonical ensembles, while they may be singular near the critical region within a microcanonical ensemble. Therefore, to describe the nature of the critical behavior in finite quantum systems the microcanonical-ensemble treatment is needed. For a quantum system with finite volume, finite particle number, and finite energy, but without continuous energy-spectrum approximation and thermodynamic limit, various thermodynamical quantities will be determined and analyzed. Based on the microcanonical partition function and the universal entropy expression, the trap-size scaling and classifications of phase transitions will be extended from the canonical to microcanonical ensemble. In discussing the physical quantities (including the condensate fluctuations, critical temperature, specific heat, and so on), the novel quantum statistical behaviors such as negative specific heat, negative compressibility, and fluctuations of thermodynamical functions, etc., are expected to be revealed and studied.

本项目基于微正则系综研究有限玻色系统的临界行为。研究远离热力学极限的有限体系时，不同的系综不再等价。有限量子体巨正则和正则的热力学函数是连续平滑的，而微正则热力学函数在临界点附近将出现奇异性。因此，为揭示有限量子体的临界行为的本质，有必要采用微正则系综理论进行分析。取有限体积、有限粒子数、有限能量、不取热力学极限、不作连续谱近似的量子系统，确定和分析各种热力学量。在得到有限量子体的微正则配分函数和普适的熵表示的基础上，我们将势阱尺寸标度理论和相变分类方法从正则系综推广到微正则系综。研究有限系统的基态粒子数涨落、临界温度和比热等物理量时，预言并分析诸如负比热、负压缩性和热力学函数震荡等新奇量子统计现象。

本项目开展有限(远离热力学极限下）量子系统的热力学和统计性质的理论研究。研究限尺寸量子效应、热涨落、耗散、相变等统计现象探索有限量子体（特别地，在有限时间热力学过程中）的新奇热力学性质和统计行为。基于微正则系综，研究有限粒子均匀玻色气体在低温下发生凝聚时的凝聚比、比热以及有限尺寸标度行为。以有限量子体系为工作物质，基于各种热力学过程，构建不同的能量转换模型(包括热机和制冷机模型），得到系统的哈密顿量、熵和温度等物理量的严格表示。研究分析了有限量子体为工质的能量转换机的性能特征并对其进行优化，解释能量转换的微观物理机制，从而揭示了有限量子体系的平衡和非平衡的热力学和统计性质。