有限玻色系统的临界行为研究

项目名称： 有限玻色系统的临界行为研究

项目编号： No.11265010

项目类型： 地区科学基金项目

立项/批准年度： 2013

项目学科： 数理科学和化学

项目作者： 王建辉

作者单位： 南昌大学

项目金额： 56万元

中文摘要： 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。

中文关键词： 有限系统；能量转换；有限尺寸效应；热力学过程；

英文摘要： 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 studie

英文关键词： finite system；energy conversion；finite size effects；thermodynamic process；