近日，俄罗斯杜霍夫全苏自动化研究所的Andrey S. Plyashechnik及其研究小组与俄罗斯科学院光谱学研究所的Alexey A. Sokolik等人合作并取得一项新进展。经过不懈努力，他们对具有固定总动量正则系综中的玻色-爱因斯坦凝聚进行了研究。相关研究成果已于2024年7月2日在国际知名学术期刊《物理评论A》上发表。

该研究团队深入探究了非相互作用均匀三维气体在正则系综条件下，当粒子数N与总动量P均保持恒定时所展现的玻色-爱因斯坦凝聚现象。利用鞍点法，研究人员导出了配分函数、自由能和不同单粒子能级占据数的统计分布的大N解析近似。在低于相变临界点的温度下，研究人员预测，对于总动量P的特定区间内，当宏观上超过一个单粒子能级被占据时，凝聚态将发生碎裂现象。

对于承载凝聚态的特定能级，其占据数分布近似呈现高斯分布特征；而对于其他非凝聚态能级，则展现出指数型的占据数分布规律。这一分析证明了在玻色-爱因斯坦凝聚存在下运动有限温度多粒子系统的伽利略不变性被打破，并将运动和旋转量子系统的理论推广到有限温度大N极限。

附：英文原文

Title: Bose-Einstein condensation in a canonical ensemble with fixed total momentum

Author: Andrey S. Plyashechnik, Alexey A. Sokolik, Yurii E. Lozovik

Issue&Volume: 2024/07/02

Abstract: We consider Bose-Einstein condensation of noninteracting homogeneous three-dimensional gas in canonical ensemble when both particle number N and total momentum P of all particles are fixed. Using the saddle-point method, we derive the large-N analytical approximations for partition function, free energy, and statistical distributions of occupation numbers of different single-particle energy levels. At temperatures below the critical point of phase transition, we predict, in some ranges of P, fragmentation of the condensate, when more than one single-particle level is macroscopically occupied. The occupation number distributions have approximately Gaussian shapes for the levels hosting the condensate, and exponential shapes for other, noncondensate levels. Our analysis demonstrates breaking of Galilean invariance of moving finite-temperature many-particle system in the presence of Bose-Einstein condensation and extends the theory of moving and rotating quantum systems to the finite-temperature large-N limit.

DOI: 10.1103/PhysRevA.110.013301

Source: https://journals.aps.org/pra/abstract/10.1103/PhysRevA.110.013301