AI 中文总结
研究大量受简谐力约束的相互作用玻色子正则系综极限态，借助预解代数，表明极限态满足KMS条件或为基态，分析不同力下情况，推导出简谐力强度与粒子数关系，涵盖玻色 - 爱因斯坦凝聚常用条件。
AI 中文摘要
在预解代数框架下研究了大量受简谐力约束的相互作用玻色子正则系综的极限态。结果表明，无论相互作用类型如何，极限态都满足KMS条件或为基态。对于吸引力情况，系综坍缩时，在极限中变得无意义的可观测量会从极限表示中消失；对于排斥力情况，若极限中出现相同状态下有无穷多个粒子的凝聚体（恰当凝聚体），也会如此。通过一个简单模型说明了所得结构及其解释。研究消失的简谐力（热力学极限）涉及动力学变化，基于对代数作用的导数进行研究，由哈密顿量与代数元素的对易子给出。为确保像仍在代数中，需对相互作用进行正则化，这对动力学影响较小且可能具有更广泛的意义。在此基础上，从极限态在无约束、空间均匀极限动力学的伴随作用下为平稳（不变）的条件出发，推导出了约束简谐力强度与系综中粒子数之间的关系，该关系包含了玻色 - 爱因斯坦凝聚研究中常用的条件。
英文摘要
The limit states of canonical ensembles of a large number of interacting bosons at a given temperature, which are confined by harmonic forces, are studied in the framework of the resolvent algebra. It is shown that the limits satisfy the KMS condition or are ground states, regardless of the type of interaction. In case of attractive forces, where the ensembles collapse, observables that become meaningless in the limit disappear from the limit representations. For repulsive forces, this can also happen if condensates with an infinite number of particles in the same state (proper condensates) appear in the limit. The resulting structures and their interpretation are illustrated by a simple model. The study of vanishing harmonic forces (thermodynamic limit) involves changes of the dynamics. It is conveniently based on derivations acting on the algebra. They are given by the commutator of the Hamiltonians with the elements of the algebra. To ensure that the images remain in the algebra, the interaction must be regularized. This is accomplished in a manner that has only a minor impact on the dynamics and may be of broader interest. With this input a relation between the strength of the confining harmonic forces and the number of particles in the ensembles is derived from the condition that the limit states are to be stationary (invariant) under the adjoint action of the unconfined, spatially homogeneous limit dynamics. This relation encompasses the conditions that are frequently used in studies of Bose-Einstein condensates.
Comments27 pages, no figures; v2: some typos removed
