Abstract

The thermodynamics of the discrete nonlinear Schrödinger equation in the vicinity of infinite temperature is explicitly solved in the microcanonical ensemble by means of large-deviation techniques. A first-order phase transition between a thermalized phase and a condensed (localized) one occurs at the infinite-temperature line. Inequivalence between statistical ensembles characterizes the condensed phase, where the grand-canonical representation does not apply. The control over finite-size corrections of the microcanonical partition function allows to design an experimental test of delocalized negative-temperature states in lattices of cold atoms.

Graphic Abstract

中文翻译：

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离散非线性Schrödinger方程的凝聚跃迁与整体不等式。

摘要

借助大偏差技术，在微规范集合中明确解决了无限温度附近离散非线性Schrödinger方程的热力学问题。在无限温线上发生了热化相与冷凝（局部）相之间的一阶相变。统计合奏之间的不等式是浓缩阶段的特征，在该阶段不适用大正则表示法。对微规范分配函数的有限大小校正的控制允许设计冷原子晶格中离域负温度状态的实验测试。

图形摘要