标题： 有限图上的玻色-哈伯德模型的多体量子吉布斯态的展开 显示英文标题

标题： Expansion of the Many-body Quantum Gibbs State of the Bose-Hubbard Model on a Finite Graph

摘要： 我们考虑在有限图上正温度下的玻色-哈伯德模型的多体量子吉布斯态。 我们将相互作用与逆温度进行缩放，对应于一个平均粒子数量级的温度的平均场极限。 对于该模型，已知当温度趋于无穷大时，多体吉布斯态会收敛到离散非线性薛定谔方程的吉布斯测度，即基于单体理论定义的吉布斯测度。 在本文中，我们通过证明将逆温度作为小参数的多体吉布斯态的任意阶展开来扩展这些结果。 展开式中的系数可以通过递归公式用真空期望值计算，并且我们显式计算了前两个系数。 显示英文摘要

摘要： We consider the many-body quantum Gibbs state for the Bose-Hubbard model on a finite graph at positive temperature. We scale the interaction with the inverse temperature, corresponding to a mean-field limit where the temperature is of the order of the average particle number. For this model it is known that the many-body Gibbs state converges, as temperature goes to infinity, to the Gibbs measure of a discrete nonlinear Schr\"odinger equation, i.e., a Gibbs measure defined in terms of a one-body theory. In this article we extend these results by proving an expansion to any order of the many-body Gibbs state with inverse temperature as a small parameter. The coefficients in the expansion can be calculated as vacuum expectation values using a recursive formula, and we compute the first two coefficients explicitly.