Galilean-Invariant可积模型中快度分布矩的精确结果
Exact Results for the Moments of the Rapidity Distribution in Galilean-Invariant Integrable Models
摘要：
研究了一类在热力学极限下的伽利略不变一维Bethe可解模型。它们的快度分布服从一个有限区间上的带差分核的积分方程，该方程不存在封闭解。我们开发了一个一般的形式主义，使一个研究的时刻的快度分布，表明它们满足差分微分方程。推导出的方程的情况下，明确分析的Lieb-Liniger模型和解析计算的时刻。此外，我们还得到了在弱排斥作用下基态能量的精确信息。所获得的结果直接输入许多物理相关的量。
英文摘要：
We study a class of Galilean-invariant one-dimensional Bethe ansatz solvable models in the thermodynamic limit. Their rapidity distribution obeys an integral equation with a difference kernel over a finite interval, which does not admit a closed-form solution. We develop a general formalism enabling one to study the moments of the rapidity distribution, showing that they satisfy a difference-differential equation. The derived equation is explicitly analyzed in the case of the Lieb-Liniger model and the moments are analytically calculated. In addition, we obtained the exact information about the ground-state energy at weak repulsion. The obtained results directly enter a number of physically relevant quantities.
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