Title: Kubo-Martin-Schwinger relation for an interacting mobile impurity Show Chinese title

Title: Kubo-Martin-Schwinger 关系对于相互作用的移动杂质

Abstract: In this work we study the Kubo-Martin-Schwinger (KMS) relation in the Yang-Gaudin model of an interacting mobile impurity. We use the integrability of the model to compute the dynamic injection and ejection Green's functions at finite temperatures. We show that due to separability of the Hilbert space with an impurity, the ejection Green's in a canonical ensemble cannot be reduced to a single expectation value as per microcanonical picture. Instead, it involves a thermal average over contributions from different subspaces of the Hilbert space which, due to the integrability, are resolved using the so-called spin rapidity. It is then natural to consider the injection and ejection Green's functions within each subspace. By means of reformulating the original KMS condition as a Riemann-Hilbert problem, we analytically demonstrate that such Green's functions obey a refined analogous relation, which is finally corroborated by numerical evaluation. Show Chinese abstract

Abstract: 在本工作中，我们研究了相互作用的移动杂质的杨-高丹模型中的库博-马丁-施温格（KMS）关系。我们利用该模型的可积性，在有限温度下计算动态注入和排出的格林函数。我们表明，由于带有杂质的希尔伯特空间的可分离性，规范系综中的排出格林函数无法像微观规范图像那样简化为单一期望值。相反，它涉及对希尔伯特空间不同子空间贡献的热平均，这些子空间由于可积性，可通过所谓的自旋快速度进行解析。因此，自然地在每个子空间内考虑注入和排出的格林函数。通过将原始的KMS条件重新表述为黎曼-希尔伯特问题，我们分析证明了这样的格林函数遵循一种改进的类似关系，最终通过数值计算得到验证。