超出标准弱耦合极限的稳态关联函数及其与KMS关系的一致性
Steady state correlation function beyond the standard weak coupling limit and consistency with KMS relation
AI总结：
该研究围绕系统热化过程中关联函数的KMS条件满足性问题，推导弱耦合极限下非马尔可夫两点函数表达式，还提出含微扰部分重求和的非微扰自洽近似方法，验证两种方法所得两点函数均满足KMS条件。
摘要：
系统与热浴相互作用时的热化是一个值得关注的问题。若系统在长时间极限下最终达到热态，其密度矩阵预计会呈现平均力吉布斯态的形式。此外，关联函数必须满足Kubo-Martin-Schwinger（KMS，久保-马丁-施温格）条件，或等价地满足涨落耗散关系（FDR，Fluctuation-Dissipation Relation）。本文在弱耦合极限框架下推导了非马尔可夫两点函数的形式化表达式。利用该表达式，我们针对特定模型显式计算了两点函数，证明其符合KMS条件。此外，我们提出了一种以自洽近似形式呈现的非微扰方法，该方法包含微扰论的部分重求和。这种方法能够捕捉强耦合现象，同时仍依赖简单的方程。值得注意的是，我们验证了通过该方法得到的两点函数同样满足KMS条件。
英文摘要：
Thermalization of a system when interacting with a thermal bath is an interesting problem. If a system eventually reaches a thermal state in the long time limit, it's expected that its density matrix would resemble the mean-force Gibbs state. Moreover, the correlation function must satisfy the Kubo-Martin-Schwinger (KMS) condition or equivalently the Fluctuation-Dissipation Relation (FDR). In this paper, we derive a formal expression for the non-Markovian two-point function within the context of the weak coupling limit. Using this expression, we explicitly compute the two-point function for specific models, demonstrating their adherence to the KMS. In addition, we have formulated a non-perturbative approach in the form of a self-consistent approximation that includes a partial resummation of perturbation theory. This approach can capture strong coupling phenomena while still relying on simple equations. Notably, we verify that the two-point function obtained through this method also satisfies the KMS condition.
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