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arXiv · 2401.16488

Steady state correlation function beyond the standard weak coupling limit and consistency with KMS relation

Sakil Khan·Lokendra Singh Rathore·Sachin Jain
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Abstract

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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Sakil Khan, Lokendra Singh Rathore, Sachin Jain. 2024-01-29. Steady state correlation function beyond the standard weak coupling limit and consistency with KMS relation. https://arxiv.org/abs/2401.16488

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