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

• URL: http://arxiv.org/abs/2401.16488v1
• Date: Mon, 29 Jan 2024 19:02:30 GMT
• Title: Steady state correlation function beyond the standard weak coupling limit and consistency with KMS relation
• Authors: Sakil Khan, Lokendra Singh Rathore, and Sachin Jain
• Abstract summary: In this paper, we derive a formal expression for the non-Markovian two-point function within the context of the weak coupling limit. We also formulate a non-perturbative approach in the form of a self-consistent approximation that includes a partial resummation of perturbation theory.
• Score: 0.08534278963977693
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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