Exact non-Markovian master equations: a generalized derivation for quadratic systems

• URL: http://arxiv.org/abs/2502.14364v1
• Date: Thu, 20 Feb 2025 08:42:09 GMT
• Title: Exact non-Markovian master equations: a generalized derivation for quadratic systems
• Authors: Antonio D'Abbruzzo, Vittorio Giovannetti, Vasco Cavina,
• Abstract summary: We derive an exact master equation that captures the dynamics of a quadratic quantum system linearly coupled to a Gaussian environment. We show an explicit and extremely compact dependence on the dressed environment correlation function. This dependence facilitates a straightforward recovery of the well-known Redfield equation at second order in the coupling.
• Score: 0.5461938536945721
• License:
• Abstract: We derive an exact master equation that captures the dynamics of a quadratic quantum system linearly coupled to a Gaussian environment. Unlike previous approaches, our formulation applies universally to both bosonic and fermionic reservoirs, and remains valid even in the presence of initial system-environment correlations. Remarkably, the master equation is written without employing field objects, path integrals, or involved superoperators. As a result, it shows an explicit and extremely compact dependence on the dressed environment correlation function: this allows us to state exactly how sequential virtual interactions between the system and the environment eventually lead to non-Markovian evolution. In the weak-coupling limit, this dependence facilitates a straightforward recovery of the well-known Redfield equation at second order in the coupling.

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