Linear response theory for quantum Gaussian processes

Abstract

Fluctuation dissipation theorems connect the linear response of a physical system to a perturbation to the steady-state correlation functions. Until now, most of these theorems have been derived for finite-dimensional systems. However, many relevant physical processes are described by systems of infinite dimension in the Gaussian regime. In this work, we find a linear response theory for quantum Gaussian systems subject to time dependent Gaussian channels. In particular, we establish a fluctuation dissipation theorem for the covariance matrix that connects its linear response at any time to the steady state two-time correlations. The theorem covers non-equilibrium scenarios as it does not require the steady state to be at thermal equilibrium. We further show how our results simplify the study of Gaussian systems subject to a time dependent Lindbladian master equation. Finally, we illustrate the usage of our new scheme through some examples. Due to broad generality of the Gaussian formalism, we expect our results to find an application in many physical platforms, such as opto-mechanical systems in the presence of external noise or driven quantum heat devices.

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Cited by in corpus (7)

• Geometry of work fluctuations versus efficiency in microscopic thermal machines
• Gaussian Thermal Operations and the Limits of Algorithmic Cooling
• Response theory for nonequilibrium steady-states of open quantum systems
• A Green's function approach to the linear response of a driven dissipative optomechanical system
• Differential Parametric Formalism for the Evolution of Gaussian States: Nonunitary Evolution and Invariant States
• Fluctuation-Dissipation Relation for Open Quantum Systems in Nonequilibrium Steady State
• Non-equilibrium quantum probing through linear response