Abstract
Continuing our inquiry into the conditions when fluctuation-dissipation relations (FDR) may appear in the context of nonequilibrium dynamics of open quantum systems (over and beyond the conventional FDR from linear response theory) we turn to nonGaussian systems and consider this issue for an anharmonic oscillator interacting with a scalar quantum field bath. We present the general {nonperturbative} expressions for the rate of energy (power) exchange between the anharmonic oscillator and the thermal bath. For the cases that a stable final equilibrium state exists, and the nonstationary components of the two-point functions of the anharmonic oscillator have negligible contributions to the evaluation of the power balance, we can show nonperturbatively that equilibration implies an FDR for the anharmonic oscillator. We then use a weakly anharmonic oscillator as an example to illustrate that those two assumptions indeed are satisfied according to our first-order perturbative results: that the net energy exchange vanishes after relaxation in the open system dynamics and an equilibrium state exists at late times.
Highlights
The open system paradigm captures physical reality better than the idealization of a system in total isolation because the environment it interacts often plays a role
The interlocking relation between the open system and its environment is registered in the fluctuation-dissipation relations (FDRs)
While they are rooted in statistical mechanics [1,2,3,4,5] the implications of FDRs are wide ranging, from condensed matter [6,7], nuclear/particle (e.g., [6,8]) to black hole physics (e.g., [9,10]) and cosmology (e.g., [11])
Summary
The open system paradigm captures physical reality better than the idealization of a system in total isolation because the environment it interacts often plays a role. The interlocking relation between the open system and its environment is registered in the fluctuation-dissipation relations (FDRs) While they are rooted in statistical mechanics [1,2,3,4,5] the implications of FDRs are wide ranging, from condensed matter [6,7], nuclear/particle (e.g., [6,8]) to black hole physics (e.g., [9,10]) and cosmology (e.g., [11]). Before we mention some more recent developments, for clarification purpose, it is perhaps useful to highlight the differences (feature A above) in the formulation of FDR between the nonequilibrium dynamics (NEq) approach which we follow in our work and the conventional linear (LRT) or nonlinear response theory
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