On superstatistics of energy for a free quantum Brownian particle

Abstract

We consider energetics of a free quantum Brownian particle coupled to thermostat of temperature T and study this problem in terms of the lately formulated quantum analogue of the energy equipartition theorem. We show how this quantum counterpart can be derived from the Callen-Welton fluctuation-dissipation relation and rephrased in terms of superstatistics. We analyse the influence of the systemthermostat coupling strength and the memory time of the dissipation kernel on statistical characteristics of the particle energy and its specific heat. arXiv:1904.07921v1 [cond-mat.stat-mech]

New trends in nonequilibrium statistical mechanics: classical and quantum systems

“…As far as quantum dissipative systems are concerned, quantum metastability has been investigated in a micromaser model based on a solid-state setup with a double quantum dot coupled to a microwave cavity [113]; the quantum jump statistics with a shifted jump operator in a chiral waveguide has been presented in [114]; the superstatistics of energy for a free quantum Brownian motion has been considered in [115]; the transmission spectra of a flux qubit coupled to a dissipative resonator in the ultrastrong coupling regime has been calculated in [116]; the coherent trapping in small quantum networks has been considered in [117]; the charge carrier density noise in graphene has been investigated in [118]; the nonequilibrium electron spin relaxation in n-type doped GaAs bulk semiconductor has been studied in [119]. In particular, in this last paper a nonmonotonic behavior has been found with a maximum of both the spin lifetime and the depolarization length, as a function of the lattice temperature.…”

The generalized Langevin equation in harmonic potentials: Anomalous diffusion and equipartition of energy

“…Definition 2.4) or which can be expressed as ϕ(t 2 ), where ϕ is a completely monotonic function. In particular, the former class includes the kernels (1.5) and (1.8), whereas the latter class includes Gaussian and Cauchy kernels, namely, e −t 2 and (t 2 + 1) −α , respectively [41,42,43]. Besides its great generality, the class of completely monotonic functions is made up of Laplace transforms of positive Radon measures, which is very convenient for the purpose of establishing analytical results (cf.…”