Quantum counterpart of energy equipartition theorem for fermionic systems

Abstract

In this brief report, following the recent developments on formulating a quantum analogue of the classical energy equipartition theorem for open systems where the heat bath comprises of independent oscillators, i.e. bosonic degrees of freedom, we present an analogous result for fermionic systems. The most general case where the system is connected to multiple reservoirs is considered and the mean energy in the steady state is expressed as an integral over the reservoir frequencies. Physically this would correspond to summing over the contributions of the bath degrees of freedom to the mean energy of the system over a suitable distribution function $\rho (\omega )$ dependent on the system parameters. This result holds for nonequilibrium steady states, even in the nonlinear regime far from equilibrium. We also analyze the zero temperature behaviour and low temperature corrections to the mean energy of the system.

References in corpus (11)

• Thermodynamics of precision in quantum non equilibrium steady states
• Nonequilibrium density matrix description of steady state quantum transport
• Low temperature Thermodynamics in the Context of Dissipative Diamagnetism
• Quantum partition of energy for a free Brownian particle: Impact of dissipation
• Quantum Langevin equation of a charged oscillator in a magnetic field and coupled to a heat bath through momentum variables
• Dissipative Quantum Systems and the Heat Capacity Enigma
• Quantum Counterpart of Classical Equipartition of Energy
• Flux-dependent occupations and occupation difference in geometrically symmetric and energy degenerate double-dot Aharonov-Bohm interferometers
• Dissipative Diamagnetism -- A Case Study for Equilibrium and Nonequilibrium Statistical Mechanics of Mesoscopic Systems
• Quantum counterpart of energy equipartition theorem for a dissipative charged magneto-oscillator: Effect of dissipation, memory, and magnetic field
• Quantum thermodynamics of nanoscale steady states far from equilibrium

Cited by in corpus (2)

• Partition of kinetic energy and magnetic moment in dissipative diamagnetism
• Correspondence Between the Energy Equipartition Theorem in Classical Mechanics and its Phase-Space Formulation in Quantum Mechanics