Quantum master equation for the microcanonical ensemble

Abstract

By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the Authors in Phys. Rev. E {\bf 68}, 066112 (2003). We show that this equation describes the dynamics of a subsystem weakly interacting with an environment of finite heat capacity and initially described by a microcanonical distribution. After applying the rotating wave approximation to the equation, we show that the subsystem dynamics preserves the energy of the total system (subsystem plus environment) and tends towards an equilibrium state which corresponds to equipartition inside the energy shell of the total system. For infinite heat capacity environments, this equation reduces to the Redfield master equation for a subsystem interacting with a thermostat. These results should be of particular interest to describe relaxation and decoherence in nanosystems where the environment can have a finite number of degrees of freedom and the equivalence between the microcanonical and the canonical ensembles is thus not always guaranteed.

8 pages, 0 figures; v2: typos in eq 42 and 43 corrected; v3: submitted to Phys.Rev.E; v4: accepted in Phys.Rev.E

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• Quantum systems correlated with a finite bath: nonequilibrium dynamics and thermodynamics
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• Non-Markovian non-stationary completely positive open quantum system dynamics
• Emergence of canonical ensembles from pure quantum states
• Kinetics and thermodynamics of a driven open quantum system
• Stochastic thermodynamics of a quantum dot coupled to a finite-size reservoir
• Open quantum systems coupled to finite baths: A hierarchy of master equations
• Typicality of nonequilibrium (quasi-)steady currents
• Emergence of steady currents due to strong prethermalization
• Heat generation and transport due to time-dependent forces
• Fluctuation-Dissipation Theorem for the Microcanonical Ensemble
• Ensemble dependence of information-theoretic contributions to the entropy production
• Microscopic contributions to the entropy production at all times: From nonequilibrium steady states to global thermalization
• Apparent Heating due to Imperfect Calorimetric Measurements
• Modeling the dynamics of quantum systems coupled to large dimensional baths using effective energy states
• Ising model in the Rényi statistics: the finite size effects