Physics – Condensed Matter – Statistical Mechanics
Scientific paper
2006-12-11
Phys. Rev. E 76, 041134 (2007)
Physics
Condensed Matter
Statistical Mechanics
8 pages, 0 figures; v2: typos in eq 42 and 43 corrected; v3: submitted to Phys.Rev.E; v4: accepted in Phys.Rev.E
Scientific paper
10.1103/PhysRevE.76.041134
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.
Esposito Massimiliano
Gaspard Pierre
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