Esposito Massimiliano, Gaspard Pierre
Center for Nonlinear Phenomena and Complex Systems, Université Libre de Bruxelles, Code Postal 231, Campus Plaine, B-1050 Brussels, Belgium.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Oct;76(4 Pt 1):041134. doi: 10.1103/PhysRevE.76.041134. Epub 2007 Oct 25.
By using projection superoperators, we present a new derivation of the quantum master equation first obtained by the authors in Phys. Rev. E 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.
通过使用投影超算符，我们给出了量子主方程的一种新推导，该方程最初由作者在《物理评论E》68, 066112 (2003) 中得到。我们表明，此方程描述了一个与具有有限热容量的环境弱相互作用的子系统的动力学，该子系统最初由微正则分布描述。在对方程应用旋转波近似后，我们表明子系统动力学保持了总系统（子系统加环境）的能量，并趋向于一个平衡态，该平衡态对应于总系统能量壳内的能量均分。对于具有无限热容量的环境，此方程简化为与恒温器相互作用的子系统的雷德菲尔德主方程。这些结果对于描述纳米系统中的弛豫和退相干应该特别有意义，在纳米系统中环境可能具有有限数量的自由度，因此微正则系综和正则系综之间的等效性并不总是能保证。
