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. 2003 Dec;68(6 Pt 2):066112. doi: 10.1103/PhysRevE.68.066112. Epub 2003 Dec 24.
A perturbative quantum master equation is derived for a system interacting with its environment, which is more general than the ones derived before. Our master equation takes into account the effect of the energy exchanges between the system and the environment and the conservation of energy in the finite total system. This master equation describes relaxation mechanisms in isolated nanoscopic quantum systems. In its most general form, this equation is non-Markovian and a Markovian version of it rules the long-time relaxation. We show that our equation reduces to the Redfield equation in the limit where the energy of the system does not affect the density of state of its environment. This master equation and the Redfield one are applied to a spin-environment model defined in terms of random matrices and compared with the solutions of the exact von Neumann equation. The comparison proves the necessity to allow energy exchange between the subsystem and the environment in order to correctly describe the relaxation in an isolated nanoscopic total system.
针对一个与其环境相互作用的系统，推导了一个微扰量子主方程，该方程比之前推导的方程更具一般性。我们的主方程考虑了系统与环境之间能量交换的影响以及有限总系统中的能量守恒。这个主方程描述了孤立纳米级量子系统中的弛豫机制。在其最一般形式下，该方程是非马尔可夫的，其马尔可夫版本支配着长时间弛豫。我们表明，在系统能量不影响其环境态密度的极限情况下，我们的方程简化为雷德菲尔德方程。这个主方程和雷德菲尔德方程被应用于一个根据随机矩阵定义的自旋 - 环境模型，并与精确的冯·诺依曼方程的解进行了比较。比较结果证明，为了正确描述孤立纳米级总系统中的弛豫，必须允许子系统与环境之间进行能量交换。
