Cheng Y C, Silbey R J
Department of Chemistry and Center for Materials Science and Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA.
J Phys Chem B. 2005 Nov 17;109(45):21399-405. doi: 10.1021/jp051303o.
In this paper, we examine the validity of the Markovian approximation and the slippage scheme used to incorporate short time transient memory effects in the Markovian master equations (Redfield equations). We argue that for a bath described by a spectral function, J(omega), that is dense and smoothly spread out over the range omega(d), a time scale of tau(b) approximately 1/omega(d) exists; for times of t > tau(b), the Markovian approximation is applicable. In addition, if J(omega) decays to zero reasonably fast in both the omega --> 0 and omega --> infinity limits, then the bath relaxation time, tau(b), is determined by the width of the spectral function and is weakly dependent on the temperature of the bath. On the basis of this criterion of tau(b), a scheme to incorporate transient memory effects in the Markovian master equation is suggested. Instead of using slipped initial conditions, we propose a concatenation scheme that uses the second-order perturbation theory for short time dynamics and the Markovian master equation at long times. Application of this concatenation scheme to the spin-boson model shows that it reproduces the reduced dynamics obtained from the non-Markovian master equation for all parameters studied, while the simple slippage scheme breaks down at high temperatures.
在本文中，我们检验了马尔可夫近似以及用于在马尔可夫主方程（雷德菲尔德方程）中纳入短时间瞬态记忆效应的滑移方案的有效性。我们认为，对于由谱函数(J(\omega))描述的浴，其在(\omega_d)范围内密集且平滑分布，存在一个时间尺度(\tau_b\approx1/\omega_d)；对于(t>\tau_b)的时间，马尔可夫近似适用。此外，如果(J(\omega))在(\omega\to0)和(\omega\to\infty)极限下都能合理快速地衰减至零，那么浴的弛豫时间(\tau_b)由谱函数的宽度决定，并且对浴的温度弱依赖。基于(\tau_b)的这一判据，我们提出了一种在马尔可夫主方程中纳入瞬态记忆效应的方案。我们不是使用滑移初始条件，而是提出一种级联方案，该方案在短时间动力学中使用二阶微扰理论，在长时间使用马尔可夫主方程。将此级联方案应用于自旋 - 玻色子模型表明它能重现所有研究参数下从非马尔可夫主方程得到的约化动力学，而简单的滑移方案在高温下失效。
