On the transition from nonadiabatic to adiabatic rate kernel: Schwinger's stationary variational principle and Pade approximation

被引:21
作者
Cho, MH [1 ]
Silbey, RJ [1 ]
机构
[1] MIT,DEPT CHEM,CAMBRIDGE,MA 02139
关键词
D O I
10.1063/1.473412
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
For a two state system coupled to each other by a nonzero matrix element Delta and to the bath arbitrarily, the generalized master equation is derived by applying the well-known projection operator techniques to the quantum Liouville equation. The time-dependent rate kernel is expressed by an infinite summation of the perturbative terms in Fourier-Laplace space. The Schwinger's stationary variation principle in Hilbert space is extended to Liouville space and then applied to the resummation of the rate kernel. The Cini-Fubini-type trial state vector in Liouville space is used to calculate the variational parameters. It is found that the resulting stationary value for the rate kernel in Fourier-Laplace space is given by the [N,N-1]-Pade approximants, in the N-dimensional subspace constructed by the N perturbatively expanded Liouville space vectors. The (first-order) simplest approximation satisfying the variational principle turns out to be equal to the [1,0] Pade approximant instead of the second-order Fermi golden rule expression. Two well-known approximations, the noninteracting blip approximation (NIBA) and nonadiabatic approximation, are discussed in the context of the I[1,0] Pade approximants, based on the variational principle. A. higher-order approximation, [2,1] Pade approximant, is also briefly discussed. (C) 1997 American Institute of Physics.
引用
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页码:2654 / 2661
页数:8
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