Stochastically averaged subdynamics of two-level systems (TLS) coupled to a colored noise: a nonperturbative time-ordered cluster cumulant method

Department of Physical Chemistry, Indian Association for the Cultivation of Science, Kolkata- 700 032, India

E-Mail : pcdm@mahendra.iacs.res.in

Present address: Department of Physical Science, R. K. M. Sikshanamandira, Belurmath, Howrah-711 202, India

Present address : Department of Chemistry, R. K. M. Residential College, Narendrapur, Kolkata-700 103, India

 Also at : Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore-560 064, India

Manuscript received 4 October 2002

We present here a non-perturbative cumulant expansion method of studying stochastically averaged dynamics of a TLS coupled to a gaussian colored noise bath. It uses a factorized cluster Ansatz for the evolution operator, U(t) suggested in an earlier formalism (Ref. 22). The factorization separates the operators involving only the system variables from those containing the intractions involving the bath variables. The stochastically averaged U(t) is obtained in a compact way by way of introducing bath-normal ordered products, which have zero bath averages for the bath-variables satisfying gaussian factorization property. We use a Wick-like operator reordering theorem (Ref. 25) to have a bath-normal ordered cluster expansion representation of U(t) and subsequently Novikov's theorem (Ref. 27) to get equations for the cluster amplitudes without free bath variables.The subdynamics of the system where the bath-variables are averaged out is governed in our method by a time-local effective hamiltonian involving system variables only. The method is efficacious when the bath is strongly colored and its coupling with the system is strong, e.g. when nonperturbative effects are prominent. The efficacy of the method is illustrated by computing power spectra from a model system which mimics nonadiabatic vibronic coupling simulated by colored noise.