Fourth-order quantum master equation and its Markovian bath limit

Seogjoo Jang, Jianshu Cao, Robert J. Silbey
2002 Journal of Chemical Physics  
Fourth-order quantum master equations ͑FQMEs͒ are derived in both time nonlocal and local forms for a general system Hamiltonian, with new detailed expressions for the fourth-order kernel, where the bath correlation functions are explicitly decoupled from the system superoperators. Further simplifications can be made for the model of linearly coupled harmonic oscillator bath. Consideration of the high temperature Ohmic bath limit leads to a general Markovian FQME with compact forms of time
more » ... forms of time independent superoperators. Two examples of this equation are then considered. For the system of a quantum particle in a continuous potential field, the equation reduces to a known form of the quantum Fokker-Planck equation, except for a fourth-order potential renormalization term that can be neglected only in the weak system-bath interaction regime. For a two-level system with off-diagonal coupling to the bath, fourth-order corrections do not alter the relaxation characteristics of the second-order equation and introduce additional coherence terms in the equations for the off-diagonal elements.
doi:10.1063/1.1445105 fatcat:j6xrnpx3t5fhxif542yh3ptnoe