Unified approach to the Bloch-Redfield theory and quantum Fokker-Planck equations

By using a rather simple algebraic approach, we revisit and further bridge between two most commonly used quantum dissipation theories, the Bloch-Redfield theory and a class of Fokker-Planck equations. The nature of the common approximation scheme involving in these two theories is analyzed in detail. While the Bloch-Redfield theory satisfies the detailed-balance relation, we also construct a class of Fokker-Planck equations that satisfy the detailed-balance relation up to the second moments in phase-space. Developed is also a generalized Fokker-Planck equation that preserves the general positivity of the reduced density operator. Both T-1-relaxation and pure-T-2 dephasing are considered, and their temperature dependence is shown to be very different. Provided is also an analogy between the quantum pure-T-2 dephasing and the classical heat transport. (C) 2000 American Institute of Physics. [S0021- 9606(00)50430-9].