Fokker-Planck quantum master equation for mixed quantum-semiclassical dynamics.

We revisit Caldeira-Leggett's quantum master equation representing mixed quantum-classical theory, but with limited applications. Proposed is a Fokker-Planck quantum master equation theory, with a generic bi-exponential correlation function description on semiclassical Brownian oscillators' environments. The new theory has caustic terms that bridge between the quantum description on primary systems and the semiclassical or quasi-classical description on environments.

Optimizing hierarchical equations of motion for quantum dissipation and quantifying quantum bath effects on quantum transfer mechanisms.

We present an optimized hierarchical equations of motion theory for quantum dissipation in multiple Brownian oscillators bath environment, followed by a mechanistic study on a model donor-bridge-acceptor system. We show that the optimal hierarchy construction, via the memory-frequency decomposition for any specified Brownian oscillators bath, is generally achievable through a universal pre-screening search. The algorithm goes by identifying the candidates for the best be just some selected Padé spectrum decomposition based schemes, together with a priori accuracy control criterions on the sole approximation, the white-noise residue ansatz, involved in the hierarchical construction.

Optimized hierarchical equations of motion theory for Drude dissipation and efficient implementation to nonlinear spectroscopies.

Hierarchical equations of motion theory for Drude dissipation is optimized, with a convenient convergence criterion proposed in advance of numerical propagations. The theoretical construction is on the basis of a Padé spectrum decomposition that has been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the a priori convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and related coherent two-dimensional spectroscopy of a model exciton dimer system.

Biexponential theory of Drude dissipation via hierarchical quantum master equation.

A nonperturbative quantum dissipation theory is developed based on an optimal construction of biexponential Drude bath correlation function for its influence on the system dynamics. It is an advanced hierarchical quantum master equation approach, aiming at a numerically efficient non-Markovian quantum dissipation propagator, with the support of a convenient criterion to estimate in advance its accuracy for general systems. Compared to its low level, single-exponential counterpart [R.