We propose a quasi-particle description for the hierarchical equations of motion formalism for quantum dissipative dynamics systems. Not only it provides an alternative mathematical means to the existing formalism, the new protocol clarifies also exp
licitly the physical meanings of the auxiliary density operators and their relations to full statistics on solvation bath variables. Combining with the standard linear response theory, we construct further the hierarchical dynamics formalism for correlated spectrum of system--bath coherence. We evaluate the spectrum matrix for a demonstrative spin-boson system-bath model. While the individual diagonal element of the spectrum matrix describes the system or the solvation bath correlation, the off-diagonal elements characterize the correlation between system and bath solvation dynamics.
To advance hierarchial equations of motion as a standard theory for quantum dissipative dynamics, we put forward a mixed Heisenberg--Schrodinger scheme with block-matrix implementation on efficient evaluation of nonlinear optical response function. T
he new approach is also integrated with optimized hierarchical theory and numerical filtering algorithm. Different configurations of coherent two-dimensional spectroscopy of model excitonic dimer systems are investigated, with focus on the effects of intermolecular transfer coupling and bi-exciton interaction.
The 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 basis of a Pad{e} spectrum decomposition that ha
s been qualified to be the best sum-over-poles scheme for quantum distribution function. The resulting hierarchical dynamics under the {em apriori} convergence criterion are exemplified with a benchmark spin-boson system, and also the transient absorption and two-dimensional spectroscopy of a model exciton dimer system.
We propose a partial fraction decomposition scheme to the construction of hierarchical equations of motion theory for bosonic quantum dissipation systems. The expansion of Bose--Einstein function in this scheme shows similar properties as it applies
for Fermi function. The performance of the resulting quantum dissipation theory is exemplified with spin--boson systems. In all cases we have tested the new theory performs much better, about an order of magnitude faster, than the best available conventional theory based on Matsubara spectral decomposition scheme.
We propose a nonperturbative quantum dissipation theory, in term of hierarchical quantum master equation. It may be used with a great degree of confidence to various dynamics systems in condensed phases. The theoretical development is rooted in an im
proved semiclassical treatment of Drude bath, beyond the conventional high temperature approximations. It leads to the new theory a simple modification but important improvement over the conventional stochastic Liouville equation theory, without extra numerical cost. Its broad range of validity and applicability is extensively demonstrated with two--level electron transfer model systems, where the new theory can be considered as the modified Zusman equation. We also present a criterion, which depends only on the system--bath coupling strength, characteristic bath memory time, and temperature, to estimate the performance of the hierarchical quantum master equation.
Exact and nonperturbative quantum master equation can be constructed via the calculus on path integral. It results in hierarchical equations of motion for the reduced density operator. Involved are also a set of well--defined auxiliary density operat
ors that resolve not just system--bath coupling strength but also memory. In this work, we scale these auxiliary operators individually to achieve a uniform error tolerance, as set by the reduced density operator. An efficient propagator is then proposed to the hierarchical Liouville--space dynamics of quantum dissipation. Numerically exact studies are carried out on the dephasing effect on population transfer in the simple stimulated Raman adiabatic passage scheme. We also make assessments on several perturbative theories for their applicabilities in the present system of study.
Exact quantum master equation for a driven Brownian oscillator system is constructed via a Wigner phase-space Gaussian wave packet approach. The interplay between external field and dissipation leads to this system an effective field correction that
enhances the polarization. This cooperative property is resulted from an effective bath response to the external field applied on the system. It is important in the low-frequency driving and intermediate bath memory region. We demonstrate this non-Markovian effect on the linear response and nonlinear dynamics and analyze the results together with analytical asymptotic expressions.
In this work, we revisit the electron transfer rate theory, with particular interests in the distinct quantum solvation effect, and the characterizations of adiabatic/nonadiabatic and Markovian/non-Markovian rate processes. We first present a full ac
count for the quantum solvation effect on the electron transfer in Debye solvents, addressed previously in J. Theore. & Comput. Chem. {bf 5}, 685 (2006). Distinct reaction mechanisms, including the quantum solvation-induced transitions from barrier-crossing to tunneling, and from barrierless to quantum barrier-crossing rate processes, are shown in the fast modulation or low viscosity regime. This regime is also found in favor of nonadiabatic rate processes. We further propose to use Kubos motional narrowing line shape function to describe the Markovian character of the reaction. It is found that a non-Markovian rate process is most likely to occur in a symmetric system in the fast modulation regime, where the electron transfer is dominant by tunneling due to the Fermi resonance.
