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A nonperturbative theory is developed, aiming at an exact and efficient evaluation of a general quantum system interacting with arbitrary bath environment at any temperature and in the presence of arbitrary time-dependent external fields. An exact hierarchical equations of motion formalism is constructed on the basis of calculus-on-path-integral algorithm, via the auxiliary influence generating functionals related to the interaction bath correlation functions in a parametrization expansion form. The corresponding continued-fraction Greens functions formalism for quantum dissipation is also presented. Proposed further is the principle of residue correction, not just for truncating the infinite hierarchy, but also for incorporating the small residue dissipation that may arise from the practical difference between the true and the parametrized bath correlation functions. The final residue-corrected hierarchical equations of motion can therefore be used practically for the evaluation of arbitrary dissipative quantum systems.
By using worldline and diagrammatic quantum Monte Carlo techniques, matrix product state and a variational approach `a la Feynman, we investigate the equilibrium properties and relaxation features of a quantum system of $N$ spins antiferromagneticall
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
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
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
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