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A nonperturbative theory is developed, aiming at an exact and efficientevaluation of a general quantum system interacting with arbitrary bathenvironment at any temperature and in the presence of arbitrary time-dependentexternal fields. An exact hierarchical equations of motion formalism isconstructed on the basis of calculus-on-path-integral algorithm, via theauxiliary influence generating functionals related to the interaction bathcorrelation functions in a parametrization expansion form. The correspondingcontinued-fraction Green's functions formalism for quantum dissipation is alsopresented. Proposed further is the principle of residue correction, not justfor truncating the infinite hierarchy, but also for incorporating the smallresidue dissipation that may arise from the practical difference between thetrue and the parametrized bath correlation functions. The finalresidue-corrected hierarchical equations of motion can therefore be usedpractically for the evaluation of arbitrary dissipative quantum systems.Comment: 12 pages, submitted to PR

Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach