Abstract

A quantum dissipation theory is formulated in terms of hierarchically coupled equations of motion for an arbitrary fermionic system coupled with grand canonical fermionic bath ensembles.¹ The theoretical construction starts with the second-quantization influence functional in path integral formalism, in which the fermionic creation and annihilation operators are represented by Grassmann variables. Temporal derivatives on influence functionals are then performed in a hierarchical manner, on the basis of calculus-on-path-integral algorithm. Both the multiple-frequency-dispersion and the non-Markovian reservoir parametrization schemes are considered for the desired hierarchy construction. The resulting formalism is in principle exact, applicable to interacting systems, with arbitrary time-dependent external fields. It renders an exact tool to evaluate various transient and stationary quantum transport properties of many-electron systems. At the second-tier truncation level the present theory recovers the real-time diagrammatic formalism developed by Schön and coworkers.² For a single-particle system, the hierarchical formalism terminates at the second tier exactly, and the Landuer-Büttiker's transport current expression is readily recovered. Numerical studies will be presented to highlight the richness of transient current through both interacting and noninteracting model systems.

© 2008 Optical Society of America