Padé spectrum decomposition is an optimal sum-over-poles expansion scheme of Fermi function and Bose function [J. Hu, R. X. Xu, and Y. J. Yan, J. Chem. Phys. 133, 101106 (2010)]. In this work, we report two additional members to this family, from which the best among all sum-over-poles methods could be chosen for different cases of application. Methods are developed for determining these three Padé spectrum decomposition expansions at machine precision via simple algorithms. We exemplify the applications of present development with optimal construction of hierarchical equations-of-motion formulations for nonperturbative quantum dissipation and quantum transport dynamics. Numerical demonstrations are given for two systems. One is the transient transport current to an interacting quantum-dots system, together with the involved high-order co-tunneling dynamics. Another is the non-Markovian dynamics of a spin-boson system.
An accurate and efficient numerical approach is developed for the transient electronic dynamics of open quantum systems at low temperatures. The calculations are based on a formally exact hierarchical equations of motion quantum dissipation theory [J. S. Jin et al., J. Chem. Phys. 128, 234703 (2008)]. We propose a hybrid scheme that combines the Matsubara expansion technique and a frequency dispersion treatment to account for reservoir correlation functions. The new scheme not just admits various forms of reservoir spectral functions but also greatly reduces the computational cost of the resulting hierarchical equations, especially in the low temperature regime. Dynamical Kondo effects are obtained and the cotunneling induced Kondo transitions are resolved in the transient current in response to time-dependent external voltages.
The generalized quantum master equation with transport particle number resolution, like its conventional unconditioned counterpart, has also the time-local and time-nonlocal prescriptions. The latter is found to be more suitable for the effect of electrodes bandwidth on quantum transport and noise spectrum for weak system-reservoir coupling, as calibrated with the exact results in the absence of Coulomb interaction. We further analyze the effect of Coulomb interaction on the noise spectrum of transport current through quantum dot systems, and show that the realistic finite Coulomb interaction and finite bandwidth are manifested only with non-Markovian treatment. We demonstrate a number of non-Markovian characteristics of shot noise spectrum, including that due to finite bandwidth and that sensitive to and enhanced by the magnitude of Coulomb interaction.
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