Pade spectrum decompositions of quantum distribution functions and optimal hierarchical equations of motion construction for quantum open systems

Journal Article · Tue Jun 28 04:00:00 EDT 2011 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3602466· OSTI ID:21560309

Jie, Hu; Meng, Luo; Feng, Jiang ^[1]; Ruixue, Xu ^[2]; Yijing, Yan ^[1]

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1. Department of Chemistry, Hong Kong University of Science and Technology, Kowloon (Hong Kong)
2. Hefei National Laboratory for Physical Sciences at the Microscale, University of Science and Technology of China, Hefei, Anhui 230026 (China)

Pade 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 Pade 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.

• OSTI ID: 21560309
• Journal Information: Journal of Chemical Physics, Journal Name: Journal of Chemical Physics Journal Issue: 24 Vol. 134; ISSN JCPSA6; ISSN 0021-9606
• Country of Publication: United States
• Language: English

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ACCURACY
ALGORITHMS
BOSONS
CHEMICAL REACTIONS
CONSTRUCTION
DECOMPOSITION
DIFFERENTIAL EQUATIONS
DISTRIBUTION FUNCTIONS
EQUATIONS
EQUATIONS OF MOTION
EXPANSION
FERMIONS
FUNCTIONS
MARKOV PROCESS
MATHEMATICAL LOGIC
NANOSTRUCTURES
PARTIAL DIFFERENTIAL EQUATIONS
QUANTUM DOTS
SPECTRA
STOCHASTIC PROCESSES
TUNNEL EFFECT