title: Extended hierarchy equation of motion for the spin-boson model.
abstract: An extended hierarchy equation of motion (HEOM) is proposed and applied to study the dynamics of the spin-boson model. In this approach, a complete set of orthonormal functions are used to expand an arbitrary bath correlation function. As a result, a complete dynamic basis set is constructed by including the system reduced density matrix and auxiliary fields composed of these expansion functions, where the extended HEOM is derived for the time derivative of each element. The reliability of the extended HEOM is demonstrated by comparison with the stochastic Hamiltonian approach under room-temperature classical ohmic and sub-ohmic noises and the multilayer multiconfiguration time-dependent Hartree theory under zero-temperature quantum ohmic noise. Upon increasing the order in the hierarchical expansion, the result obtained from the extended HOEM systematically converges to the numerically exact answer.
authors.affiliation: Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China.
authors.forename: Zhoufei
authors.initials: Z
authors.lastname: Tang
authors.affiliation: Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China.
authors.forename: Xiaolong
authors.initials: X
authors.lastname: Ouyang
authors.affiliation: Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China.
authors.forename: Zhihao
authors.initials: Z
authors.lastname: Gong
authors.affiliation: Department of Chemistry, University of Colorado Denver, Denver, Colorado 80217-3364, USA.
authors.forename: Haobin
authors.initials: H
authors.lastname: Wang
authors.affiliation: Physics Department, Zhejiang University, 38 ZheDa Road, Hangzhou, Zhejiang 310027, China.
authors.forename: Jianlan
authors.initials: J
authors.lastname: Wu