A semiclassical initial‐value representation for quantum propagator and boltzmann operator. Issue 10 (27th December 2018)

• Record Type: Journal Article
• Authors: Yan, Yun‐An; Liu, Jian; Shao, Jiushu
• Other Names: Mo Yirong guestEditor.; Wu Wei guestEditor.; Cao Zexing guestEditor.
• Is Part Of: Journal of computational chemistry. Volume 40:Issue 10(2019)
• Page Start: 1161
• Page End: 1171
• Publication Date: 2018-12-27
• Subjects: correction operator -- Boltzmann operator -- imaginary‐time semiclassical approximation -- semiclassical dynamics; Chemistry -- Data processing -- Periodicals; 542.85
• DOI: 10.1002/jcc.25751
• Languages: English
• ISSNs: 0192-8651

Abstract

Abstract : Starting from the position‐momentum integral representation, we apply the correction operator method to the derivation of a uniform semiclassical approximation for the quantum propagator and then extend it to approximate the Boltzmann operator. In this approach, the involved classical dynamics is determined by the method itself instead of given beforehand. For the approximate Boltzmann operator, the corresponding classical dynamics is governed by a complex Hamiltonian, which can be described as a pair of real Hamiltonian systems. It is demonstrated that the semiclassical Boltzmann operator is exact for linear systems. A quantum propagator in the complex time is thus proposed and preliminary numerical results show that it is a reasonable approximation for calculating thermal correlation functions of general systems. © 2018 Wiley Periodicals, Inc. Abstract : A consistent semiclassical position‐momentum representation is suggested for the Boltzmann operator based on the correction operator method. This approximate Boltzmann operator is exact for linear systems and produces the identity operator for zero imaginary‐time. Numerical simulations show that the approximation is reliable at high to intermediate temperatures for nonlinear systems. Combined with the real‐time propagation, the current method can be used to calculate the reaction rate constants for chemical reactions.