A semiclassical initial-value representation for quantum propagator and boltzmann operator |
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| Authors: | Yun-An Yan Jian Liu Jiushu Shao |
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| Affiliation: | 1. School of Physics and Optoelectronic Engineering, Ludong University, Shandong 264025 China;2. Beijing National Laboratory for Molecules Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing, 100871 China;3. College of Chemistry and Center of Advanced Quantum Studies, Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing, 100875 China |
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| 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. |
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| Keywords: | correction operator Boltzmann operator imaginary-time semiclassical approximation semiclassical dynamics |
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