Two-oscillator mapping modification of the Poisson bracket mapping equation formulation of the quantum-classical Liouville equation

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Mapping basis solutions provide efficient ways for simulating mixed quantum-classical (MQC) dynamics in complex systems by matching multiple quantum states of interest to some fictitious physical states. Recently, various MQC methods were devised such that two harmonic oscillators are employed to represent each electronic state, showing improvements over one-oscillator-based methods. Here, we introduce and analyze newly modified mapping approximations of the quantum-classical Liouville equation (QCLE) using two oscillators for each electronic state. We design two separate mapping relations that we can adopt toward simulating dynamics and computing expectation values. Through the process, two MQC methods can be constructed, one of which actually reproduces the population dynamics of the forward and backward trajectory solution of QCLE. By applying the methods to spin-boson systems with a range of parameters, we find out that the choice of mapping relations greatly affects the simulation results. We also show that further improvement is possible through using modified identity operator formulations. Our findings may be helpful in constructing improved MQC methods in the future.
Publisher
AMER INST PHYSICS
Issue Date
2020-12
Language
English
Article Type
Article
Citation

JOURNAL OF CHEMICAL PHYSICS, v.153, no.21

ISSN
0021-9606
DOI
10.1063/5.0027799
URI
http://hdl.handle.net/10203/279316
Appears in Collection
CH-Journal Papers(저널논문)
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