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On the classical limit of a time-dependent self-consistent field system: Analysis and computation

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posted on 22.03.2021, 21:15 by S Jin, C Sparber, Z Zhou
© American Institute of Mathematical Sciences. We consider a coupled system of Schrödinger equations, arising in quantum mechanics via the so-called time-dependent self-consistent field method. Using Wigner transformation techniques we study the corresponding classical limit dynamics in two cases. In the first case, the classical limit is only taken in one of the two equations, leading to a mixed quantum-classical model which is closely connected to the well-known Ehrenfest method in molecular dynamics. In the second case, the classical limit of the full system is rigorously established, resulting in a system of coupled Vlasov-type equations. In the second part of our work, we provide a numerical study of the coupled semiclassically scaled Schrödinger equations and of the mixed quantum-classical model obtained via Ehrenfest's method. A second order (in time) method is introduced for each case. We show that the proposed methods allow time steps independent of the semi-classical parameter(s) while still capturing the correct behavior of physical observables. It also becomes clear that the order of accuracy of our methods can be improved in a straightforward way.

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Publisher Statement

This is a pre-copy-editing, author-produced PDF of an article accepted for publication in Kinetic and Related Models following peer review. The definitive publisher-authenticated version On the classical limit of a time-dependent self-consistent field system: Analysis and computation is available online at: https://doi.org/10.3934/krm.2017011

Citation

Jin, S., Sparber, C.Zhou, Z. (2017). On the classical limit of a time-dependent self-consistent field system: Analysis and computation. Kinetic and Related Models, 10(1), 263-298. https://doi.org/10.3934/krm.2017011

Publisher

American Institute of Mathematical Sciences (AIMS)

Language

en

issn

1937-5093

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