Dissipative dynamics with the corrected propagator method. Numerical comparison between fully quantum and mixed quantum/classical simulations

Gelman, David; Schwartz, Steven D.

doi:10.1016/j.chemphys.2010.01.021

Cited by 2 publications

(2 citation statements)

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“…For comparison, the quantum-classical TDSCF method, which serves as the zeroth-order approximate propagator, fails to produce a good accuracy even at T = 300 K (showing rate constants at least twice as large as the exact quantum results). 28 Previous applications 22,23 of the corrected propagator method have shown its ability to capture important quantum effects (such as tunneling) in systems where single configurational TDSCF failed. 7 Since the mean-field adiabatic approximation serves as a zeroth-order propagator in our method, we can conclude that the correction term essentially leads to the correct quantum dynamics of the primary system.…”

Section: Discussionmentioning

confidence: 99%

“…Previously, the method has been applied to describe the dissipative dynamics in one-dimensional systems coupled to a harmonic bath at zero temperature. 23 The results have been compared to the exact quantum-mechanical simulations with the surrogate Hamiltonian method. 24 Overall, a good agreement between the two methods has been demonstrated, and the corrected propagator was able to capture the correct dynamics (including the tunneling effect), while the adiabatic and the meanfield approximations failed.…”

Section: Introductionmentioning

confidence: 99%

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Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

Gelman

Schwartz

2011

The Journal of Chemical Physics

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The recently proposed mixed quantum-classical method is extended to applications at finite temperatures. The method is designed to treat complex systems consisting of a low-dimensional quantum part (the primary system) coupled to a dissipative bath described classically. The method is based on a formalism showing how to systematically correct the approximate zeroth-order evolution rule. The corrections are defined in terms of the total quantum Hamiltonian and are taken to the classical limit by introducing the frozen Gaussian approximation for the bath degrees of freedom. The evolution of the primary system is governed by the corrected propagator yielding the exact quantum dynamics. The method has been tested on a standard model system describing proton transfer in a condensed-phase environment: a symmetric double-well potential bilinearly coupled to a bath of harmonic oscillators. Flux correlation functions and thermal rate constants have been calculated at two different temperatures for a range of coupling strengths. The results have been compared to the fully quantum simulations of Topaler and Makri [J. Chem. Phys. 101, 7500 (1994)] with the real path integral method.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

Gelman

Schwartz

2011

The Journal of Chemical Physics

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Bohmian trajectory from the “classical” Schrödinger equation

Sengupta

Khatua

Chattaraj

2014

Chaos: An Interdisciplinary Journal of Nonlinear Science

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The quantum-classical correspondence is studied for a periodically driven quartic oscillator exhibiting integrable and chaotic dynamics, by studying the Bohmian trajectory of the corresponding "classical" Schrödinger equation. Phase plots and the Kolmogorov-Sinai entropy are computed and compared with the classical trajectory as well as the Bohmian trajectory obtained from the time dependent Schrödinger equation. Bohmian mechanics at the classical limit appears to mimick the behavior of a dissipative dynamical system.

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Dissipative dynamics with the corrected propagator method. Numerical comparison between fully quantum and mixed quantum/classical simulations

Cited by 2 publications

References 65 publications

Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

Finite temperature application of the corrected propagator method to reactive dynamics in a condensed-phase environment

Bohmian trajectory from the “classical” Schrödinger equation

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