Quasiclassical Correlation Functions from the Wigner Density Using the Stability Matrix

Amartya Bose, Nancy Makri

Research output: Contribution to journalArticle

Abstract

Accounting for zero-point energy in the initial conditions of classical trajectory calculations of time correlation functions requires sampling from a quantized phase space distribution, which is often chosen as the Weyl-Wigner transform of a thermalized operator. The numerical construction of the latter and its use as a sampling function can be challenging. We show that the operator dependence of the phase space distribution can be transferred to the dynamics, allowing sampling from the simpler Wigner phase space density. The method involves augmenting the classical equations of motion with additional differential equations for elements of the stability matrix. We also propose a local harmonic approximation for the dynamical derivatives, which significantly reduces the computational cost required to obtain correlation functions of nonlinear operators. We illustrate the method with application to linear and nonlinear correlation functions of model Hamiltonians. While the local harmonic approximation is not always successful in predicting nonlinear correlation functions of one degree of freedom, it quantitatively captures the full quasiclassical results for systems in contact with dissipative environments.

Original languageEnglish (US)
Pages (from-to)2165-2174
Number of pages10
JournalJournal of Chemical Information and Modeling
Volume59
Issue number5
DOIs
StatePublished - May 28 2019

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Stiffness matrix
Sampling
Hamiltonians
Equations of motion
Mathematical operators
Differential equations
Trajectories
contact
Derivatives
energy
costs
Costs

ASJC Scopus subject areas

  • Chemistry(all)
  • Chemical Engineering(all)
  • Computer Science Applications
  • Library and Information Sciences

Cite this

Quasiclassical Correlation Functions from the Wigner Density Using the Stability Matrix. / Bose, Amartya; Makri, Nancy.

In: Journal of Chemical Information and Modeling, Vol. 59, No. 5, 28.05.2019, p. 2165-2174.

Research output: Contribution to journalArticle

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