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Multi-time formulation of Matsubara dynamics.

Kenneth A Jung1, Pablo E Videla1, Victor S Batista1

  • 1Department of Chemistry, Yale University, P.O. Box 208107, New Haven, Connecticut 06520-8107, USA.

The Journal of Chemical Physics
|July 22, 2019
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Summary
This summary is machine-generated.

This study generalizes Matsubara dynamics for multitime correlation functions. The new multitime Matsubara dynamics approximation serves as a benchmark for developing semiclassical methods in quantum dynamics.

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Area of Science:

  • Quantum Dynamics
  • Statistical Mechanics
  • Computational Physics

Background:

  • Matsubara dynamics is a key theory for single-time correlation functions.
  • Calculating multitime correlation functions in quantum systems is complex.
  • Existing methods often lack generalizability for higher-order functions.

Purpose of the Study:

  • To generalize Matsubara dynamics for multitime correlation functions.
  • To establish a benchmark theory for Boltzmann-preserving semiclassical approximations.
  • To explore the connection between path integral imaginary time-ordering and classical dynamics.

Main Methods:

  • Extension of the Matsubara approximation to two-time correlation functions.
  • Generalization to multitime fully symmetrized Kubo transformed correlation functions.
  • Development of a multitime Matsubara dynamics approximation.

Main Results:

  • The Matsubara approximation is applicable to two-time correlation functions.
  • A multitime Matsubara dynamics approximation for multitime correlation functions is derived.
  • A connection between imaginary time-ordering and classical dynamics is revealed.

Conclusions:

  • The generalized multitime Matsubara dynamics provides a benchmark for future semiclassical approximations.
  • This formulation highlights the link between quantum path integrals and classical dynamics.
  • Further development is needed for practical applications due to a phase-term.