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An exact imaginary-time path-integral phase-space formulation of multi-time correlation functions.

Pablo E Videla1, Victor S Batista1

  • 1Department of Chemistry, Yale Energy Sciences Institute and Yale Quantum Institute, Yale University, 225 Prospect Street, New Haven, Connecticut 06520, USA.

The Journal of Chemical Physics
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This study introduces an exact phase-space path-integral method for quantum mechanics, simplifying time correlation function calculations using ring-polymer dynamics. The approach reveals quantum dynamics through "interfering trajectories" in phase space.

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Area of Science:

  • Quantum mechanics
  • Theoretical chemistry
  • Statistical mechanics

Background:

  • Developing accurate semiclassical approximations for quantum dynamics is crucial.
  • Time correlation functions are key to understanding molecular dynamics and reaction rates.
  • Existing methods often struggle with the complexity of multi-time correlations.

Purpose of the Study:

  • To present an exact phase-space path-integral formalism for multi-time quantum correlation functions.
  • To provide a general framework for semiclassical approximations in quantum dynamics.
  • To offer a new interpretation of quantum dynamics via phase-space trajectories.

Main Methods:

  • Utilizing an exact representation of quantum mechanics in phase space.
  • Employing a path-integral formalism with ring-polymer dynamics in imaginary time.
  • Exploiting the permutation symmetry of imaginary-time path integrals.

Main Results:

  • Developed a formalism expressing correlations as products of invariant phase-space functions.
  • Naturally recovered the classical limit for multi-time correlation functions.
  • Provided an interpretation of quantum dynamics as interfering ring-polymer trajectories.

Conclusions:

  • The phase-space formulation offers a rigorous framework for quantum dynamics.
  • The method simplifies calculations of time correlation functions.
  • Future developments can leverage the cyclic permutation invariance of imaginary-time path integrals.