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Continuum limit semiclassical initial value representation for dissipative systems.

Eli Pollak1

  • 1Chemical Physics Department, Weizmann Institute of Science, 76100 Rehovoth, Israel. eli.pollak@weizmann.ac.il

The Journal of Chemical Physics
|August 28, 2007
PubMed
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This study derives the continuum limit for the semiclassical initial value representation of dissipative systems. This method incorporates the harmonic bath

Area of Science:

  • Quantum dynamics
  • Statistical mechanics
  • Condensed matter physics

Background:

  • Dissipative systems are crucial in quantum mechanics and statistical mechanics.
  • Traditional semiclassical initial value representation (SC-IVR) methods often discretize the harmonic bath.
  • Integrating out the harmonic bath in the continuum limit is challenging for SC-IVR.

Purpose of the Study:

  • To derive the continuum limit of the semiclassical initial value representation for dissipative systems.
  • To extend SC-IVR methods beyond discretized bath treatments.
  • To accurately model the influence of a harmonic bath on system dynamics.

Main Methods:

  • Utilizing path integral formulation with factorized initial conditions.
  • Developing a generalized Langevin equation for classical system dynamics.

Related Experiment Videos

  • Deriving the continuum limit of SC-IVR by modifying the system's action with a nonlocal term.

    • Main Results:

    • The continuum limit of SC-IVR for dissipative systems is successfully derived.
    • The modified action includes a nonlocal term accounting for bath influence.
    • The first-order correction term to the SC-IVR approximation in the continuum limit is obtained.

    Conclusions:

    • The derived method enables accurate semiclassical treatment of dissipative systems without bath discretization.
    • This advancement facilitates the study of quantum dynamics in complex environments.
    • The findings offer a more rigorous approach to modeling open quantum systems.