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Iterative blip-summed path integral for quantum dynamics in strongly dissipative environments.

Nancy Makri1

  • 1Departments of Chemistry and Physics, University of Illinois, Urbana, Illinois 61801, USA.

The Journal of Chemical Physics
|April 10, 2017
PubMed
Summary

This study introduces an iterative blip-summed path integral decomposition. The method efficiently calculates quantum system dynamics, especially for complex, dissipative baths, reducing computational cost.

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Area of Science:

  • Quantum mechanics
  • Chemical physics
  • Computational methods

Background:

  • Calculating the reduced density matrix for quantum systems interacting with dissipative baths is computationally intensive.
  • The Feynman-Vernon influence functional is key to incorporating bath effects in path integral formulations.

Purpose of the Study:

  • To describe an iterative decomposition of the blip-summed path integral.
  • To develop a more efficient method for calculating quantum system dynamics in the presence of dissipative baths.

Main Methods:

  • Iterative evaluation of a forward-backward path sum for the reduced density matrix.
  • Propagation of an array storing blip configurations within a defined memory interval.
  • Utilizing blip decomposition to avoid exponential path segment enumeration.

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Main Results:

  • The blip-summed path integral method yields numerically exact results, free of statistical error.
  • Significant reduction in computational effort for strongly dissipative and sluggish baths compared to non-decomposed methods.
  • Rapid convergence demonstrated even with extremely long bath memory, as shown in a two-level system application.

Conclusions:

  • The iterative blip decomposition offers a computationally efficient and accurate approach for quantum dynamics.
  • This method is particularly advantageous for systems with long bath memory and strong dissipation.
  • The algorithm's efficiency stems from rapid blip series convergence and avoidance of explicit path segment calculations.