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Communication: Systematic elimination of Stokes divergences emanating from complex phase space caustics.

Werner Koch1, David J Tannor1

  • 1Weizmann Institute of Science, Rehovot, Israel.

The Journal of Chemical Physics
|March 17, 2018
PubMed
Summary

Stokes phenomenon causes unphysical divergences in asymptotic expansions. This study rigorously determines Stokes lines using deviations from second order, enabling accurate wavepacket reconstruction for various systems.

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Area of Science:

  • Mathematical Physics
  • Quantum Mechanics
  • Complex Analysis

Background:

  • Asymptotic expansions of complex functions can exhibit unphysical divergences beyond Stokes lines.
  • Stokes lines can emanate from phase space caustics, leading to a physically unrealistic double coverage of space.
  • Previous work by Adachi laid foundational but concise findings on this phenomenon.

Purpose of the Study:

  • To develop a rigorous method for determining Stokes lines.
  • To identify and remove unphysical divergences in asymptotic expansions.
  • To enable accurate wavepacket reconstruction using complex-valued classical trajectories.

Main Methods:

  • Analyzing deviations from second-order approximations.
  • Utilizing symmetry properties related to phase space caustics.
  • Applying the method to diverse physical systems like Morse, Quartic, Coulomb, and Eckart.

Main Results:

  • A rigorous method for identifying Stokes lines has been established.
  • Unphysical divergences in asymptotic expansions can be successfully removed.
  • Excellent wavepacket reconstruction was demonstrated for multiple systems.

Conclusions:

  • The developed method provides a robust way to handle Stokes phenomenon.
  • Accurate wavepacket reconstruction is achievable by removing unphysical contributions.
  • This approach has significant applications in quantum mechanics and mathematical physics.