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Improved semiclassical density matrix: taming caustics.

C A A de Carvalho1, R M Cavalcanti, E S Fraga

  • 1Instituto de Física, Universidade Federal do Rio de Janeiro, Caixa Postal 68528, Rio de Janeiro, RJ 21945-970, Brazil. aragao@if.ufrj.br

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|June 13, 2002
PubMed
Summary

We developed a straightforward method to handle caustics in semiclassical thermal density matrices using Euclidean action extrema. This approach utilizes complex trajectories for particle dynamics on a line.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics

Background:

  • Caustics pose challenges in semiclassical approximations.
  • Calculating thermal density matrices requires handling complex systems.

Purpose of the Study:

  • To present a simple method for dealing with caustics.
  • To simplify semiclassical thermal density matrix calculations.

Main Methods:

  • Utilizing the extrema of the Euclidean action.
  • Employing complex trajectories.
  • Focusing on diagonal elements of the thermal density matrix.

Main Results:

  • A simplified method for caustics in semiclassical approximations.
  • Successful application to the quartic double-well potential.

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Conclusions:

  • The method provides an effective way to manage caustics.
  • Knowledge of Euclidean action extrema is sufficient for this approach.