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Semiclassical evaluation of expectation values.

K M Mittal1,2, O Giraud1, D Ullmo1

  • 1Université Paris-Saclay, CNRS, LPTMS, 91405 Orsay, France.

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Summary
This summary is machine-generated.

Semiclassical mechanics can lose quantum interference effects due to the stationary phase approximation. This study introduces new semiclassical expressions to accurately capture these effects in operator expectation value evolution.

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Area of Science:

  • Quantum mechanics
  • Semiclassical mechanics
  • Computational physics

Background:

  • Semiclassical mechanics preserves phase information and interference effects using classical dynamics.
  • Coherence in semiclassical descriptions relies on the stationary phase approximation.
  • The stationary phase approximation can eliminate crucial quantum interference effects.

Purpose of the Study:

  • To address the loss of quantum interference in semiclassical mechanics when using the stationary phase approximation.
  • To develop new semiclassical expressions for the time evolution of operator expectation values.
  • To provide a deeper understanding of interference effects in the deep semiclassical regime.

Main Methods:

  • Analyzing the evaluation of the time evolution of operator expectation values.
  • Including contributions beyond the stationary phase approximation.
  • Analytically treating integrals within the stationary phase approximation, leaving simple numerical integrals.

Main Results:

  • New semiclassical expressions for expectation value evolution are derived.
  • The necessity of including non-stationary point contributions is explained.
  • The developed method simplifies numerical integration compared to initial value representation methods.

Conclusions:

  • The proposed method accurately captures quantum interference effects lost by standard stationary phase approximation.
  • The approach offers an efficient and accurate way to study systems in the deep semiclassical regime.
  • This work provides new insights into the origin and geometric interpretation of quantum interference effects.