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Sampling the thermal Wigner density via a generalized Langevin dynamics.

Thomas Plé1, Simon Huppert1, Fabio Finocchi1

  • 1Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France.

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This study introduces a novel method for calculating the Wigner thermal density using a generalized Langevin equation. This approach accurately models complex quantum dynamics, including zero-point energy effects and momentum-coordinate correlations.

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Area of Science:

  • Quantum Dynamics
  • Statistical Mechanics

Background:

  • The Wigner thermal density is crucial for semiclassical quantum dynamics.
  • It initializes classical trajectories for approximate quantum simulations.

Purpose of the Study:

  • To develop an original computational approach for the Wigner thermal density.
  • To address challenges in modeling nonclassical quantum features.

Main Methods:

  • A generalized Langevin equation is proposed for Wigner density computation.
  • This involves coordinate-dependent friction and generalized forces.
  • Auxiliary calculations are used to estimate these nontrivial quantities.

Main Results:

  • The new sampling scheme accurately computes Wigner density.
  • It effectively captures nonclassical features like zero-point energy and negative Wigner densities.
  • The algorithm's convergence is systematically verifiable.

Conclusions:

  • The proposed method offers an accurate and efficient approach for Wigner density calculation.
  • It provides a valuable tool for semiclassical quantum dynamics.
  • Potential improvements for numerical efficiency are discussed.