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Wigner phase space distribution via classical adiabatic switching.

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This study introduces an efficient approximate method for calculating the Wigner phase space density, overcoming computational challenges in complex quantum systems. The technique uses classical trajectories and adiabatic switching for accurate Wigner distribution generation.

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Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Computational physics

Background:

  • Evaluating the Wigner phase space density for many-body systems is computationally intensive due to oscillatory integrals.
  • Existing methods for Wigner transform face significant computational difficulties.

Purpose of the Study:

  • To develop a simple, efficient, and approximate procedure for generating the Wigner distribution.
  • To overcome the computational challenges associated with the traditional Wigner transform.

Main Methods:

  • Propagating phase space distributions via classical trajectories from a zeroth-order Hamiltonian.
  • Gradually switching on perturbations and utilizing the classical adiabatic theorem.
  • Generalizing to finite temperatures using a density rescaling factor and integrating trajectories under the full Hamiltonian for time-dependent properties.

Main Results:

  • The adiabatic switching procedure accurately reproduces the Wigner density for harmonic oscillator eigenstates and WKB-approximated anharmonic Hamiltonians.
  • The method preserves thermodynamic properties due to invariance under classical propagation.
  • Numerical tests show excellent agreement with full quantum mechanical methods across a wide temperature range for 1D and dissipative systems.

Conclusions:

  • The proposed method offers a computationally efficient and accurate alternative for Wigner distribution calculation.
  • It is well-suited for quasiclassical trajectory calculations, requiring only force fields as input.
  • The approach simplifies the evaluation of Wigner phase space density for complex quantum systems.