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Semiclassical trace formulas for noninteracting identical particles.

Jamal Sakhr1, Niall D Whelan

  • 1Department of Physics and Astronomy, McMaster University, Hamilton, Ontario, Canada.

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics
|October 26, 2005
PubMed
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We adapted the Gutzwiller trace formula for noninteracting identical particles, addressing challenges from conserved energy and particle symmetries. This work presents new many-body trace formulas for quantum systems.

Area of Science:

  • Quantum mechanics
  • Statistical mechanics
  • Mathematical physics

Background:

  • The Gutzwiller trace formula relates classical periodic orbits to quantum mechanics.
  • Standard formulas fail for noninteracting identical particles due to continuous energy symmetries and discrete permutations.

Purpose of the Study:

  • Extend the Gutzwiller trace formula to systems of noninteracting identical particles.
  • Derive many-body trace formulas for full and symmetry-reduced densities of states.
  • Test the theoretical results using numerical simulations.

Main Methods:

  • Utilizing the Creagh and Littlejohn formalism for semiclassical dynamics with continuous symmetries.
  • Extending the Gutzwiller trace formula to account for particle identity and conserved energies.

Related Experiment Videos

  • Performing numerical studies on a three-particle cardioid billiard system.

    • Main Results:

    • Developed a generalized Gutzwiller trace formula applicable to noninteracting identical particles.
    • Derived many-body trace formulas for both full and symmetry-reduced densities of states.
    • Demonstrated the validity of the derived formulas through numerical simulations.

    Conclusions:

    • The extended trace formula accurately describes quantum systems with noninteracting identical particles.
    • The formalism successfully incorporates continuous and discrete symmetries.
    • Numerical results confirm the theoretical predictions, validating the new approach.