Semiclassical trace formulas for two identical particles

2000/01/24 by Jamal Sakhr, Niall D. Whelan
Chemistry · Physics and Astronomy · #Advanced Chemical Physics Studies #Classical mechanics #Formalism (music) #Molecular Spectroscopy and Structure #Periodic orbits #Physics #Quantum #Quantum chaos and dynamical systems #Quantum mechanics #Semiclassical physics #Theoretical physics #cond-mat.mes-hall #nlin.CD

paper · pdf · doi:10.1103/physreva.62.042109

published as Phys. Rev. A vol.62, 042109 (2000).

arxiv created 2000/01/24 · openalex publication_date 2000/09/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Semiclassical periodic orbit theory is used in many branches of physics. However, most applications of the theory have been to systems that involve only single-particle dynamics. In this paper, we develop a semiclassical formalism to describe the density-of-states for two noninteracting particles. This includes accounting properly for particle exchange symmetry. As specific examples, we study two identical particles in a disk and in a cardioid. In each case, we demonstrate that the semiclassical formalism correctly reproduces the quantum densities.

Citations

• Periodic Orbits and Classical Quantization Conditions
• Orbital Magnetism in the Ballistic Regime: Geometrical Effects
• Edge diffraction, trace formulae and the cardioid billiard
• On the use of windows for harmonic analysis with the discrete Fourier transform
• Semiclassical approach to orbital magnetism of interacting diffusive quantum systems