Semiclassical Trace Formulas for Noninteracting Identical Particles

Details Semiclassical Trace Formulas for Noninteracting Identical Particles Semiclassical Trace Formulas for Noninteracting Identical Particles

2001-01-25

arxiv.org/abs/nlin/0101047v2

Phys.Rev.E67:066213,2003

Nonlinear Sciences

Chaotic Dynamics

29 pages, 11 figures, submitted to PRE

Scientific paper

10.1103/PhysRevE.67.066213

We extend the Gutzwiller trace formula to systems of noninteracting identical particles. The standard relation for isolated orbits does not apply since the energy of each particle is separately conserved causing the periodic orbits to occur in continuous families. The identical nature of the particles also introduces discrete permutational symmetries. We exploit the formalism of Creagh and Littlejohn [Phys. Rev. A 44, 836 (1991)], who have studied semiclassical dynamics in the presence of continuous symmetries, to derive many-body trace formulas for the full and symmetry-reduced densities of states. Numerical studies of the three-particle cardioid billiard are used to explicitly illustrate and test the results of the theory.

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