Semiclassical trace formulas for noninteracting identical particles

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 67, Issue 6 2, 2003, Pages

  Sakhr, Jamal ^a   Whelan, Niall D ^a  

^a MCMASTER UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

ASYMPTOTIC STABILITY; CONVOLUTION; EIGENVALUES AND EIGENFUNCTIONS; ELECTRONIC DENSITY OF STATES; FERMIONS; FOURIER TRANSFORMS; GREEN'S FUNCTION; HAMILTONIANS; NUMERICAL METHODS; PHASE SPACE METHODS; QUANTUM THEORY;

DISCRETE PERMUTATIONAL SYMMETRY; NONINTERACTING IDENTICAL PARTICLE; SYMMETRY-REDUCED DENSITY OF STATE; THREE-PARTICLE CARDIOID BILLIARD;

PARTICLES (PARTICULATE MATTER);

EID: 42749104991     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

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72. The division of N of the energy argument simply states that the total energy must be evenly divided among all of the particles. The set of orbits corresponding to this cycle is clearly the same as the set of orbits of the one-particle dynamics (almost by definition) and the amplitudes and actions are the same as the one-particle case since the N particles collectively execute one complete motion (or a multiple repetition) of the periodic orbit. This is observed for N=3 in Sec. V B.
73. 1/2 ∈ (0,0,1) and Î denotes the identity operator.