The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles

Details The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles The Calogero-Moser equation system and the ensemble average in the Gaussian ensembles

2003-10-09

arxiv.org/abs/cond-mat/0310214v1

Physics

Condensed Matter

Statistical Mechanics

accepted by J. Phys. A

Scientific paper

10.1088/0305-4470/37/1/009

From random matrix theory it is known that for special values of the coupling constant the Calogero-Moser (CM) equation system is nothing but the radial part of a generalized harmonic oscillator Schroedinger equation. This allows an immediate construction of the solutions by means of a Rodriguez relation. The results are easily generalized to arbitrary values of the coupling constant. By this the CM equations become nearly trivial. As an application an expansion for in terms of eigenfunctions of the CM equation system is obtained, where X and Y are matrices taken from one of the Gaussian ensembles, and the brackets denote an average over the angular variables.

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