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

Abstract

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 <exp[i(XY)]> 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.

accepted by J. Phys. A

References in corpus (6)

• Distribution of reflection coefficients in absorbing chaotic microwave cavities
• An exact formula for general spectral correlation function of random Hermitian matrices
• Characteristic polynomials of real symmetric random matrices
• Increasing subsequences and the hard-to-soft edge transition in matrix ensembles
• Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations
• Correlation functions of the BC Calogero-Sutherland model

Cited by in corpus (5)

• Matrix oscillator and Calogero-type models
• Exchange operator formalism for N-body spin models with near-neighbors interactions
• Calogero model with Yukawa like interaction
• Jastrow-like ground states for quantum many-body potentials with near-neighbors interactions
• Linearized transverse diffeomorphism invariant spin-2 theories via gauge invariants