Energy correlations for a random matrix model of disordered bosons

Details Energy correlations for a random matrix model of disordered bosons Energy correlations for a random matrix model of disordered bosons

2006-07-10

arxiv.org/abs/cond-mat/0607243v2

J. Math. Phys. 47 (2006) 103304

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

20 pages, 3 figures, references added

Scientific paper

10.1063/1.2356798

Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the physical system determines a probability measure with support on this cone. The present paper analyzes a discrete family of such measures of exponential type, and does so in an attempt to capture, by a simple random matrix model, some generic statistical features of the characteristic frequencies of disordered bosonic quasi-particle systems. The level correlation functions of the said measures are shown to be those of a determinantal process, and the kernel of the process is expressed as a sum of bi-orthogonal polynomials. While the correlations in the bulk scaling limit are in accord with sine-kernel or GUE universality, at the low-frequency end of the spectrum an unusual type of scaling behavior is found.

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