A method for constructing random matrix models of disordered bosons

DOI10.1088/1751-8113/44/33/335207zbMATH Open1225.82031arXiv1012.3791OpenAlexW1964520140MaRDI QIDQ3091851

Kathrin Schaffert, Alan Huckleberry

Publication date: 14 September 2011

Published in: Journal of Physics A: Mathematical and Theoretical (Search for Journal in Brave)

Abstract: Random matrix models of disordered bosons consist of matrices in the Lie algebra g=sp_n(R). Assuming dynamical stability, their eigenvalues are required to be purely imaginary. Here a method is proposed for constructing ensembles (E,P) of G-invariant sets E of such matrices with probability measures P. These arise as moment map direct images from phase spaces X which play an important role in complex geometry and representation theory. In the toy-model case of n=1, where X is the complex bidisk and P is the direct image of the uniform measure, an explicit description of the spectral measure is given.

Full work available at URL: https://arxiv.org/abs/1012.3791

Mathematics Subject Classification ID

Disordered systems (random Ising models, random Schrödinger operators, etc.) in equilibrium statistical mechanics (82B44) Random matrices (algebraic aspects) (15B52)

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