Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy

2004/07/02 by R. Teodorescu, E. Bettelheim, O. Agam +2
Physics and Astronomy · Mathematics · #hep-th #cond-mat.mes-hall #math-ph #math.MP #nlin.SI

paper · pdf · doi:10.1016/j.nuclphysb.2004.08.013

published as Nucl.Phys. B700 (2004) 521-532 · 14 pages

arxiv created 2004/07/02 · arxiv updated 2009/12/01

Abstract

We continue the analysis of the spectral curve of the normal random matrix ensemble, introduced in an earlier paper. Evolution of the full quantum curve is given in terms of compatibility equations of independent flows. The semiclassical limit of these flows is expressed through canonical differential forms of the spectral curve. We also prove that the semiclassical limit of the evolution equations is equivalent to Whitham hierarchy.

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