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

Nuclear Physics B
 Pub Date:
 November 2004
 DOI:
 10.1016/j.nuclphysb.2004.08.013
 arXiv:
 arXiv:hepth/0407017
 Bibcode:
 2004NuPhB.700..521T
 Keywords:

 High Energy Physics  Theory;
 Condensed Matter  Mesoscopic Systems and Quantum Hall Effect;
 Mathematical Physics;
 Mathematics  Mathematical Physics;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems
 EPrint:
 14 pages