Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy
High Energy Physics - Theory
2007-05-23 v1 Mesoscale and Nanoscale Physics
Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
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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Cite
@article{arxiv.hep-th/0407017,
title = {Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy},
author = {R. Teodorescu and E. Bettelheim and O. Agam and A. Zabrodin and P. Wiegmann},
journal= {arXiv preprint arXiv:hep-th/0407017},
year = {2007}
}
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14 pages