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Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy |
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| Authors: | R Teodorescu E Bettelheim O Agam A Zabrodin P Wiegmann |
| Institution: | aJames Frank Institute, University of Chicago, 5640 S. Ellis ave., Chicago, IL 60637, USA bRacah Institute of Physics, Hebrew University, Givat Ram, 91904 Jerusalem, Israel cInstitute of Biochemical Physics, Kosygina str. 4, 117334 Moscow, Russia dITEP, Bol. Cheremushkinskaya str. 25, 117259 Moscow, Russia eJames Frank Institute, Enrico Fermi Institute, University of Chicago, 5640 S. Ellis ave., Chicago, IL 60615, USA fLandau Institute, Moscow, Russia |
| 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. |
| Keywords: | Integrable systems Random matrix theory |
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