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

R. Teodorescu; E. Bettelheim; O. Agam; A. Zabrodin; P. Wiegmann

doi:10.1016/j.nuclphysb.2004.08.013

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

R. Teodorescu^*, E. Bettelheim, O. Agam, A. Zabrodin, P. Wiegmann

^*Corresponding author for this work

Racah Institute of Physics

Research output: Contribution to journal › Article › peer-review

20 Scopus citations

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.

Original language	English
Pages (from-to)	521-532
Number of pages	12
Journal	Nuclear Physics B
Volume	700
Issue number	1-3
DOIs	https://doi.org/10.1016/j.nuclphysb.2004.08.013
State	Published - 15 Nov 2004

Bibliographical note

Funding Information:
We are indebted to A. Kapaev, V. Kazakov, I. Krichever, I. Kostov, A. Marshakov and M. Mineev-Weinstein for useful discussions, interest in the subject and help. P.W. and R.T. were supported by the NSF MRSEC Program under DMR-0213745, NSF DMR-0220198 and by the Humboldt foundation. A.Z. and P.W. acknowledge support by the LDRD project 20020006ER “Unstable Fluid/Fluid Interfaces” at Los Alamos National Laboratory and M. Mineev-Weinstein for the hospitality in Los Alamos. A.Z. was also supported in part by RFBR grant 03-02-17373,w and by the grant for support of scientific schools NSh-1999.2003.2. P.W. is grateful to K.B. Efetov for the hospitality in Ruhr-Universitaet Bochum and to A. Cappelli for the hospitality in the University of Florence.

Keywords

Integrable systems
Random matrix theory

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10.1016/j.nuclphysb.2004.08.013

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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",

author = "R. Teodorescu and E. Bettelheim and O. Agam and A. Zabrodin and P. Wiegmann",

note = "Funding Information: We are indebted to A. Kapaev, V. Kazakov, I. Krichever, I. Kostov, A. Marshakov and M. Mineev-Weinstein for useful discussions, interest in the subject and help. P.W. and R.T. were supported by the NSF MRSEC Program under DMR-0213745, NSF DMR-0220198 and by the Humboldt foundation. A.Z. and P.W. acknowledge support by the LDRD project 20020006ER “Unstable Fluid/Fluid Interfaces” at Los Alamos National Laboratory and M. Mineev-Weinstein for the hospitality in Los Alamos. A.Z. was also supported in part by RFBR grant 03-02-17373,w and by the grant for support of scientific schools NSh-1999.2003.2. P.W. is grateful to K.B. Efetov for the hospitality in Ruhr-Universitaet Bochum and to A. Cappelli for the hospitality in the University of Florence. ",

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AU - Zabrodin, A.

AU - Wiegmann, P.

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N2 - 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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Semiclassical evolution of the spectral curve in the normal random matrix ensemble as Whitham hierarchy

Abstract

Bibliographical note

Keywords

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