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arXiv:1211.4428

Bethe ansatz and Hirota equation in integrable models

Anton Vladimirovich Zabrodin

Published Nov 19, 2012• 7 citations
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Abstract

In this short review the role of the Hirota equation and the tau-function in the theory of classical and quantum integrable systems is outlined.
DOI
10.48550/arxiv.1211.4428

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A brief non-technical review of the recent study of classical integrable structures in quantum integrable systems is given. It is explained how to identify the standard objects of quantum integrable systems (transfer matrices, Baxter's QQQ-operators, etc) with elements of classical non-linear integrable difference equations (τττ-functions, Baker-Akhiezer functions, etc). The nested Bethe ansatz equations for Ak−1A_{k-1}Ak−1​-type models emerge as discrete time equations of motion for zeros of classical τττ-functions and Baker-Akhiezer functions. The connection with discrete time Ruijsenaars-Schneider system of particles is discussed.
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