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Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE

Olivier Babelon, Karol K. Kozlowski, Vincent Pasquier

SciPost Phys. 5, 035 (2018) · published 18 October 2018


We construct a basis of solutions of the scalar $\boldsymbol{ \texttt{t} }- \boldsymbol{ \texttt{Q} }$ equation describing the spectrum of the $q$-Toda and Toda$_2$ chains by using auxiliary non-linear integral equations. Our construction allows us to provide quantisation conditions for the spectra of these models in the form of thermodynamic Bethe Ansatz-like equations.

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Baxter T-Q equation Non-linear integral equations (NLIE) Thermodynamic Bethe Ansatz (TBA) Toda chains

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