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

O. Babelon (1) , K. Kozlowski (2) , V. Pasquier (3)

1 LPTHE - Laboratoire de Physique Théorique et Hautes Energies
2 ENS de Lyon - École normale supérieure de Lyon
3 IPHT - Institut de Physique Théorique - UMR CNRS 3681

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

Domaines: Physique mathématique [math-ph]

O. Babelon, K. Kozlowski, V. Pasquier. Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE. SciPost Physics, 2018, 5 (4), pp.035. ⟨10.21468/SciPostPhys.5.4.035⟩. ⟨cea-01787571⟩