Abstract : 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.
https://hal-cea.archives-ouvertes.fr/cea-01787571 Contributor : Emmanuelle De LaborderieConnect in order to contact the contributor Submitted on : Monday, May 7, 2018 - 4:19:57 PM Last modification on : Tuesday, January 4, 2022 - 4:54:30 AM Long-term archiving on: : Tuesday, September 25, 2018 - 2:18:38 AM
O. Babelon, K. Kozlowski, V. Pasquier. Solution of Baxter equation for the $q$-Toda and Toda$_2$ chains by NLIE. SciPost Physics, SciPost Foundation, 2018, 5 (4), pp.035. ⟨10.21468/SciPostPhys.5.4.035⟩. ⟨cea-01787571⟩