Analytical solution of the classical Bethe-ansatz equation for the Toda chain

Alessandro Cuccoli, Roberto Livi, M. Spicci +2 more

A review of the classical and quantum thermodynamic properties of the Toda chain is provided, together with a survey of the techniques that have been used to work them out, i.e., the bilateral Laplace transform method for the classical system, the Bethe–Ansatz and the variational path-integral approach for the quantum one. For the classical Toda chain we also recall some of the main dynamical features, i.e. the integrability of the model and the soliton-like solutions of the equations of motion. In the quantum case a comparison between the Bethe–Ansatz and the variational method is made. In particular it is shown as the latter offers the possibility of also evaluating static correlation functions.

Franz G. Mertens

Zengo Tsuboi, Atsuo Kuniba

Commuting transfer matrices of vertex models obey the functional relations which can be viewed as an type Toda field equation on discrete spacetime. Based on analytic Bethe ansatz we present, for , a new expression of its solution in terms of determinants and Pfaffians.

L.V. Avdeev, Alexey A. Vladimirov

B -D Dorfel, Alexey A. Vladimirov

O. Babelon, Karol Kajetan Kozlowski, Vincent Pasquier

We construct a basis of solutions of the scalar t-Q equation describing the spectrum of the q-Toda and Toda _2 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.