Institut für Theoretische Physik, Universität Bayreuth, D-95440 Bayreuth, Germany
We investigate the correlation functions of the periodic Toda chain at finite temperature numerically by using a combination of Monte-Carlo and molecular-dynamics methods. Intermediate steps allow comparison to known analytical results, e.g. excitation spectra. We also show an analytic approach to the force-force-correlation functions of the Toda chain extending an idea of the soliton gas theory: Non-interacting cnoidal waves describe excited waves of all kinds, from harmonic to solitary behaviour. The obtained shape of the force-force structure factor for a fixed wavenumber is a smooth, asymmetric single peak with a steep high-frequency side. Numerical and analytical results are in good agreement.
See also