Thermodynamics and ergodicity of finite one-dimensional Toda and Morse lattices

Abstract

The thermodynamics of finite one-dimensional lattices of particles interacting via Toda or Morse potentials is considered. An analysis is performed in canonical and microcanonical ensembles in ‘temperature–lattice deformation’ variables. Analytical results are obtained for thermodynamical values. It is demonstrated that small number of particles, e.g. N = 10 , is enough to get accurate approximation in the thermodynamical limit N → ∞ . The problem of the deformation rate is also investigated. It is found that the temperature increases at high deformation rate, and decreases at slow deformations. The Morse lattice was analyzed in numerical MD simulations in both canonical and microcanonical ensembles. The results are in qualitative agreement with the results for the Toda lattice. The finite Morse lattice is ergodic and the Toda lattice is non-ergodic. An excellent agreement between analytical and numerical results is obtained.