Thermal stability of extended nonlinear structures related to the Davydov soliton

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Abstract
A Gibbs approach to the much studied problem of the thermal stability of nonlinear structures such as Davydov solitons is used with focus on spatially extended systems. The systems studied consist of a quantum-mechanical quasiparticle such as an electron or an excitation, interacting strongly with classical vibrations of the lattice, the entire assembly being in thermal equilibrium with a heat bath. The technique used for the study of thermal stability consists of the diagonalization of an N×N matrix where N is the number of sites among which the quasiparticle moves, followed by M thermal integrations where M is the number of vibrational coordinates with which the quasiparticle interacts. A basic duality emerges regarding the effect of temperature on the stability of nonlinear structures: temperature is found to help the nonlinearity in certain parameter and temperature regimes by inducing disorder and to destroy the nonlinearity in other regimes, e.g., always at large temperatures as a consequence of Boltzmann equalization. Particularly interesting features are found at low temperatures. A magnetic analogy reported earlier for smaller systems is reinforced by the present analysis for extended systems.