Nonlinear Structures and Thermodynamic Instabilities in a One-Dimensional Lattice System

Abstract

The equilibrium states of the discrete Peyrard-Bishop Hamiltonian with one end fixed are computed exactly from the two-dimensional nonlinear Morse map. These exact nonlinear structures are interpreted as domain walls, interpolating between bound and unbound segments of the chain. Their free energy is calculated to leading order beyond the Gaussian approximation. Thermodynamic instabilities (e.g., DNA unzipping and/or thermal denaturation) can be understood in terms of domain wall formation.