Nonlinear structures and thermodynamic instabilities in a one-dimensional lattice system

TL;DR

This paper analyzes the equilibrium states of a one-dimensional lattice system using the Peyrard-Bishop Hamiltonian, revealing nonlinear domain wall structures that explain thermodynamic instabilities like DNA unzipping.

Contribution

It provides exact calculations of nonlinear domain wall structures in the Peyrard-Bishop model and links their formation to thermodynamic instabilities.

Findings

Exact nonlinear domain wall solutions are derived.

Free energy of domain walls is computed beyond Gaussian approximation.

Thermodynamic instabilities are explained via domain wall formation.

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 (DW), interpolating between bound and unbound segments of the chain. The free energy of the DWs 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 DW formation.