Surface Energy and Boundary Layers for a Chain of Atoms at Low Temperature

Jansen, Sabine; König, Wolfgang; Schmidt, Bernd und Theil, Florian (2020): Surface Energy and Boundary Layers for a Chain of Atoms at Low Temperature. In: Archive for Rational Mechanics and Analysis, Bd. 239, Nr. 2: S. 915-980

Abstract

We analyze the surface energy and boundary layers for a chain of atoms at low temperature for an interaction potential of Lennard-Jones type. The pressure (stress) is assumed to be small but positive and bounded away from zero, while the temperature beta-1 goes to zero. Our main results are: (1) As beta ->infinity at fixed positive pressure p>0, the Gibbs measures mu beta and nu beta for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals (E) over bar(bulk) and (E) over bar(surf). The minimizer of the surface functional corresponds to zero temperature boundary layers;(2) The surface correction to the Gibbs free energy converges to the zero temperature surface energy, characterized with the help of the minimum of E over bar surf;(3) The bulk Gibbs measure and Gibbs free energy can be approximated by their Gaussian counterparts;(4) Bounds on the decay of correlations are provided, some of them uniform in beta.

• Dokumententyp: Zeitschriftenartikel
• Fakultät: Mathematik, Informatik und Statistik > Mathematik
• Themengebiete: 500 Naturwissenschaften und Mathematik > 510 Mathematik
• ISSN: 0003-9527
• Sprache: Englisch