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- ItemDistribution of cracks in a chain of atoms at low temperature(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2020) Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, FlorianWe consider a one-dimensional classical many-body system with interaction potential of Lennard--Jones type in the thermodynamic limit at low temperature 1/β ∈ (0, ∞). The ground state is a periodic lattice. We show that when the density is strictly smaller than the density of the ground state lattice, the system with N particles fills space by alternating approximately crystalline domains (clusters) with empty domains (voids) due to cracked bonds. The number of domains is of the order of N exp(-β e surf /2) with e surf > 0 a surface energy.
- ItemSurface energy and boundary layers for a chain of atoms at low temperature(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2019) Jansen, Sabine; König, Wolfgang; Schmidt, Bernd; Theil, FlorianWe 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 small but positive and bounded away from zero, while the temperature goes to zero. Our main results are: (1) As _x000C_ the temperature goes to zero and at fixed positive pressure, the Gibbs measures _x0016__x000C_for infinite chains and semi-infinite chains satisfy path large deviations principles. The rate functions are bulk and surface energy functionals. 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 the surface energy functional. (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 _x000C_the inverse temperature.