Statistical Mechanics of Discrete Multicomponent Fragmentation

Statistical mechanics of a discrete nonlinear system

Statistical mechanics of the discrete nonlinear Schrodinger equation is studied by means of analytical and numerical techniques. The lower bound of the Hamiltonian permits the construction of standard Gibbsian equilibrium measures for positive temperatures. Beyond the line of T = infinity, we identify a phase transition through a discontinuity in the partition function. The phase transition is ...

Statistical Mechanics and Combinatorics of Some Discrete Lattice Models

OF THE DISSERTATION Statistical Mechanics and Combinatorics of Some Discrete Lattice Models by Arvind Ayyer Dissertation Director: Professor Joel L. Lebowitz Many problems in statistical physics involve enumeration of certain objects. In this thesis, we apply ideas from combinatorics and statistical physics to understand three different lattice models. I We investigate the structure of the none...

Statistical mechanics of a discrete Schrödinger equation with saturable nonlinearity.

We study the statistical mechanics of the one-dimensional discrete nonlinear Schrödinger (DNLS) equation with saturable nonlinearity. Our study represents an extension of earlier work [Phys. Rev. Lett. 84, 3740 (2000)] regarding the statistical mechanics of the one-dimensional DNLS equation with a cubic nonlinearity. As in this earlier study, we identify the spontaneous creation of localized ex...

Statistical Mechanics

Statistical Mechanics

where pi ≡ p(x = i). If only M of the K states have non-zero probability and that probability is 1/M then S = logM . In this special case the entropy is the log of the number of occupied states. An analog of this special case in the continuous domain occurs in Liouville’s Theorem. This states that if the volume of phase space (i.e. of the x variable, but now multivariate and continuous) is some...