Semiclassical statistical mechanics of fluids. II. An improved mean field effective pair potential

Semiclassical Statistical Mechanics ∗

We use a semiclassical approximation to derive the partition function for an arbitrary potential in one-dimensional Quantum Statistical Mechanics, which we view as an example of finite temperature scalar Field Theory at a point. We rely on Catastrophe Theory to analyze the pattern of extrema of the corresponding path-integral. We exhibit the propagator in the background of the different extrema...

Semiclassical Statistical Mechanics

Statistical Mechanics of the Nonlinear Schr6dinger Equation. II. Mean Field Approximation

We investigate a mean field approximation to the statistical mechanics of complex fields with dynamics governed by the nonlinear Schr6dinger equation. Such fields, whose Hamiltonian is unbounded below, may model plasmas, lasers, and other physical systems. Restricting ourselves to one-dimensional systems with periodic boundary conditions, we find in the mean field approximation a phase transiti...

Abstract: a Mean-field Statistical Mechanics Model for Regulation Networks

A MEAN-FIELD STATISTICAL MECHANICS MODEL FOR REGULATION NETWORKS EDUARDO JORDAO NEVES Let G = {1, . . . , n} represent the set of biochemical components interacting in a regulation network and denote by xi(t) ∈ R the density of component i at time t. In its simpler version the Interacting Markov Chains (IMC) model approach associates Ni two-state Markov chains to each component i. These N = ∑n ...

Chaos and Statistical Mechanics in the Hamiltonian Mean Field model

We study the dynamical and statistical behavior of the Hamiltonian Mean Field (HMF) model in order to investigate the relation between microscopic chaos and phase transitions. HMF is a simple toy model of N fully-coupled rotators which shows a second order phase transition. The canonical thermodynamical solution is briefly recalled and its predictions are tested numerically at finite N . The Vl...