Related papers: Integer Lattice Gases at Equilibrium
A condensed history and theoretical development of lattice-gas automata in the Boltzmann limit is presented. This is provided as background to set up the context for understanding the implementation of the lattice-gas method on two parallel…
We introduce a random matrix framework for studying statistical-mechanical lattice systems through spectral observables. Equilibrium configurations sampled from a Boltzmann measure are mapped to matrix ensembles whose covariance structure…
We construct a four-dimensional lattice-gas model with finite-range interactions that has non-periodic, ``quasicrystalline'' Gibbs states at low temperatures. Such Gibbs states are probability measures which are small perturbations of…
We consider random matrices that have invariance properties under the action of unitary groups (either a left-right invariance, or a conjugacy invariance), and we give formulas for moments in terms of functions of eigenvalues. Our main tool…
This paper studies automatic structures for subsemigroups of Baumslag--Solitar semigroups (that is, semigroups presented by $\ < x,y \mid (yx^m, x^ny)\ >$, where $m$ and $n$ are natural numbers). A geometric argument (a rarity in the field…
In this paper we study the space evolution in the Rule 54 reversible cellular automaton, which is a paradigmatic example of a deterministic interacting lattice gas. We show that the spatial translation of time configurations of the…
Lattice models are valuable tools to gain insight into the statistical physics of heteropolymers. We rigorously map the partition function of these models into a vacuum expectation value of a $\mathbb{Z}_2$ lattice gauge theory (LGT), with…
The recent development of the lattice gas automata method and its extension to the lattice Boltzmann method have provided new computational schemes for solving a variety of partial differential equations and modeling chemically reacting…
The language of operator algebras is of great help for the formulation of questions and answers in quantum statistical mechanics. In Chapter 1 we present a minimal mathematical introduction to operator algebras, with physical applications…
We prove an identity for five arguments, valid in the lattice of natural numbers with gcd and lcm as lattice operations. More generally, this identity characterizes arbitrary distributive lattices. Fixing three of the five arguments, we…
Several cellular automata (CA) models have been developed to simulate self-organization of multiple levels of structures. However, they do not obey microscopic reversibility and conservation laws. In this paper, we describe the construction…
The statistical properties of a two dimensional lattice of elastic lines in a random medium are studied using the Bethe ansatz. We present a novel mapping of the dilute random line lattice onto the weak coupling limit of a pure Bose gas…
We propose an experimentally feasible method to generate a one-dimensional optical lattice potential in an ultracold Bose gas system that depends on the transverse momentum of the atoms. The optical lattice is induced by the artificial…
A manifestly covariant relativistic statistical mechanics of the system of $N$ indistinguishable events with motion in space-time parametrized by an invariant ``historical time'' $\tau $ is considered. The relativistic mass distribution for…
We describe a technique for solving the combined collisionless Boltzmann and Poisson equations in a discretised, or lattice, phase space. The time and the positions and velocities of `particles' take on integer values, and the forces are…
The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A…
Monte Carlo method within, so called, classical fields approximation is applied to one dimensional weakly interacting repulsive Bose gas trapped in a harmonic potential. Equilibrium statistical properties of the condensate are calculated…
We consider an isolated system in an arbitrary state and provide a general formulation using first principles for an additive and non-negative statistical quantity that is shown to reproduce the equilibrium thermodynamic entropy of the…
We simulate self-reproducing micellar systems using a recently introduced lattice-gas automaton. This dynamical model correctly describes the equilibrium and non-equilibrium properties of mixtures of oil, water and surfactants. The…
The treatment of the number-theoretical problem of integer partitions within the approach of statistical mechanics is discussed. Historical overview is given and known asymptotic results for linear and plane partitions are reproduced. From…