Periodicity and Growth in a Lattice Gas with Dynamical Geometry.pdf

PERIODICITY AND GROWTH IN A LATTICE GAS WITH DYNAMICAL GEOMETRY 5 0 KARIN BAUR, JEFFREY M. RABIN, AND DAVID A. MEYER 0 2 n u Abstract J 0 We study a one-dimensional lattice gas “dynamical geometry model” in which 3 local reversible interactions of counter-rotating groups of particles on a ring can create or destroy lattice sites. We exhibit many periodic orbits and show that ] all other solutions have asymptotically growing lattice length in both directions of G time. We explain why the length grows as √t in all cases examined. We completely C. solve the dynamics for small numbers of particles with arbitrary initial conditions. n i l n [ 1. Introduction 1 v Lattice models are ubiquitous in physics, whether as regularizations for contin- 5 uum theories (quantum field theory, quantum gravity), scaffolding for numerical 6 methods (classical field theories, continuum mechanics), or because the lattice is 0 6 physically real (condensed matter physics). In virtually all applications, however, 0 the lattice structure and size are fixed, or at least not dynamical. (In numerical 5 computation the lattice may be refined to maintain precision, but the evolution of 0 the lattice is not part of the physical dynamics under study.) Among the exceptions / n known to us are the causal dynamical triangulation approach to quantum gravity i [AJL05] and the variable-