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Periodicity and Growth in a Lattice Gas with Dynamical Geometry
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-
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