Lattice-gas simulations of dynamical geometry in one dimension

Details Lattice-gas simulations of dynamical geometry in one dimension Lattice-gas simulations of dynamical geometry in one dimension

2005-06-28

arxiv.org/abs/cond-mat/0506742v1

Phil.Trans.Roy.Soc.Lond. 362 (2004) 1667-1677

Physics

Condensed Matter

Statistical Mechanics

Scientific paper

10.1098/rsta.2004.1409

We present numerical results obtained using a lattice-gas model with dynamical geometry defined by Hasslacher and Meyer (Int. J. Mod. Phys. C. 9 1597 (1998)). The (irreversible) macroscopic behaviour of the geometry (size) of the lattice is discussed in terms of a simple scaling theory and obtained numerically. The emergence of irreversible behaviour from the reversible microscopic lattice-gas rules is discussed in terms of the constraint that the macroscopic evolution be reproducible. The average size of the lattice exhibits power law growth with exponent 1/2 at late times. The deviation of the macroscopic behaviour from reproducibility for particular initial conditions (``rogue states'') is investigated as a function of system size. The number of such ``rogue states'' is observed to decrease with increasing system size. Two mean-field analyses of the macroscopic behaviour are also presented.

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