A Study of a Lattice Based Symmetry Broken Dimer Evaporation-Dseposition Process

Abstract

The analytic and computational study of the probabilistic mechanics of particles is simplified by latticizing space. In this project, we consider a two dimensional, square lattice, with particles interacting via nearest neighbour dimer evaporation-deposition processes. We then use the quantum spin analogy developed by Stinchcombe et al. to analyse the system. Here, we study the analogous Hamiltonians of two systems, one with evaporation and deposition allowed in both spatial directions, and the other with this symmetry, broken. We note that despite differences in the Hamiltonian, both systems have the same ground state, and differ in dynamics of the excitations.