Tunneling of the Kawasaki dynamics at low temperatures in two dimensions

Abstract

Consider a lattice gas evolving according to the conservative Kawasaki dynamics at inverse temperature $\beta$ on a two dimensional torus ${\Lambda }_L=\{0,...,L-1{\}}^2$ . We prove the tunneling behavior of the process among the states of minimal energy. More precisely, assume that there are $n^2\ll L$ particles and that the initial state is the configuration in which all sites of the square $\mb x + \{0,..., n-1\}^2$ are occupied. We show that in the time scale $e^{2\beta }$ the process is close to a Markov process on ${\Lambda }_L$ which jumps from any site $\mb x$ to any other site $\mb y\not =\mb x$ at a strictly positive rate which can be expressed in terms of the jump rates of simple random walks.

References in corpus (4)

• Metastability in Glauber dynamics in the low-temperature limit: Beyond exponential asymptotics
• Dynamics of trap models
• Thermodynamic Limit for the Invariant Measures in Supercritical Zero Range Processes
• Metastability for a non-reversible dynamics: the evolution of the condensate in totally asymmetric zero range processes