%0 Journal Article
%T Out-of-Equilibrium Dynamics of the Bose-Hubbard Model
%A Malcolm P. Kennett
%J ISRN Condensed Matter Physics
%D 2013
%R 10.1155/2013/393616
%X The Bose-Hubbard model is the simplest model of interacting bosons on a lattice. It has recently been the focus of much attention due to the realization of this model with cold atoms in an optical lattice. The ability to tune parameters in the Hamiltonian as a function of time in cold atom systems has opened up the possibility of studying out-of-equilibrium dynamics, including crossing the quantum critical region of the model in a controlled way. In this paper, I give a brief introduction to the Bose Hubbard model, and its experimental realization and then give an account of theoretical and experimental efforts to understand out-of-equilibrium dynamics in this model, focusing on quantum quenches, both instantaneous and of finite duration. I discuss slow dynamics that have been observed theoretically and experimentally for some quenches from the superfluid phase to the Mott insulating phase and the picture of two timescales, one for fast local equilibration and another for slow global equilibration, that appears to characterize this situation. I also discuss the theoretical and experimental observation of the Lieb-Robinson bounds for a variety of quenches and the Kibble-Zurek mechanism in quenches from the Mott insulator to superfluid. I conclude with a discussion of open questions and future directions. 1. Introduction The Bose-Hubbard model (BHM) is a minimal model of interacting bosons on a lattice. The original focus of work on the BHM [1] was in the context of experiments on superconductor-insulator transitions in granular superconductors [2] and Josephson junction arrays [3] and for 4He in porous media [4]. The proposal by Jaksch et al. [5] that the BHM could be realized by cold atoms in an optical lattice and the subsequent experimental demonstration of a superfluid to Mott insulator transition in this system by Greiner et al. [6] has lead the focus of work on this model to shift to cold atoms. The tunability of parameters in cold atom systems [7, 8], particularly as a function of time, naturally leads to interest in the out-of-equilibrium dynamics of the BHM especially in the vicinity of a quantum critical point [6]. The out-of-equilibrium dynamics of interacting quantum systems is an area of very active research, due to the challenge of understanding such a nontrivial problem. Unlike equilibrium statistical mechanics, where there are clear prescriptions for determining the state of a system, in out-of-equilibrium systems, not only do the current parameters of the Hamiltonian play a role, but also its history. Finding general principles and
%U http://www.hindawi.com/journals/isrn.cmp/2013/393616/