Dynamics and Thermodynamics of Many-particle Cold Atom Systems

Abstract

Abstract : As a result of the work related to and supported by this AFOSR grant, PI and collaborators we formulated theory of adiabatic dynamics in gapless systems and showed that non-adiabatic effects can be very strong in low dimensional systems. We also related universal non-adiabatic response to fidelity susceptibility and for the first time rigorously showed how universal results similar to Kibble-Zurek scaling emerge from the scaling dimension of the quench operator. Our findings are directly relevant to adiabatic quantum computation and dynamics of cold atoms. We also analyzed situations directly relevant to cold atom physics (like loading bosons into one-dimensional optical lattices) and predicted universal results, which can be measured in current experimental setups. Another major effort related to the proposal was developing phase space methods for quantum dynamics and applying these methods to cold atom systems. Other work included understanding phase diagram of strongly disordered bosons in one-dimension, verification of the instanton method to the decay of superfluid current in one-dimensional optical lattices, understanding of shot noise (which is different in nature from the Hanbury-Brown-Twiss effect and noise correlations) on the time of flight experiments in cold atoms, and understanding quench dynamics in low-dimensional models related to cold atoms (like sine-Gordon model).