EXACT STUDIES OF EQUILIBRIUM AND NONEQUILIBRIUM PROPERTIES OF CORRELATED BOSONS IN ONE-DIMENSIONAL LATTICES

In this thesis, we study both equilibrium and nonequilibrium properties of hard-core bosons trapped in one-dimensional lattices. To perform many-body analyses of large systems, we utilize exact numerical approaches in-cluding an approach based on the Bose-Fermi mapping and the Lanczos method. We study noise correlations of hard-core bosons in homogeneous lattices, period-two superlattices, and disordered lattices, and focus on the scaling of such correlations with system size in the superfluid and insulat-ing phases. We find that superfluid phases exhibit a leading linear scaling, while the leading terms in the scaling of the Mott-insulting and Bose-glass phases are constants. We also characterize the disorder-induced phase tran-sition between a superfluid and a Bose-glass phase in an incommensurate lattice system by determining the critical exponents in the scaling of the momentum distribution and the noise correlations. We show that the phase transition is signaled by peaks in the first derivatives of the noise correla