Abstract
Progress in quantum technologies have renewed interests in open quantum manybody systems, where effects of environmental coupling can be significant. In particular, dephasing can cause a system to lose coherence and has been implemented very recently, in a controlled manner, in ultracold atoms and optical lattices set-up. This thesis aims to understand the effects of dephasing on the dynamics of 1-D interacting bosons, where the interplay between interactions and dissipation can result in novel phenomena. By use of a number-conserving time-dependent matrix product state algorithm, moderately large system sizes were studied. The first work looks at the propagation of correlations in a 1-D bosonic lattice, under the effects of dephasing. Dephasing is found to affect single-particle and densitydensity correlations differently. A quasi-particle picture of doublons and holons was developed to further understand the effect of the dissipation on the propagation of correlations. The superfluid ground state of 1-D bosons, with nearest-neighbour interactions, can be well-described by the universal description of Luttinger liquids. The evolutions of the density profiles and density-density correlations is found to retain Luttinger-like behaviour during the heating process. This strongly indicates universality in the nonequilibrium dynamics. Lastly, the dynamics of density fluctuations in a double well of strongly interacting bosons, coupled to finite temperature baths via dephasing, is studied. It is found that the power-law regimes, as observed in the infinite temperature limit, persist with finitetemperature baths. The period and exponent of algebraic behaviour is dependent on the bath’s temperatures and cut-off frequencies, showing that one can gain insights to the properties of structured baths, by looking at the heating dynamics.