Impact of dephasing probes on various incommensurate lattice models

Abstract

This thesis aims to study quantum transport and quantum dynamics properties in one dimensional quasi-periodic lattice systems. In particular we aim here to understand the impact of external probes on both the steady state and in transient. We therefore focus on two different setups: (i) a quasi-periodic lattice subjected to a chemical potential difference at its two end that drives current through the lattice and hence in a non-equilibrium steady state. We then perturb the system by a single dephasing probe and analyze the steady state transport properties. (ii) In another setup we consider a quasi-periodic lattice which is initially filled with a certain number of electrons at the central part of the lattice and is further subjected to dephasing probes at the filled sites. We then investigate the dynamics of the electron density and the scaling of the density front under two distinct scenarios: (a) when the number of probes connected to the lattice chain is of the same order as the number of filled electrons and (b) when the number of probes scales as root N