Quantum Transport in 1D and Quasi-1D Lattice Systems

Abstract

This thesis aims to study quantum transport in one-dimensional and quasi one-dimensional lattice systems. The first part deals with non-interacting fermions showing long-range power-law decaying hopping on an open one-dimensional lattice subjected to dephasing noise. Firstly, the steady-state transport driven by boundary baths has been explored by finding the scaling of current with system size. Subsequently, time dynamics is studied by investigating wave-packet spreading. Both of these help to classify transport in the system. Universal super-diffusive transport is observed in the numerical simulations. Analytical calculations support the results obtained. The next part of the thesis deals with ladder set-ups, which are quasi one-dimensional systems. Fermionic transport has been studied in primarily two set-ups: (i) symmetric hopping in the ladder in the presence of a gauge field and (ii) asymmetric hopping in the two legs of the ladder. Transfer matrices and their exceptional points have been studied owing to their connection with transport, and previously known relations in one dimension are generalized to a ladder set-up. A transport-based phase diagram with the phase boundaries corresponding to the exceptional points has been obtained.