Study of transport in the Harper model in the presence of thermal noise
Date
2022-01
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Benemérita Universidad Autónoma de Puebla
Abstract
"In this thesis we study quantum transport of the Harper model in the presence of thermal noise. The Harper model is paradigmatic model for quantum transport which presents a metal-insulator transition in one dimension. The Harper model represents a particle hopping in a one dimensional chain with a quasi-periodic potential. Throughout the thesis, different figures of merit for transport efficiency have been studied. Specifically, we analyzed the spreading of a wave packet initially localized at the center of the chain, we calculated the diffusion coefficient using the Green-Kubo expression and we have analyzed the steady-state current. A Lindblad master equation was used to model the interaction of the system with the environment. Here the environment is dominated by uncorrelated white noise, so the Haken-Strobl approximation was used to model the environment. The steady-state current was computed using different approaches: using a Master equation which includes pumping and draining from the first and the last site, using a Master equation to compute the Average Transfer Time, and finally, we found the current in terms of the diffusion coefficient using the Green-Kubo expression".
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