Investigating the Validity of Quantum Master Equations

Abstract

From well-established subjects like electronics to modern subjects like quantum technology, every field dealing with the physics of nanoscale uses the formalism of open quantum systems. The master equation formalism is one of the most widely used approaches in studying open quantum systems. In this approach, the dynamics of the reduced density matrix of the system is governed by an integro-differential equation called the master equation. There are multiple approximations---Born, Markov and Secular approximations---that go into deriving a master equation. This thesis aims to provide a thorough analysis of these approximations and improve the understanding of the regime(s) of validity master equations. We do this by studying a model system using both the Markovian and the Non-Markovian versions of the master equation within the Born approximation. We then compare these results with exact results obtained by using the Langevin equation approach, which is an exact approach.