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%*********************************** Fifth Chapter *****************************
\chapter{Density Measurement Induced Dynamics}
% Title of the Fifth Chapter
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\section{Introduction}
In the previous chapter we have introduced a theoretical framework
which will allow us to study measurement backaction using
discontinuous quantum jumps and non-Hermitian evolution due to null
outcomes. We have also wrapped our quantum gas model in this quantum
trajectory formalism by considering ultracold bosons in an optical
lattice coupled to a cavity which collects and enhances light
scattered in one particular direction. One of the most important
conclusions of the previous chapter was that the introduction of
measurement introduces a new energy and time scale into the picture.
In this chapter, we investigate the effect of quantum measurement
backaction on the many-body state of atoms.
\section{Large-Scale Dynamics due to Weak Measurement}
\section{Three-Way Competition}
\section{Emergent Long-Range Correlated Tunnelling}
\section{Non-Hermitian Dynamics in the Quantum Zeno Limit}
\section{Steady-State of the Non-Hermitian Hamiltonian}
\section{Conclusions}
