Mathematics Colloquia and Seminars

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In quantum mechanics, the role of an observer is fundamentally different from that of a classical observer.  The quantum mechanical observer necessarily plays an active role in the dynamics of the system that it is observing.  This apparent difficulty may be turned into a tool to drive an initially trivial system into a complicated quantum many-body state simply by observing it.  I will present two remarkable examples of states induced by measurement. In the first, we examine the role of a moving density measuring device interacting with a system of fermions, and in particular, show that it would leave behind a wake of purely quantum origin. In the second example, inspired by topological Floquet insulators, we will see how a suitably chosen set of density measurements, repeated periodically, will induce robust chiral edge motion of fermions. These examples show how quantum mechanical observation can be added as a versatile tool to the arsenal of quantum engineering in condensed matter systems. In the last part of the talk I will explore special ratios of interaction and hopping in periodically applied hopping models and show how they give rise to interesting quasi solvable dynamics at certain Diophantine points and its stability to perturbations.