Energy preserving evolutions over bosonic systems

Paul Gondolf 

In the talk we are going to investigate solutions of linear differential equations, beginning with the simplest cases and then building towards increasingly abstract notions. We will end with the concept of a semigroup on a Banach space. In physics, such differential equations and their solutions are of great importance with the most prominent example being the Schrödinger and a lesser known one the Lindblad equation. As the latter is suitable to describe the dynamics of an open quantum system it has gained some attention as a model for quantum devices susceptible to noise, e.g. a quantum computer. In contrast to a plethora of works tackling the finite-dimensional Lindblad, the infinite-dimensional setting is (mathematically) relatively unexplored. This is the point where my last project tried to close some gaps and I will end my talk by explaining the results we obtained.