The question in the title will provide an excuse to introduce Lindblad/GKSL propagation which describes the evolution of a small system coupled to a larger environment. This evolution is central in physics and, more recently, in quantum computing yet it is practically unknown to PDE specialists (including the speaker, until about two years ago). 

 

One reason that the Lindblad evolution is of interest is that, as recently revisited in physics by Hernández--Ranard--Riedel, it provides a model for the longtime persistence of classical/quantum correspondence.  Furthermore, it provides a way to understand the question of finding quantum Gibbs samplers in quantum computing. We will address a simple version of this problem for pseudodifferential operators following recent finite dimensional advances by Chen--Kastoryano--Gilyen.

 

The talk is based on joint work with Jeff Galkowski, with numerics provided by Zhen Huang, and on recent advances by Zhenhao Li and Hart Smith.