Why is our world classical despite being governed by quantum mechanics?

This question has been much discussed in physics and one suggestion is that the
long time persistence of classical/quantum correspondence is due to interaction of a
small, observed system with a larger environment. Lindblad or GKSL evolution is one of the
standard models for describing such interactions. In that context the question of the
length of time of classical/quantum agreement was recently revisited in physics by
Hernández-Ranard-Riedel.

In my talk I will introduce the concept of Lindblad evolution and present results showing
that the evolution of a quantum observable remains close to the classical Fokker-Planck
evolution in the Hilbert-Schmidt norm for times vastly exceeding the Ehrenfest time (the
limit of such an agreement when there is no interaction with a larger system). The time
scale is the same as in two recent papers by Hernández-Ranard-Riedel but the statement
andmethods are different. The talk is based on joint work with J Galkowski and numerical
results obtained jointly with Z Huang. I will also comment on recent progress on trace
class estimates by Z Li and on the hypoelliptic case by H Smith.