Analysis Seminar: Maciej Zworski (Berkeley)

Speaker: Maciej Zworski (Berkeley)

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

Abstract: 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 and methods 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.