Collective quantum dynamics: from information scrambling to emergent hydrodynamics (Prof. M. Knap)
14:30 - 15:30
Prof. Dr. Michael Knap
Herbert Walther Lecture Hall
Generic, clean quantum many-body systems approach a thermal equilibrium after a long time evolution. In order to reach a global equilibrium, conserved quantities have to be transported across the whole system which is a rather slow process governed by diffusion.
By contrast, the scrambling of quantum information is ballistic and hence
can be characterized by a "butterfly" velocity. One way of
characterizing the propagation of quantum information is to study out-of-time
ordered (OTO) correlation functions, which are unconventional correlation
functions with time arguments that are not ordered from early to late times.
Using matrix-product-operator based numerical simulations, we compute both
time-ordered and OTO correlators at high temperatures in a one-dimensional
Bose-Hubbard model, where well defined quasi-particles cease to exist. For the
time-ordered correlators of conserved quantities, we demonstrate an emergent
hydrodynamic description at late times and compute the associated diffusion
constant. Unconventional OTO correlators exhibit by contrast the fast ballistic
information propagation, even in the high temperature regime. Furthermore, we
discuss how these fundamental properties of nonequilibrium quantum dynamics can
be characterized in experiments.