# Condensed Matter Physics Seminar

*Speaker:*
Sergey Syzranov, University of California at Santa Cruz
(currently at the University of Maryland)

*Title:* Quantum information scrambling and out-of-time-order correlators in finite open systems

*Refreshments available at 3:45 pm.*

*Date:* Mon, 11 Sep 2017, 4:10 pm – 5:10 pm

*Type:* Seminar

*Location:* 1400 BPS Bldg.

*Abstract:*

Quantum information scrambling and out-of-time-order correlators in
finite open systems
Quantum information scrambling and chaotic behaviour in quantum systems are characterised by fourpoint
out-of-time-order correlators (OTOCs) of the form <A(t)B(0)C(t)D(0)>, where A, B, C and D
are local Hermitian operators. Such quantities are also expected to distinguish between many-bodylocalised
and many-body-delocalised phases of disordered interacting systems. This talk is devoted to
OTOCs in an open quantum system weakly coupled to a dissipative environment. Such an open
system may serve as a model of, *e.g.*, a small region (“localisation cell”) in a disordered interacting
medium coupled to the rest of this medium considered as an environment. I will demonstrate that for a
system with discrete energy levels the OTOC saturates exponentially to a constant value at large times
t, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing
on the case of a two-level system, we calculate microscopically the characteristic times of the
saturation and the value of the saturation constant. Because some OTOCs are immune to dephasing
processes and some are not, such correlators may decay on two sets of parametrically different time
scales related to inelastic transitions between the system levels and to pure dephasing processes,
respectively. In the case of a classical environment, the evolution of OTOCs can be mapped onto the
evolution of the density matrix of two systems coupled to the same dissipative environment, which
allows for explicit experimental measurements of OTOCs.