Speaker
Lara Faoro
Description
In a chaotic classical system a small perturbation leads to the
exponential divergence of trajectories characterized by
Lyapunov time. As a result, the observables in two copies of
the system experiencing different perturbations quickly
become uncorrelated. In a many body system a local
perturbation initially destroys the correlations locally, then
the region where the correlations are destroyed quickly grows
with time. This phenomena is known as butterfly effect. The
concept of butterfly effect can be generalized to a closed
chaotic quantum system even though such generic system
does not necessarily have a direct analogue of Lyapunov
divergence of trajectories because quantum mechanics
prohibits the infinitesimal shift of the trajectory. The
convenient measure of the butterfly effect is provided by the
out-of-time-order correlator (OTOC) . In this work, we extend
the Keldysh technique to enable the computation of OTOC.
We show that the behavior of these correlators is described
by equations that display initially an exponential instability
which is followed by a linear propagation of the decoherence
between two initially identically copies of the quantum many
body systems with interactions. At large times the
decoherence propagation (quantum butterfly effect) is
described by a diffusion equation with non-linear dissipation
known in the theory of combustion waves. The solution of
this equation is a propagating non-linear wave moving with
constant velocity despite the diffusive character of the
underlying dynamics. Our general conclusions are illustrated
by the detailed computations for the specific models
describing the electrons interacting with bosonic degrees of
freedom (phonons, two-level-systems etc.) or with each
other.
