Lecturer: Dr. Yevgeny Bar Lev
Affiliation: Columbia University
Abstract:
Remarkably, a generic interacting system
with many degrees of freedom is often
well described by a random matrix drawn
from an appropriate ensemble, which
solely relies on the symmetries of the
system. This is one of the central
premises of quantum chaos theory which
explains the fascinating universality of
statistical properties of eigenvalues and
eigenstates of generic systems. Such
systems, slightly pushed out-of-
equilibrium, are normally expected to
relax diffusively. In this talk I will show
that disordered and interacting systems
which exhibit a many-body localization
(MBL) transition, behave in a strikingly
different manner than expected from the
above tenets in both one dimensional
[1,2] and two dimensional systems [3].
These systems thermalize sub diffusively,
have a vanishing diffusion coefficient and
cannot be described by usual random
matrix ensembles [4]. I will show the
implications of these results on
thermalization in closed quantum
systems, and will derive a general relation
between statistical properties of matrix
elements of physical observables and a
dynamical property of the system [4]. I
will finish my talk by presenting some
promising future directions [5].
References:
[1] Bar Lev and Reichman, Phys.
Rev. B 89, 220201(R) (2014).
[2] Bar Lev, Cohen and
Reichman, Phys. Rev. Lett. 114,
100601 (2015).
[3] Bar Lev and Reichman, EPL 113,
46001 (2016).
[4] Luitz and Bar Lev, Phys. Rev. Lett.
117, 170404 (2016).
[5] Luitz and Bar Lev, Ann.
Phys. arXiv:1610.08993 (invited
review, 2016).