Emil
Yuzbashyan

Center for Materials Theory

Rutgers,
Physics and Astronomy

**Quantum
integrability in systems with finite number of energy
levels**

Since the discovery
of quantum mechanics, from the Bohr atom and the harmonic
oscillator, to the present day, quantum integrable models
have played a central role in our understanding of physics at
the quantum level. Recently, the field has acquired a
new prominence with a range of solid state and cold atom
experiments which demonstrate that integrable systems fail to
equilibrate, and thereby defy a conventional statistical
description. Roughly speaking, a quantum integrable system is
one whose quantum Hamiltonian contains additional integrals of
motion beyond the usual total energy and momenta. Yet a
complete, unambiguous notion of quantum integrability has long
remained elusive, and our understanding of its nonequilibrium
and other manifestations is correspondingly incomplete. In the
opposite case of chaotic systems, Random Matrix Theory
famously provides a tremendously successful analysis of their
universal properties. In this talk, I will propose a
surprisingly simple and yet unambiguous notion of
quantum integrability which leads to a clear explanation and
delineation of its various features, culminating in Integrable
Matrix Theory: a counterpart of Random Matrix Theory for
integrable quantum Hamiltonians.

*Coffee and Tea at 4:30 p.m.*