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Relaxation dynamics and thermalization in isolated quantum systems

### Marcos Rigol

**Wednesday, 7 December 2011, 13:30**

Matfys library

**Abstract**:

Little more than fifty years ago, Fermi, Pasta, and Ulam set up a
numerical experiment to prove the ergodic hypothesis for a one-dimensional
lattice of harmonic oscillators when nonlinear couplings were added. Much to
their surprise, the system exhibited long-time periodic dynamics with no
signals of ergodic behavior. Those results motivated intense research, which
ultimately gave rise to the modern chaos theory and to a better understanding
of the basic principles of classical statistical mechanics. More recently,
experiments with ultracold gases in one-dimensional geometries have
challenged our understanding of the quantum domain. After bringing a nearly
isolated system out of equilibrium, no signals of relaxation to the expected
thermal equilibrium distribution were observed. Some of those results can be
understood in the framework of integrable quantum systems, but then it
remains the question of why thermalization did not occur even when the system
was supposed to be far from integrability. In the latter regime,
thermalization is expected to occur and can be understood on the basis of the
eigenstate thermalization hypothesis. In this talk, we discuss some of the early
theoretical and experimental results on this topic. We then show how
thermalization breaks down in finite one-dimensional quantum systems
as one approaches an integrable point. We establish a direct connection
between the presence or absence of thermalization and the validity or
failure of the eigenstate thermalization hypothesis, respectively.