*
Dear Friends,
On Thursday, April 25, there will be an ITAMP topical lunch discussion.
Tea Room (P-226) @ CfA (60 Garden Street)
Time: 12:00-1:30
As always pizza will be served.
Speaker: Prof. Maxim Olshanii (University of Massachusetts Boston)
Title: Geometry of Quantum Observables, Integrability-Thermalizability
Transition, and Extended Thermodynamics of Integrable and/or Mesoscopic
Systems
Abstract:
The concept of ergodicity—convergence of the temporal averages of
observables to their ensemble averages—is the cornerstone of
thermodynamics. The transition from a predictable, integrable behavior to
ergodicity is one of the most difficult physical phenomena to treat; the
celebrated KAM theorem is the prime example. This preentation is founded on
an observation that for many classical and quantum observables, the sum of
the ensemble variance of the temporal average and the ensemble average of
temporal variance remains approximately constant across the
integrability-ergodicity transition. We show that this property induces a
particular geometry of quantum observables—Frobenius or Hilbert-Schmidt
one—that naturally encodes all the phenomena associated with the emergence
of ergodicity: the Eigenstate Thermalization effect, decrease in the
inverse participation ratio, and the disappearance of the integrals of
motion. As an application, we use this geometry to solve a known problem of
optimization of the set of integrals of motion needed to describe the
steady state of an integrable or near-integrable system.
Looking forward to seeing you there,
Misha Lemeshko*
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Dr. Mikhail Lemeshko
Institute for Theoretical Atomic, Molecular, and Optical Physics (ITAMP)
Harvard-Smithsonian Center for Astrophysics MS-14
60 Garden St.
Cambridge, MA 02138
U.S.A.
mlemeshko(a)cfa.harvard.edu
http://sites.google.com/site/mishalemeshko/
Tel. +1 (617) 496-7610
Fax +1 (617) 496-7668