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Claude Cohen Tannoudji

Prix Nobel en 1997 pour le ralentissement et le piégeage des atomes par la lumière laser.

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Accueil du site > Séminaires > LKB > A Simple Exactly Solvable Model for Quantum Nonequilibrium Dynamics

A Simple Exactly Solvable Model for Quantum Nonequilibrium Dynamics

Séminaire de Maxim Olshanii (University of Massachusetts Boston)

Vendredi 20 mai 2011 à 9h15 dans la salle de réunion du siege de l’IFRAF, au 4e étage du batiment Rataud, à l’ENS 45 rue d’Ulm 75005 Paris.

Résumé :

In this talk, we will present a simple exactly solvable model that describes an integrable system perturbed by a non-integrable perturbation. The range of applications for the model is limited to the situations where the perturbation obeys no selection rules, e.g. a collection of impurities (including a single impurity) perturbing a regular lattice.

In addition to a conventional random matrix description for the perturbation, the model also contains a new element : an ensemble of random permutations of the eigenstates across a window in the spectrum of the integrable part of the Hamiltonian.

For a lattice with impurities, the model accurately describes the decay of the memory of the initial deviation from the equipartition of energy as the strength of the non-integrable perturbation increases ; the full range of regimes is covered, from the integrable point through the fully developed quantum chaos. Generally, the model predicts that the memory of the initial conditions in systems with no selection rules is universally governed by a single parameter---one of the inverse participation ratios---for all functions of the integrals of motion as observables and for all initial conditions. In a related development, we apply our results to study the transverse vs longitudinal energy equipartition for two atoms in a transversally hot atom waveguide

[Vladimir Yurovsky & Maxim Olshanii, Phys. Rev. Lett. 106, 025303 (2011)].

In collaboration with : Vladimir Yurovsky, Marcos Rigol, Kurt Jacobs, Vanja Dunjko, Harry Kennard.


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