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Claude Cohen Tannoudji

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Accueil du site > Archives > Visite de Maxim Olshanii (University of Massachusetts, Boston)

Visite de Maxim Olshanii (University of Massachusetts, Boston)

Maxim Olshanii, en visite au LPL, donnera une série de trois cours

Le premier cours aura lieu le 17 mai 2011 à 11h en salle de conférence D102. Deux autres cours suivront fin mai et début juin.

voir aussi

Talk 1 [« big picture », the one I gave at Harvard-MIT]

« Roaming the (integrable-chaotic)x(classical-quantum) Plane Using Cold Atoms : Eigenstate Thermalization, Generalized Gibbs Ensemble, Quantum Anomalies, and Other Stories »

Abstract : In this presentation, I will show where several recent projects in our group are situated on the vast [(integrable-chaotic)x(classical-quantum)] two-dimensional plane of dynamical systems of interest. I will start from our work demonstrating that the Eigenstate Thermalization effect of Deutsch-Srednicki qualifies as the origin of irreversibility in (otherwise disctrete-spectrum, linear) Quantum Mechanics [1].

I will next present our suggestion for a conceptually and computationally simple thermodynamic ensemble that describes the outcome of the time evolution of a completely integrable quantum system [2].

We will briefly discuss the integrability breaking in the mean-field Bose-Hubbard model [3], and in two systems of waveguide-confined bosons : three transversally cold [4] and two transversally hot [5] atoms respectively ; the related universalities in the disappearance of the integrals of motion in quantum systems with no selection rules---Anderson model in particular---will be mentioned.

Next, we will look at the connection between the Quantum-Mechanical Supersymmetry (QM-SUSY) and both the solitons in the sine-Gordon and Nonlinear Schodinger equations [6] and scattering solutions of the Bogoliubov-de-Gennes equations for a one-dimensional attractive BEC.

Finally, I will discuss the breaking, under quantization, of the classical Pitaevkii-Rosch dynamical symmetry in a two-dimensional harmonically trapped Bose gas [7].

[1] Nature, 452, 854 (2008)
[2] PRL 98, 050405 (2007)
[3] PRL 102, 025302 (2009)
[4] PRL 96, 163201 (2006)
[5] PRL 106, 025303 (2011)
[6] arXiv:1012.2843 (2010)
[7] PRL 105, 095302 (2010)

In collaboration with : Marcos Rigol, Vladimir Yurovsky, Amy Cassidy, Andrew Koller, Kurt Jacobs, Helene Perrin, Vincent Lorent, Abraham Ben-Reuven, Vanja Dunjko, Douglas Mason, Yassine Ait El Aoud, Cavan Stone, and Harry Kennard

Talk 2 [our work on anomaly, with lots of new results on the algebraic origins of our symmetry]

« An example of a quantum anomaly in physics of cold atomic gases »

In this presentation, we show that for the a two-dimensional harmonically trapped Bose gas, the Pitaevskii-Rosch dynamical symmetry becomes weakly broken under quantization. The very same symmetry remains intact for the unitary three-dimensional gases.

We interpret this effect as a quantum-mechanical symmetry breaking---otherwise known as quantum anomaly---, give a detailed quantitative analysis of its empirical manifestations, and suggest a detailed experimental scheme for its detection.

In collaboration with Hélène Perrin and Vincent Lorent (Université Paris-Nord, France)

Talk 3 [attempt for quantum KAM]

« A Simple Exactly Solavable Model for Quantum Nonequilibrium Dynamics »

Abstract :

In this talk, we will present a simple exactly solvablemodel 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

Voir en ligne : http://www-lpl.univ-paris13.fr:8083/

Post-scriptum :

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