Thesis of Vincent Vuatelet

Thèse de Vincent Vuatelet - laboratoire Phlam

Abstract : 

The Kicked Rotor, paradigm of quantum chaos, is the analog in momentum space of a disordered Anderson system, due to the fact that the system displays the phenomenon of so-called dynamic localization. We study the effect of interactions on dynamical localization in a strongly interacting Bose gas, called the Tonks-Girardeau gas. Exploiting this limit and the Bose-Fermi mapping, we study the physics of a Tonks-Girardeau gas kicked through the reduce one-body density matrix of the system. We find similarity of the system with a Bose gas at finite temperature, we characterize the observables of the system, in particular its energy, its momentum distribution, and the correlations. We relate the emerging effective temperature to the localization characteristics of the system, being in a dynamically localized N-body phase. We also present a characterization of the quasi-periodic version of the Kicked Rotor, analog of a three-dimensional Anderson system, marked by a phase transition between a localized and diffusive regime. We finally analyze the momentum distribution at the critical threshold, and characterize its behavior in its center, at small and large momenta, marked by three different scalings.

Keywords : Condensed Matter,Quantum Chaos,Kicked rotor