Thermalization of Interacting Quasi-One-Dimensional Systems.

Many experimentally relevant systems are quasi-one-dimensional, consisting of nearly decoupled chains. In these systems, there is a natural separation of scales between the strong intrachain interactions and the weak interchain coupling. When the intrachain interactions are integrable, weak interchain couplings play a crucial part in thermalizing the system. Here, we develop a Boltzmann-equation formalism involving a collision integral that is asymptotically exact for any interacting integrable system, and apply it to develop a quantitative theory of relaxation in coupled Bose gases in the experimentally relevant Newton's cradle setup. We find that relaxation involves a broad spectrum of timescales. We provide evidence that the Markov process governing relaxation at late times is gapless; thus, the approach to equilibrium is generally nonexponential, even for spatially uniform perturbations.

Edge Singularities and Quasilong-Range Order in Nonequilibrium Steady States.

The singularities of the dynamical response function are one of the most remarkable effects in many-body interacting systems. However in one dimension these divergences only exist strictly at zero temperature, making their observation very difficult in most cold atomic experimental settings. Moreover the presence of a finite temperature destroys another feature of one-dimensional quantum liquids: the real space quasilong-range order in which the spatial correlation functions exhibit power-law decay. We consider a nonequilibrium protocol where two interacting Bose gases are prepared either at different temperatures or chemical potentials and then joined. We show that the nonequilibrium steady state emerging at large times around the junction displays edge singularities in the response function and quasilong-range order.

Metastable criticality and the super Tonks-Girardeau gas.

We consider a 1D Bose gas with attractive interactions in a highly excited state containing no bound states. We show that in this so-called super Tonks-Girardeau gas, relaxation processes are suppressed, making the system metastable over long time scales. We compute dynamical correlation functions, revealing the structure of excitations, an enhancement of umklapp correlations and new branches due to intermediate bound states. These features give a clear signature of the super Tonks-Girardeau regime and can be used to experimentally identify it. We demonstrate that, despite its off-equilibrium nature, the system displays critical behavior: correlation functions are characterized by asymptotic power-law decay described by the Luttinger liquid framework.