Session T9: Invited Session: Thermalization and Non-Equilibrium Dynamics in Isolated Quantum Systems

Non-Equilibrium Thermodynamic Relations in Driven Systems

In this talk I will review some recent results on non-equilibrium thermodynamic relations, which follow from combining unitary dynamics with the Eigenstate thermalization hypothesis. In particular, I will mention fluctuation theorems, general properties of energy and entropy production in driven systems (both open and thermally isolated), and fundamental limitations on efficiency of non-equilibrium heat engines.   

Quantum dynamics of a single, mobile spin impurity

Quantum magnetism describes the properties of many materials such as transition metal oxides and cuprate superconductors. One of its elementary processes is the propagation of spin excitations. Here we study the quantum dynamics of a deterministically created spin-impurity atom, as it propagates in a one-dimensional lattice system. We probe the full spatial probability distribution of the impurity at different times using single-site-resolved imaging of bosonic atoms in an optical lattice. In the Mott-insulating regime, a post-selection of the data allows to reduce the effect of temperature, giving access to a space- and time-resolved measurement of the quantum-coherent propagation of a magnetic excitation in the Heisenberg model. Extending the study to the bath's superfluid regime, we determine quantitatively how the bath strongly affects the motion of the impurity. The experimental data shows a remarkable agreement with theoretical predictions allowing us to determine the effect of temperature on the coherence and velocity of impurity motion. Our results pave the way for a new approach to study quantum magnetism, mobile impurities in quantum fluids, and polarons in lattice systems.   

Dynamics and description after relaxation of disordered quantum systems after a sudden quench

After a sudden quench, the dynamics and thermalization of isolated quantum systems are topics that have generated increasing attention in recent years. This is in part motivated be the desire of gaining a deeper understanding of how statistical behavior emerges out of the unitary evolution in isolated quantum systems and in part by novel experiments with ultracold gases. Several studies have found that while unitary dynamics in generic systems lead to thermal behavior of observables after relaxation, the same is not true for integrable systems. The latter need to be described using generalized ensembles, which take into account the existence of relevant sets of conserved quantities. In this talk, we discuss how delocalization-to-localization transitions in integrable and non-integrable disordered quantum systems change the picture above. We find that the relaxation dynamics, whenever relaxation takes place, is close to power law in those systems. In addition, statistical mechanics descriptions break down in the localized regimes. We discuss how this relates to the failure of eigenstate thermalization in the presence of localization.   

Conduction properties of strongly interacting Fermions

We experimentally study the transport process of ultracold fermionic atoms through a mesoscopic, quasi two-dimensional channel connecting macroscopic reservoirs. By observing the current response to a bias applied between the reservoirs, we directly access the resistance of the channel in a manner analogous to a solid state conduction measurement. The resistance is further controlled by a gate potential reducing the atomic density in the channel, like in a field effect transistor. In this setup, we study the flow of a strongly interacting Fermi gas, and observe a striking drop of resistance with increasing density in the channel, as expected at the onset of superfluidity. We relate the transport properties to the in-situ evolution of the thermodynamic potential, providing a model independant thermodynamic scale. The resistance is compared to that of an ideal Fermi gas in the same geometry, which shows an order of magnitude larger resistance, originating from the contact resistance between the channel and the reservoirs. The extension of this study to a channel containing a tunable disorder is briefly outlined.   

Analytical methods for studying quantum quenches in integrable models

I consider the non-equilibrium time evolution in integrable models after a quantum quench. For the case of a magnetic field quench in the transverse field Ising chain I present detailed results for the time evolution of local observables, which are shown to relax to a generalised Gibbs ensemble (GGE) [2] at late times. More generally, the reduced density matrix of a subsystem is shown to relax to a GGE in a power-law fashion in time. Dynamical response functions are studied as a function of the time after the quench and are shown to approach values given by the GGE as well. Finally generalizations to the sine-Gordon model [3] are discussed. \\[4pt] [1] P. Calabrese, F.H.L. Essler and M. Fagotti, Phys. Rev. Lett. 106, 227203 (2011); J. Stat. Mech. P07016 (2012); J. Stat. Mech. P07022 (2012);\\[0pt] [2] M. Rigol, V. Dunjko, V. Yurovsky, and M. Olshanii, Phys. Rev. Lett. 98, 50405 (2007); M. Rigol, V. Dunjko, and M. Olshanii, Nature 452, 854 (2008).\\[0pt] [3] D. Schuricht and F.H.L. Essler, in preparation.