General rightsIt is not permitted to download or to forward/distribute the text or part of it without the consent of the author(s) and/or copyright holder(s), other than for strictly personal, individual use, unless the work is under an open content license (like Creative Commons). Disclaimer/Complaints regulationsIf you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library: http://uba.uva.nl/en/contact, or a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible. The nonequilibrium dynamics of integrable systems are highly constrained by the conservation of certain charges. There is substantial evidence that after a quantum quench they do not thermalize but their asymptotic steady state can be described by a generalized Gibbs ensemble (GGE) built from the conserved charges. Most of the studies on the GGE so far have focused on models that can be mapped to quadratic systems, while analytic treatment in nonquadratic systems remained elusive. We obtain results on interaction quenches in a nonquadratic continuum system, the one-dimensional (1D) Bose gas described by the integrable Lieb-Liniger model. The direct implementation of the GGE prescription is prohibited by the divergence of the conserved charges, which we conjecture to be endemic to any continuum integrable systems with contact interactions undergoing a sudden quench. We compute local correlators for a noninteracting initial state and arbitrary final interactions as well as two-point functions for quenches to the Tonks-Girardeau regime. We show that in the long time limit integrability leads to significant deviations from the predictions of the grand canonical ensemble, allowing for an experimental verification in cold-atom systems.

We consider the interplay of disorder and interactions upon the gapless surface states of 3D topological superconductors. The combination of topology and superconducting order inverts the action of time-reversal symmetry, so that extrinsic time-reversal invariant surface perturbations appear only as "pseudomagnetic" fields (Abelian and non-Abelian vector potentials, which couple to spin and valley currents). The main effect of disorder is to induce multifractal scaling in surface state wave functions. These critically delocalized, yet strongly inhomogeneous states renormalize interaction matrix elements relative to the clean system. We compute the enhancement or suppression of interaction scaling dimensions due to the disorder exactly, using conformal field theory. We determine the conditions under which interactions remain irrelevant in the presence of disorder for symmetry classes AIII and DIII. In the limit of large topological winding numbers (many surface valleys), we show that the effective field theory takes the form of a Finkel'stein nonlinear sigma model, augmented by the Wess-Zumino-Novikov-Witten term. The sigma model incorporates interaction effects to all orders and provides a framework for a controlled perturbative expansion; the inverse spin or thermal conductance is the small parameter. For class DIII, we show that interactions are always irrelevant, while in class AIII, there is a finite window of stability, controlled by the disorder. Outside of this window, we identify new interaction-stabilized fixed points.

We derive an exact analytic expression for the three-body local correlations in the Lieb-Liniger model of 1D Bose gas with contact repulsion. The local three-body correlations control the thermalization and particle loss rates in the presence of terms which break integrability, as is realized in the case of 1D ultracold bosons. Our result is valid not only at finite temperature but also for a large class of nonthermal excited states in the thermodynamic limit. We present finite temperature calculations in the presence of external harmonic confinement within local density approximation, and for a highly excited state that resembles an experimentally realized configuration.

We study the preparation (pump) and the detection (probe) of far-from-equilibrium BCS superconductor dynamics in THz pump-probe experiments. In a recent experiment [R. Matsunaga, Y. I. Hamada, K. Makise, Y. Uzawa, H. Terai, Z. Wang, and R. Shimano, Phys. Rev. Lett. 111, 057002 (2013)], an intense monocycle THz pulse with center frequency ω ≃ ∆ was injected into a superconductor with BCS gap ∆; the subsequent post-pump evolution was detected via the optical conductivity. It was argued that nonlinear coupling of the pump to the Anderson pseudospins of the superconductor induces coherent dynamics of the Higgs (amplitude) mode ∆(t). We validate this picture in a two-dimensional BCS model with a combination of exact numerics and the Lax reduction method, and we compute the nonequilibrium phase diagram as a function of the pump intensity. The main effect of the pump is to scramble the orientations of Anderson pseudospins along the Fermi surface by twisting them in the xy-plane. We show that more intense pump pulses can induce a far-from-equilibrium phase of gapless superconductivity ("phase I"), originally predicted in the context of interaction quenches in ultracold atoms. We show that the THz pump method can reach phase I at much lower energy densities than an interaction quench, and we demonstrate that Lax reduction (tied to the integrability of the BCS Hamiltonian) provides a general quantitative tool for computing coherent BCS dynamics. We also calculate the Mattis-Bardeen optical conductivity for the nonequilibrium states discussed here.