Nonequilibrium dynamical mean-field calculations based on the non-crossing approximation and its generalizations

We solve the impurity problem which arises within nonequilibrium dynamical mean-field theory for the Hubbard model by means of a self-consistent perturbation expansion around the atomic limit. While the lowest order, known as the non-crossing approximation (NCA), is reliable only when the interaction U is much larger than the bandwidth, low-order corrections to the NCA turn out to be sufficient to reproduce numerically exact Monte Carlo results in a wide parameter range that covers the insulating phase and the metal-insulator crossover regime at not too low temperatures. As an application of the perturbative strong-coupling impurity solver we investigate the response of the double occupancy in the Mott insulating phase of the Hubbard model to a dynamical change of the interaction or the hopping, a technique which has been used as a probe of the Mott insulating state in ultracold fermionic gases.Comment: 14 pages, 9 figure

Measuring correlated electron dynamics with time-resolved photoemission spectroscopy

Time-resolved photoemission experiments can reveal fascinating quantum dynamics of correlated electrons. However, the thermalization of the electronic system is typically so fast that very short probe pulses are necessary to resolve the time evolution of the quantum state, and this leads to poor energy resolution due to the energy-time uncertainty relation. Although the photoemission intensity can be calculated from the nonequilibrium electronic Green functions, the converse procedure is therefore difficult. We analyze a hypothetical time-resolved photoemission experiment on a correlated electronic system, described by the Falicov-Kimball model in dynamical mean-field theory, which relaxes between metallic and insulating phases. We find that the real-time Green function which describes the transient behavior during the buildup of the metallic state cannot be determined directly from the photoemission signal. On the other hand, the characteristic collapse-and-revival oscillations of an excited Mott insulator can be observed as oscillating weight in the center of the Mott gap in the time-dependent photoemission spectrum.Comment: 12 pages, 5 figure

Reduced leakage current in Josephson tunnel junctions with codeposited barriers

Josephson junctions were fabricated using two different methods of barrier formation. The trilayers employed were Nb/Al-AlOx/Nb on sapphire, where the first two layers were epitaxial. The oxide barrier was formed either by exposing the Al surface to O2 or by codepositing Al in an O2 background. The codeposition process yielded junctions that showed the theoretically predicted subgap current and no measurable shunt conductance. In contrast, devices with barriers formed by thermal oxidation showed a small shunt conductance in addition to the predicted subgap current.Comment: 3 pages, 4 figure

Broken particle-hole symmetry at atomically flat a-axis YBa2Cu3O7-d interfaces

We have studied quasiparticle tunneling into atomically flat a-axis films of YBa2Cu3O7-d and DyBa2Cu3O7-d through epitaxial CaTiO3 barriers. The junction heterostructures were grown by oxide molecular beam epitaxy and were carefully optimized using in-situ monitoring techniques, resulting in unprecedented crystalline perfection of the superconductor/insulator interface. Below Tc, the tunneling conductance shows the evolution of a large unexpected asymmetrical feature near zero bias. This is evidence that superconducting YBCO crystals, atomically truncated along the lobe direction with a titanate layer, have intrinsically broken particle-hole symmetry over macroscopically large areas.Comment: 15 pages, 4 figures; v2 includes minor changes in concluding paragraph to match PRL versio

Crossover from adiabatic to sudden interaction quenches in the Hubbard model: Prethermalization and nonequilibrium dynamics

The recent experimental implementation of condensed matter models in optical lattices has motivated research on their nonequilibrium behavior. Predictions on the dynamics of superconductors following a sudden quench of the pairing interaction have been made based on the effective BCS Hamiltonian; however, their experimental verification requires the preparation of a suitable excited state of the Hubbard model along a twofold constraint: (i) a sufficiently nonadiabatic ramping scheme is essential to excite the nonequilibrium dynamics, and (ii) overheating beyond the critical temperature of superconductivity must be avoided. For commonly discussed interaction ramps there is no clear separation of the corresponding energy scales. Here we show that the matching of both conditions is simplified by the intrinsic relaxation behavior of ultracold fermionic systems: For the particular example of a linear ramp we examine the transient regime of prethermalization [M. Moeckel and S. Kehrein, Phys. Rev. Lett. 100, 175702 (2008)] under the crossover from sudden to adiabatic switching using Keldysh perturbation theory. A real-time analysis of the momentum distribution exhibits a temporal separation of an early energy relaxation and its later thermalization by scattering events. For long but finite ramping times this separation can be large. In the prethermalization regime the momentum distribution resembles a zero temperature Fermi liquid as the energy inserted by the ramp remains located in high energy modes. Thus ultracold fermions prove robust to heating which simplifies the observation of nonequilibrium BCS dynamics in optical lattices.Comment: 27 pages, 8 figures Second version with small modifications in section

Vanishing of phase coherence in underdoped Bi_2Sr_2CaCu_2O_8+d

Coherent time-domain spectroscopy is used to measure the screening and dissipation of high-frequency electromagnetic fields in a set of underdoped Bi_2Sr_2CaCu_2O_8+d thin films. The measurements provide direct evidence for a phase-fluctuation driven transition from the superconductor to normal state, with dynamics described well by the Berezinskii-Kosterlitz-Thouless theory of vortex-pair unbinding.Comment: Nature, Vol. 398, 18 March 1999, pg. 221 4 pages with 4 included figure

Dynamical Mean-Field Theory

The dynamical mean-field theory (DMFT) is a widely applicable approximation scheme for the investigation of correlated quantum many-particle systems on a lattice, e.g., electrons in solids and cold atoms in optical lattices. In particular, the combination of the DMFT with conventional methods for the calculation of electronic band structures has led to a powerful numerical approach which allows one to explore the properties of correlated materials. In this introductory article we discuss the foundations of the DMFT, derive the underlying self-consistency equations, and present several applications which have provided important insights into the properties of correlated matter.Comment: Chapter in "Theoretical Methods for Strongly Correlated Systems", edited by A. Avella and F. Mancini, Springer (2011), 31 pages, 5 figure

Anomalous superconducting state gap size versus Tc behavior in underdoped Bi_2Sr_2Ca_1-xDy_xCu_2O_8+d

We report angle-resolved photoemission spectroscopy measurements of the excitation gap in underdoped superconducting thin films of Bi_2Sr_2Ca_{1-x}Dy_xCu_2O_{8+d}. As Tc is reduced by a factor of 2 by underdoping, the superconducting state gap \Delta does not fall proportionally, but instead stays constant or increases slightly, in violation of the BCS mean-field theory result. The different doping dependences of \Delta and kT_c indicate that they represent different energy scales. The measurements also show that \Delta is highly anisotropic and consistent with a d_{x^2-y^2} order parameter, as in previous studies of samples with higher dopings. However, in these underdoped samples, the anisotropic gap persists well above T_c. The existence of a normal state gap is related to the failure of \Delta to scale with T_c in theoretical models that predict pairing without phase coherence above T_c.Comment: 10 pages, 4 postscript figures, revtex forma

HIPAD - A Hybrid Interior-Point Alternating Direction algorithm for knowledge-based SVM and feature selection

We consider classification tasks in the regime of scarce labeled training data in high dimensional feature space, where specific expert knowledge is also available. We propose a new hybrid optimization algorithm that solves the elastic-net support vector machine (SVM) through an alternating direction method of multipliers in the first phase, followed by an interior-point method for the classical SVM in the second phase. Both SVM formulations are adapted to knowledge incorporation. Our proposed algorithm addresses the challenges of automatic feature selection, high optimization accuracy, and algorithmic flexibility for taking advantage of prior knowledge. We demonstrate the effectiveness and efficiency of our algorithm and compare it with existing methods on a collection of synthetic and real-world data.Comment: Proceedings of 8th Learning and Intelligent OptimizatioN (LION8) Conference, 201