Various theoretical methods address transport effects in quantum dots beyond single-electron tunneling while accounting for the strong interactions in such systems. In this paper we report a detailed comparison between three prominent approaches to quantum transport: the fourth-order Bloch-Redfield quantum master equation ͑BR͒, the real-time diagrammatic technique ͑RT͒, and the scattering rate approach based on the T-matrix ͑TM͒. Central to the BR and RT is the generalized master equation for the reduced density matrix. We demonstrate the exact equivalence of these two techniques. By accounting for coherences ͑nondiagonal elements of the density matrix͒ between nonsecular states, we show how contributions to the transport kernels can be grouped in a physically meaningful way. This not only significantly reduces the numerical cost of evaluating the kernels but also yields expressions similar to those obtained in the TM approach, allowing for a detailed comparison. However, in the TM approach an ad hoc regularization procedure is required to cure spurious divergences in the expressions for the transition rates in the stationary ͑zero-frequency͒ limit. We show that these problems derive from incomplete cancellation of reducible contributions and do not occur in the BR and RT techniques, resulting in well-behaved expressions in the latter two cases. Additionally, we show that a standard regularization procedure of the TM rates employed in the literature does not correctly reproduce the BR and RT expressions. All the results apply to general quantum dot models and we present explicit rules for the simplified calculation of the zero-frequency kernels. Although we focus on fourth-order perturbation theory only, the results and implications generalize to higher orders. We illustrate our findings for the single impurity Anderson model with finite Coulomb interaction in a magnetic field.

We study the propagation of a density wave in a magnetically trapped Bose-Einstein condensate at finite temperatures. The thermal cloud is in the hydrodynamic regime and the system is therefore described by the two-fluid model. A phase-contrast imaging technique is used to image the cloud of atoms and allows us to observe small density excitations. The propagation of the density wave in the condensate is used to determine the speed of sound as a function of the temperature. We find the speed of sound to be in good agreement with calculations based on the Landau two-fluid model.

We observe the formation of shock waves in a Bose-Einstein condensate containing a large number of sodium atoms. The shock wave is initiated with a repulsive blue-detuned light barrier, intersecting the BoseEinstein condensate, after which two shock fronts appear. We observe breaking of these waves when the size of these waves approaches the healing length of the condensate. At this time, the wave front splits into two parts and clear fringes appear. The experiment is modeled using an effective one-dimensional Gross-Pitaevskiilike equation and gives excellent quantitative agreement with the experiment, even though matter waves with wavelengths two orders of magnitude smaller than the healing length are present. In these experiments, no significant heating or particle loss is observed.

We investigate linear and nonlinear transport in a double quantum dot system weakly coupled to spin-polarized leads. In the linear regime, the conductance as well as the nonequilibrium spin accumulation are evaluated in analytic form. The conductance as a function of the gate voltage exhibits four peaks of different height, with mirror symmetry with respect to the charge neutrality point. As the polarization angle is varied, due to exchange effects, the position and shape of the peaks change in a characteristic way which preserves the electron-hole symmetry of the problem. In the nonlinear regime various spin-blockade effects are observed. Moreover, negative differential conductance features occur for noncollinear magnetizations of the leads. In the considered sequential tunneling limit, the tunneling magnetoresistance (TMR) is always positive with a characteristic gate voltage dependence for noncollinear magnetization. If a magnetic field is added to the system, the TMR can become negative.

Phase contrast imaging is used to observe Bose-Einstein condensates at finite temperature in situ. The imaging technique is used to accurately derive the absolute phase shift of a probe laser beam due to both the condensate and the thermal cloud. The accuracy of the method is enhanced by using the periodicity of the intensity signal as a function of the accumulated phase. The measured density profiles can be described using a two-relevant-parameter fit, in which only the chemical potential and the temperature are to be determined. This allows us to directly compare the measured density profiles to different mean-field models in which the interaction between the condensed and the thermal atoms is taken into account to various degrees.