Superconductivity in the attractive Hubbard model: functional renormalization group analysis

We present a functional renormalization group analysis of superconductivity in the ground state of the attractive Hubbard model on a square lattice. Spontaneous symmetry breaking is treated in a purely fermionic setting via anomalous propagators and anomalous effective interactions. In addition to the anomalous interactions arising already in the reduced BCS model, effective interactions with three incoming legs and one outgoing leg (and vice versa) occur. We accomplish their integration into the usual diagrammatic formalism by introducing a Nambu matrix for the effective interactions. From a random-phase approximation generalized through use of this matrix we conclude that the impact of the 3+1 effective interactions is limited, especially considering the effective interactions important for the determination of the order parameter. The exact hierarchy of flow equations for one-particle irreducible vertex functions is truncated on the two-particle level, with higher-order self-energy corrections included in a scheme proposed by Katanin. Using a parametrization of effective interactions by patches in momentum space, the flow equations can be integrated numerically to the lowest scales without encountering divergences. Momentum-shell as well as interaction-flow cutoff functions are used, including a small external field or a large external field and a counterterm, respectively. Both approaches produce momentum-resolved order parameter values directly from the microscopic model. The size of the superconducting gap is in reasonable agreement with expectations from other studies.Comment: 22 pages, 16 figures, references added, some changes in the introductio

A Droplet within the Spherical Model

Various substances in the liquid state tend to form droplets. In this paper the shape of such droplets is investigated within the spherical model of a lattice gas. We show that in this case the droplet boundary is always diffusive, as opposed to sharp, and find the corresponding density profiles (droplet shapes). Translation-invariant versions of the spherical model do not fix the spatial location of the droplet, hence lead to mixed phases. To obtain pure macroscopic states (which describe localized droplets) we use generalized quasi-averaging. Conventional quasi-averaging deforms droplets and, hence, can not be used for this purpose. On the contrary, application of the generalized method of quasi-averages yields droplet shapes which do not depend on the magnitude of the applied external field.Comment: 22 pages, 2 figure

Theoretical aspects of the CEBAF 89-009 experiment on inclusive scattering of 4.05 GeV electrons from nuclei

We compare recent CEBAF data on inclusive electron scattering on nuclei with predictions, based on a relation between structure functions (SF) of a nucleus, a nucleon and a nucleus of point-nucleons. The latter contains nuclear dynamics, e.g. binary collision contributions in addition to the asymptotic limit. The agreement with the data is good, except in low-intensity regions. Computed ternary collsion contributions appear too small for an explanation. We perform scaling analyses in Gurvitz's scaling variable and found that for $y_G\gtrless 0$, ratios of scaling functions for pairs of nuclei differ by less than 15-20% from 1. Scaling functions for $0$ are, for increasing $Q^2$, shown to approach a plateau from above. We observe only weak $Q^2$-dependence in FSI, which in the relevant kinematic region is ascribed to the diffractive nature of the NN amplitudes appearing in FSI. This renders it difficult to separate asymptotic from FSI parts and seriously hampers the extraction of $n(p)$ from scaling analyses in a model-independnent fashion.Comment: 11 p. Latex file, 2 ps fig

Bose-Einstein condensation in the presence of a uniform field and a point-like impurity

The behavior of an ideal $D$-dimensional boson gas in the presence of a uniform gravitational field is analyzed. It is explicitly shown that, contrarily to an old standing folklore, the three-dimensional gas does not undergo Bose-Einstein condensation at finite temperature. On the other hand, Bose-Einstein condensation occurs at $T\neq 0$ for $D=1,2,3$ if there is a point-like impurity at the bottom of the vessel containing the gas.Comment: 14 pages, REVTEX. Revised version, accepted for publication in Phys. Rev.

How to turn the Fast-Track into a Fast-Track: Process integration for evaluation of the quality of Digital Health Applications (DiGAs) on the example of the German Fast-Track Process

In this paper, we address the research question of which integration points in the \textit{German Fast-Track process} are particularly well suited for the integration of evaluation platforms for digital health applications. For this purpose, possible integration points are first identified and then analyzed with the help of a utility analysis with regard to the posed research question. Finally, a recommendation for action is made based on the results of the conducted utility analysis

The programming of sequences of saccades

Saccadic eye movements move the high-resolution fovea to point at regions of interest. Saccades can only be generated serially (i.e., one at a time). However, what remains unclear is the extent to which saccades are programmed in parallel (i.e., a series of such moments can be planned together) and how far ahead such planning occurs. In the current experiment, we investigate this issue with a saccade contingent preview paradigm. Participants were asked to execute saccadic eye movements in response to seven small circles presented on a screen. The extent to which participants were given prior information about target locations was varied on a trial-by-trial basis: participants were aware of the location of the next target only, the next three, five, or all seven targets. The addition of new targets to the display was made during the saccade to the next target in the sequence. The overall time taken to complete the sequence was decreased as more targets were available up to all seven targets. This was a result of a reduction in the number of saccades being executed and a reduction in their saccade latencies. Surprisingly, these results suggest that, when faced with a demand to saccade to a large number of target locations, saccade preparation about all target locations is carried out in paralle

Confinement and scaling in deep inelastic scattering

We show that parton confinement in the final state generates large $1/Q^2$ corrections to Bjorken scaling, thus leaving less room for the logarithmic corrections. In particular, the $x$-scaling violations at large $x$ are entirely described in terms of power corrections. For treatment of these non-perturbative effects, we derive a new expansion in powers of $1/Q^2$ for the structure function that is free of infra-red singularities and which reduces corrections to the leading term. The leading term represents scattering from an off-mass-shell parton, which keeps the same virtual mass in the final state. It is found that this quasi-free term is a function of a new variable $\bar x$, which coincides with the Bjorken variable $x$ for $Q^2\to\infty$. The two variables are very different, however, at finite $Q^2$. In particular, the variable $\bar x$ depends on the invariant mass of the spectator particles. Analysis of the data at large $x$ shows excellent scaling in the variable $\bar x$, and determines the value of the diquark mass to be close to zero. $\bar x$-scaling allows us to extract the structure function near the elastic threshold. It is found to behave as $F_2\sim (1-x)^{3.7}$. Predictions for the structure functions based on $\bar x$-scaling are made.Comment: Discussion of target mass corrections is added. Accepted for publication in Phys. Rev.

Numerical study of the spherically-symmetric Gross-Pitaevskii equation in two space dimensions

We present a numerical study of the time-dependent and time-independent Gross-Pitaevskii (GP) equation in two space dimensions, which describes the Bose-Einstein condensate of trapped bosons at ultralow temperature with both attractive and repulsive interatomic interactions. Both time-dependent and time-independent GP equations are used to study the stationary problems. In addition the time-dependent approach is used to study some evolution problems of the condensate. Specifically, we study the evolution problem where the trap energy is suddenly changed in a stable preformed condensate. In this case the system oscillates with increasing amplitude and does not remain limited between two stable configurations. Good convergence is obtained in all cases studied.Comment: 9 latex pages, 7 postscript figures, To appear in Phys. Rev.

Inclusive quasi-elastic electron-nucleus scattering

This article presents a review of the field of inclusive quasi-elastic electron-nucleus scattering. It discusses the approach used to measure the data and includes a compilation of data available in numerical form. The theoretical approaches used to interpret the data are presented. A number of results obtained from the comparison between experiment and calculation are then reviewed. The analogies and differences to other fields of physics exploiting quasi-elastic scattering from composite systems are pointed out.Comment: Accepted for publication in Reviews of Modern Physic