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

Fermionic functional renormalization group for first-order phase transitions: a mean-field model

First-order phase transitions in many-fermion systems are not detected in the susceptibility analysis of common renormalization-group (RG) approaches. Here we introduce a counterterm technique within the functional renormalization-group (fRG) formalism which allows access to all stable and metastable configurations. It becomes possible to study symmetry-broken states which occur through first-order transitions as well as hysteresis phenomena. For continuous transitions, the standard results are reproduced. As an example, we study discrete-symmetry breaking in a mean-field model for a commensurate charge-density wave. An additional benefit of the approach is that away from the critical temperature for the breaking of discrete symmetries large interactions can be avoided at all RG scales.Comment: 17 pages, 8 figures. v2 corrects typos, adds references and a discussion of the literatur

Development of semiconductor detectors for fast neutron radiography

A high-energy neutron detector has been developed using a semiconductor diode fabricated from bulk gallium arsenide wafers with a polyethylene neutron converter layer. Typical thickness of the diode layer is 250 to 300 μm with bias voltages of 30 to 150 volts. Converter thicknesses up to 2030 μm have been tested. GaAs neutron detectors offer many advantages over existing detectors including positional information, directional dependence, gamma discrimination, radiation hardness, and spectral tailoring. Polyethylene-coated detectors have been shown to detect 14 MeV neutrons directly from a D-T neutron generator without interference from gamma rays or scattered neutrons. An array of small diode detectors can be assembled to perform fast neutron radiography with direct digital readout and real-time display of the image produced. In addition, because the detectors are insensitive to gamma rays and low energy neutrons, highly radioactive samples (such as spent nuclear fuel or transuranic waste drums) could be radiographed. © 2001 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/87673/2/1118_1.pd

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.

Description of recent large-qq neutron inclusive scattering data from liquid 4^4He

We report dynamical calculations for large-$q$ structure functions of liquid $^4$He at $T$=1.6 and 2.3 K and compare those with recent MARI data. We extend those calculations far beyond the experimental range q\le 29\Ain in order to study the approach of the response to its asymptotic limit for a system with interactions having a strong short-range repulsion. We find only small deviations from theoretical $1/q$ behavior, valid for smooth $V$. We repeat an extraction by Glyde et al of cumulant coefficients from data. We argue that fits determine the single atom momentum distribution, but express doubt as to the extraction of meaningful Final State Interaction parameters.Comment: 37 pages, 13 postscript fig

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

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

Beyond the binary collision approximation for the large-qq response of liquid 4^4He

We discuss corrections to the linear response of a many-body system beyond the binary collision approximation. We first derive for smooth pair interactions an exact expression of the response $\propto 1/q^2$, considerably simplifying existing forms and present also the generalization for interactions with a strong, short-range repulsion. We then apply the latter to the case of liquid $^4$He. We display the numerical influence of the $1/q^2$ correction around the quasi-elastic peak and in the low-intensity wings of the response, far from that peak. Finally we resolve an apparent contradiction in previous discussions around the fourth order cumulant expansion coefficient. Our results prove that the large-$q$ response of liquid $^4$He can be accurately understood on the basis of a dynamical theory.Comment: 19 p. Figs. available on reques

Four-quasiparticle alignments in 66Ge

13 págs.; 7 figs.; 1 tab. ; PACS number(s): 23.20.Lv, 21.10.Re, 25.70.Hi, 27.50.1eThe neutron-deficient nucleus 66Ge was populated at high spin in two experiments using the reaction 40Ca(32S, α2p) at beam energies of 105 and 95 MeV. In the first experiment, a self-supporting 40Ca target was used, while a gold-backed target of similar thickness was used in the second experiment, γ rays were detected with the EUROBALL array, combined with the charged-particle detector array EUCLIDES and the Neutron Wall. The level scheme of 66Ge was extended up to E ≈ 18 MeV and Iπ = (23-). Above angular momentum 10+, we found two sequences, connected by energetically staggered ΔI = 1 M 1 transitions. The total Routhian surface calculations describe 66Ge at lower spins as a γ-soft nucleus having a moderate deformation of β2 ≈ 0.23, while a triaxial deformation is predicted for the band structures above Iπ = 10+. To our knowledge, this is the first observation of staggered Ml transitions in a deformed four-quasiparticle π(g9/2 2) ν(g9/2 2) structure. ©2003 American Physical SocietyThis work was supported by BMBF 06 GO¨ 951 and TMR/LSF Contract No. HPRI-CT-1999-00078. The authors are indebted to the crew of the VIVITRON accelerator and the EUROBALL facility at IReS for their dedicated efforts and cooperation.Peer Reviewe