Temperature and finite-size effects in collective modes of superfluid Fermi gases

We study the effects of superfluidity on the monopole and quadrupole collective excitations of a dilute ultra-cold Fermi gas with an attractive interatomic interaction. The system is treated fully microscopically within the Bogoliubov-de Gennes and quasiparticle random-phase approximation methods. The dependence on the temperature and on the trap frequency is analyzed and systematic comparisons with the corresponding hydrodynamic predictions are presented in order to study the limits of validity of the semiclassical approach.Comment: 9 pages, 4 figure

Comparing Tycho-2 Astrometry with UCAC1

The Tycho-2 Catalogue, released in February 2000, is based on the ESA Hipparcos space mission data and various ground-based catalogs for proper motions. An external comparison of the Tycho-2 astrometry is presented here using the first U.S. Naval Observatory CCD Astrograph Catalog (UCAC1). The UCAC1 data were obtained from observations performed at CTIO between February 1998 and November 1999, using the 206 mm aperture 5-element lens astrograph and a 4k x 4k CCD. Only small systematic differences in position between Tycho-2 and UCAC1 up to 15 milliarcseconds (mas) are found, mainly as a function of magnitude. The standard deviations of the distributions of the position differences are in the 35 to 140 mas range, depending on magnitude. The observed scatter in the position differences is about 30% larger than expected from the combined formal, internal errors, also depending on magnitude. The Tycho-2 Catalogue has the more precise positions for bright stars (V <= 10 mag) while the UCAC1 positions are significantly better at the faint end (11 mag <= V <= 12.5 mag) of the magnitude range in common. UCAC1 goes much fainter (to R=16) than Tycho-2; however complete sky coverage is not expected before mid 2003.Comment: LaTeX, 8 pages, 3 PS figures, accepted by AJ (Aug 2000) see also http://ad.usno.navy.mil/ad/ucac/ request for UCAC1 CD-ROM: e-mail to [email protected] request for Tycho-2 CD-ROM: e-mail to [email protected] or [email protected]

Anderson impurity model in nonequilibrium: analytical results versus quantum Monte Carlo data

We analyze the spectral function of the single-impurity two-terminal Anderson model at finite voltage using the recently developed diagrammatic quantum Monte Carlo technique as well as perturbation theory. In the (particle-hole-)symmetric case we find an excellent agreement of the numerical data with the perturbative results of second order up to interaction strengths $U/\Gamma \approx 2$, where $\Gamma$ is the transparency of the impurity-electrode interface. The analytical results are obtained in form of the nonequilibrium self-energy for which we present explicit formulas in the closed form at arbitrary bias voltage. We observe an increase of the spectral density around zero energy brought about by the Kondo effect. Our analysis suggests that a finite applied voltage $V$ acts as an effective temperature of the system. We conclude that at voltages significantly larger than the equilibrium Kondo temperature there is a complete suppression of the Kondo effect and no resonance splitting can be observed. We confirm this scenario by comparison of the numerical data with the perturbative results.Comment: 8 pages, 6 figure

The Right to Contest AI

Artificial intelligence (AI) is increasingly used to make important decisions, from university admissions selections to loan determinations to the distribution of COVID-19 vaccines. These uses of AI raise a host of concerns about discrimination, accuracy, fairness, and accountability. In the United States, recent proposals for regulating AI focus largely on ex ante and systemic governance. This Article argues instead—or really, in addition—for an individual right to contest AI decisions, modeled on due process but adapted for the digital age. The European Union, in fact, recognizes such a right, and a growing number of institutions around the world now call for its establishment. This Article argues that despite considerable differences between the United States and other countries, establishing the right to contest AI decisions here would be in keeping with a long tradition of due process theory. This Article then fills a gap in the literature, establishing a theoretical scaffolding for discussing what a right to contest should look like in practice. This Article establishes four contestation archetypes that should serve as the bases of discussions of contestation both for the right to contest AI and in other policy contexts. The contestation archetypes vary along two axes: from contestation rules to standards and from emphasizing procedure to establishing substantive rights. This Article then discusses four processes that illustrate these archetypes in practice, including the first in-depth consideration of the GDPR’s right to contestation for a U.S. audience. Finally, this Article integrates findings from these investigations to develop normative and practical guidance for establishing a right to contest AI

Perturbation of magnetostatic modes observed by ferromagnetic resonance force microscopy

Magnetostatic modes of yttrium iron garnet (YIG) films are investigated by ferromagnetic resonance force microscopy. A thin-film "probe" magnet at the tip of a compliant cantilever introduces a local inhomogeneity in the internal field of the YIG sample. This influences the shape of the sample's magnetostatic modes, thereby measurably perturbing the strength of the force coupled to the cantilever. We present a theoretical model that explains these observations; it shows that the tip-induced variation of the internal field creates either a local "potential barrier" or "potential well" for the magnetostatic waves. The data and model together indicate that local magnetic imaging of ferromagnets is possible, even in the presence of long-range spin coupling, through the introduction of localized magnetostatic modes predicted to arise from sufficiently strong tip fields

The Right to Contest AI

Artificial intelligence (AI) is increasingly used to make important decisions, from university admissions selections to loan determinations to the distribution of COVID-19 vaccines. These uses of AI raise a host of concerns about discrimination, accuracy, fairness, and accountability. In the United States, recent proposals for regulating AI focus largely on ex ante and systemic governance. This Article argues instead—or really, in addition—for an individual right to contest AI decisions, modeled on due process but adapted for the digital age. The European Union, in fact, recognizes such a right, and a growing number of institutions around the world now call for its establishment. This Article argues that despite considerable differences between the United States and other countries, establishing the right to contest AI decisions here would be in keeping with a long tradition of due process theory. This Article then fills a gap in the literature, establishing a theoretical scaffolding for discussing what a right to contest should look like in practice. This Article establishes four contestation archetypes that should serve as the bases of discussions of contestation both for the right to contest AI and in other policy contexts. The contestation archetypes vary along two axes: from contestation rules to standards and from emphasizing procedure to establishing substantive rights. This Article then discusses four processes that illustrate these archetypes in practice, including the first in-depth consideration of the GDPR’s right to contestation for a U.S. audience. Finally, this Article integrates findings from these investigations to develop normative and practical guidance for establishing a right to contest AI

Numerical solution of the Boltzmann equation for the collective modes of trapped Fermi gases

We numerically solve the Boltzmann equation for trapped fermions in the normal phase using the test-particle method. After discussing a couple of tests in order to estimate the reliability of the method, we apply it to the description of collective modes in a spherical harmonic trap. The numerical results are compared with those obtained previously by taking moments of the Boltzmann equation. We find that the general shape of the response function is very similar in both methods, but the relaxation time obtained from the simulation is significantly longer than that predicted by the method of moments. It is shown that the result of the method of moments can be corrected by including fourth-order moments in addition to the usual second-order ones and that this method agrees very well with our numerical simulations.Comment: 13 pages, 8 figures, accepted for publication in Phys. Rev.