Simple parametrization for the ground-state energy of the infinite Hubbard chain incorporating Mott physics, spin-dependent phenomena and spatial inhomogeneity

Simple analytical parametrizations for the ground-state energy of the one-dimensional repulsive Hubbard model are developed. The charge-dependence of the energy is parametrized using exact results extracted from the Bethe-Ansatz. The resulting parametrization is shown to be in better agreement with highly precise data obtained from fully numerical solution of the Bethe-Ansatz equations than previous expressions [Lima et al., Phys. Rev. Lett. 90, 146402 (2003)]. Unlike these earlier proposals, the present parametrization correctly predicts a positive Mott gap at half filling for any U>0. The construction is extended to spin-dependent phenomena by parametrizing the magnetization-dependence of the ground-state energy using further exact results and numerical benchmarking. Lastly, the parametrizations developed for the spatially uniform model are extended by means of a simple local-density-type approximation to spatially inhomogeneous models, e.g., in the presence of impurities, external fields or trapping potentials. Results are shown to be in excellent agreement with independent many-body calculations, at a fraction of the computational cost.Comment: New Journal of Physics, accepte

Coulomb potential from a particle in uniform ultrarelativistic motion

The Coulomb potential produced by an ultrarelativistic particle (such as a heavy ion) in uniform motion is shown in the appropriate gauge to factorize into a longitudinal Dirac delta function of (z - t) times the simple two dimensional potential solution in the transverse direction. This form makes manifest the source of the energy independence of the interaction.Comment: 5 pages, latex, revtex source, no figure

Effect of spatial inhomogeneity on the mapping between strongly interacting fermions and weakly interacting spins

A combined analytical and numerical study is performed of the mapping between strongly interacting fermions and weakly interacting spins, in the framework of the Hubbard, t-J and Heisenberg models. While for spatially homogeneous models in the thermodynamic limit the mapping is thoroughly understood, we here focus on aspects that become relevant in spatially inhomogeneous situations, such as the effect of boundaries, impurities, superlattices and interfaces. We consider parameter regimes that are relevant for traditional applications of these models, such as electrons in cuprates and manganites, and for more recent applications to atoms in optical lattices. The rate of the mapping as a function of the interaction strength is determined from the Bethe-Ansatz for infinite systems and from numerical diagonalization for finite systems. We show analytically that if translational symmetry is broken through the presence of impurities, the mapping persists and is, in a certain sense, as local as possible, provided the spin-spin interaction between two sites of the Heisenberg model is calculated from the harmonic mean of the onsite Coulomb interaction on adjacent sites of the Hubbard model. Numerical calculations corroborate these findings also in interfaces and superlattices, where analytical calculations are more complicated.Comment: 7 pages, 6 figure

Fronto-striatal cognitive deficits at different stages of Parkinson's disease

Groups of patients with idiopathic Parkinson's disease, either medicated or unmedicated, were compared with matched groups of normal controls on a computerized battery previously shown to be sensitive to frontal lobe dysfunction, including tests of planning, spatial working memory and attentional set-shifting. In a series of problems based on the 'Tower of London' test, medicated patients with Parkinson's disease were shown to be impaired in the amount of time spent thinking about (planning) the solution to each problem. Additionally, an impairment in terms of the accuracy of the solution produced on this test was only evident in those patients with more severe clinical symptoms and was accompanied by deficits in an associated test of spatial short-term memory. Medicated patients with both mild and severe clinical symptoms were also impaired on a related test of spatial working memory. In contrast, a group of patients who were unmedicated and 'early in the course' of the disease were unimpaired in all three of these tests. However, all three Parkinson's disease groups were impaired in the test of attentional set-shifting ability, although unimpaired in a test of pattern recognition which is insensitive to frontal lobe damage. These data are compared with those previously published from a group of young neurosurgical patients with localized excisions of the frontal lobes and are discussed in terms of the specific nature of the cognitive deficit at different stages of Parkinson's disease

Angular dependence of superconductivity in superconductor / spin valve heterostructures

We report measurements of the superconducting transition temperature, $T_c$, in CoO/Co/Cu/Co/Nb multilayers as a function of the angle $\alpha$ between the magnetic moments of the Co layers. Our measurements reveal that $T_c(\alpha)$ is a nonmonotonic function, with a minimum near $\alpha={\pi}/{2}$. Numerical self-consistent solutions of the Bogoliubov - de Gennes equations quantitatively and accurately describe the behavior of $T_c$ as a function of $\alpha$ and layer thicknesses in these superconductor / spin-valve heterostructures. We show that experimental data and theoretical evidence agree in relating $T_c(\alpha)$ to enhanced penetration of the triplet component of the condensate into the Co/Cu/Co spin valve in the maximally noncollinear magnetic configuration.Comment: 9 pages, 9 figure

Cognitive performance in multiple system atrophy

The cognitive performance of a group of patients with multiple system atrophy (MSA) of striato-nigral predominance was compared with that of age and IQ matched control subjects, using three tests sensitive to frontal lobe dysfunction and a battery sensitive to memory and learning deficits in Parkinson's disease and dementia of the Alzheimer type. The MSA group showed significant deficits in all three of the tests previously shown to be sensitive to frontal lobe dysfunction. Thus, a significant proportion of patients from the MSA group failed an attentional set-shifting test, specifically at the stage when an extra-dimensional shift was required. They were also impaired in a subject-ordered test of spatial working memory. The MSA group showed deficits mostly confined to measures of speed of thinking, rather than accuracy, on the Tower of London task. These deficits were seen in the absence of consistent impairments in language or visual perception. Moreover, the MSA group showed no significant deficits in tests of spatial and pattern recognition previously shown to be sensitive to patients early in the course of probable Alzheimer's disease and only a few patients exhibited impairment on the Warrington Recognition Memory Test. There were impairments on other tests of visual memory and learning relative to matched controls, but these could not easily be related to fundamental deficits of memory or learning. Thus, on a matching-to-sample task the patients were impaired at simultaneous but not delayed matching to sample, whereas difficulties in a pattern-location learning task were more evident at its initial, easier stages. The MSA group showed no consistent evidence of intellectual deterioration as assessed from their performance on subtests of the Wechsler Adult Intelligence Scale (WAIS) and the National Adult Reading Test (NART). Consideration of individual cases showed that there was some heterogeneity in the pattern of deficits in the MSA group, with one patient showing no impairment, even in the face of considerable physical disability. The results show a distinctive pattern of cognitive deficits, unlike those previously seen using the same tests in patients with Parkinson's and Alzheimer's diseases, and suggesting a prominent frontal-lobe-like component. The implications for concepts of 'subcortical' dementia and 'fronto-striatal' cognitive dysfunction are considered

Displacement effect in strong-field atomic ionization by an XUV pulse

We study strong-field atomic ionization driven by an XUV pulse with a non\-zero displacement, the quantity defined as the integral of the pulse vector potential taken over the pulse duration. We demonstrate that the use of such pulses may lead to an extreme sensitivity of the ionization process to subtle changes of the parameters of a driving XUV pulse, in particular, the ramp-on/off profile and the carrier envelope phase. We illustrate this sensitivity for atomic hydrogen and lithium driven by few-femto\-second XUV pulses with intensity in the $\rm 10^{14}~W/cm^2$ range. We argue that the observed effect is general and should modify strong-field ionization of any atom, provided the ionization rate is sufficiently high.Comment: 5 pages, 7 figure

Momentum conservation and local field corrections for the response of interacting Fermi gases

We reanalyze the recently derived response function for interacting systems in relaxation time approximation respecting density, momentum and energy conservation. We find that momentum conservation leads exactly to the local field corrections for both cases respecting only density conservation and respecting density and energy conservation. This rewriting simplifies the former formulae dramatically. We discuss the small wave vector expansion and find that the response function shows a high frequency dependence of $\omega^{-5}$ which allows to fulfill higher order sum rules. The momentum conservation also resolves a puzzle about the conductivity which should only be finite in multicomponent systems