230 research outputs found
Mott transition of fermionic atoms in a three-dimensional optical trap
We study theoretically the Mott metal-insulator transition for a system of
fermionic atoms confined in a three-dimensional optical lattice and a harmonic
trap. We describe an inhomogeneous system of several thousand sites using an
adaptation of dynamical mean field theory solved efficiently with the numerical
renormalization group method. Above a critical value of the on-site
interaction, a Mott-insulating phase appears in the system. We investigate
signatures of the Mott phase in the density profile and in time-of-flight
experiments.Comment: 4 pages and 5 figure
Kondo proximity effect: How does a metal penetrate into a Mott insulator?
We consider a heterostructure of a metal and a paramagnetic Mott insulator
using an adaptation of dynamical mean field theory to describe inhomogeneous
systems. The metal can penetrate into the insulator via the Kondo effect. We
investigate the scaling properties of the metal-insulator interface close to
the critical point of the Mott insulator. At criticality, the quasiparticle
weight decays as 1/x^2 with distance x from the metal within our mean field
theory. Our numerical results (using the numerical renormalization group as an
impurity solver) show that the prefactor of this power law is extremely small.Comment: 4 pages, 3 figure
Variations in cognitive functioning in genetic generalized epilepsy: four case studies
Introduction. The traditional view of cognition in idiopathic or genetic generalized epilepsy (GGE) is that "one size fits all" i.e. only very mild generalized impairment might be detected, if any. This paper describes four case studies of cognitive functioning in GGE patients with photosensitivity and reflexive seizures.
Aim. The aim was to discover whether each individual's set of cognitive deficits varied in accordance with his/her other clinical phenomena such as photosensitivity and kinds of reflexive seizures.
Method. Neurological and cognitive performance was assessed by comprehensive evaluation of each patient based on interviews, neurologist's EEG reports and neuropsychological tests. Assessment of cognitive domains included estimated pre-morbid I.Q. based on reading ability and demographic norms, current I.Q., attention factors, verbal memory, visual memory and executive functions.
Results. Clinical signs and investigative studies indicated that two cases typically began reflexive seizure episodes with facial myoclonia which evolved into tonic-clonic convulsions or generalized myoclonic seizures. These patients had widespread attention and working memory deficits, some severe, together with lowered intelligence scores. In contrast, two other cases (with no history of myoclonus) had generalized reflexive seizures originating in the occipital lobes, very mild localized visual dysfunction and high intelligence.
Conclusions. The systematic variation in extent and nature of cognitive dysfunction illustrated in these cases with reflexive seizures (preceded by myoclonia or visual phenomena) would be explained by a more recent conceptualization of GGE as encompassing regional differences in variable hyperexcitability located at cortical levels or functional neural networks
Isospin-0 s-wave scattering length from twisted mass lattice QCD
We present results for the isospin-0 s-wave scattering length
calculated with Osterwalder-Seiler valence quarks on Wilson twisted mass gauge
configurations. We use three ensembles with unitary (valence) pion
mass at its physical value (250MeV), at 240MeV (320MeV) and
at 330MeV (400MeV), respectively. By using the stochastic Laplacian
Heaviside quark smearing method, all quark propagation diagrams contributing to
the isospin-0 correlation function are computed with sufficient
precision. The chiral extrapolation is performed to obtain the scattering
length at the physical pion mass. Our result agrees reasonably well with various experimental measurements and
theoretical predictions. Since we only use one lattice spacing, certain
systematics uncertainties, especially those arising from unitary breaking, are
not controlled in our result.Comment: 21 pages, 5 figures, 6 table
First Physics Results at the Physical Pion Mass from Wilson Twisted Mass Fermions at Maximal Twist
We present physics results from simulations of QCD using dynamical
Wilson twisted mass fermions at the physical value of the pion mass. These
simulations were enabled by the addition of the clover term to the twisted mass
quark action. We show evidence that compared to previous simulations without
this term, the pion mass splitting due to isospin breaking is almost completely
eliminated. Using this new action, we compute the masses and decay constants of
pseudoscalar mesons involving the dynamical up and down as well as valence
strange and charm quarks at one value of the lattice spacing,
fm. Further, we determine renormalized quark masses as well as their
scale-independent ratios, in excellent agreement with other lattice
determinations in the continuum limit. In the baryon sector, we show that the
nucleon mass is compatible with its physical value and that the masses of the
baryons do not show any sign of isospin breaking. Finally, we compute
the electron, muon and tau lepton anomalous magnetic moments and show the
results to be consistent with extrapolations of older ETMC data to the
continuum and physical pion mass limits. We mostly find remarkably good
agreement with phenomenology, even though we cannot take the continuum and
thermodynamic limits.Comment: 45 pages, 15 figure
The Euler-Maruyama approximation for the absorption time of the CEV diffusion
A standard convergence analysis of the simulation schemes for the hitting
times of diffusions typically requires non-degeneracy of their coefficients on
the boundary, which excludes the possibility of absorption. In this paper we
consider the CEV diffusion from the mathematical finance and show how a weakly
consistent approximation for the absorption time can be constructed, using the
Euler-Maruyama scheme
An Optimization Approach to Weak Approximation of Lévy-Driven Stochastic Differential Equations
We propose an optimization approach to weak approximation of Lévy-driven stochastic differential equations. We employ a mathematical programming framework to obtain numerically upper and lower bound estimates of the target expectation, where the optimization procedure ends up with a polynomial programming problem. An advantage of our approach is that all we need is a closed form of the Lévy measure, not the exact simulation knowledge of the increments or of a shot noise representation for the time discretization approximation. We also investigate methods for approximation at some different intermediate time points simultaneously
Dynamical Mean-Field Theory
The dynamical mean-field theory (DMFT) is a widely applicable approximation
scheme for the investigation of correlated quantum many-particle systems on a
lattice, e.g., electrons in solids and cold atoms in optical lattices. In
particular, the combination of the DMFT with conventional methods for the
calculation of electronic band structures has led to a powerful numerical
approach which allows one to explore the properties of correlated materials. In
this introductory article we discuss the foundations of the DMFT, derive the
underlying self-consistency equations, and present several applications which
have provided important insights into the properties of correlated matter.Comment: Chapter in "Theoretical Methods for Strongly Correlated Systems",
edited by A. Avella and F. Mancini, Springer (2011), 31 pages, 5 figure
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