7,019 research outputs found
Partial normalizations of coxeter arrangements and discriminants
We study natural partial normalization spaces of Coxeter arrangements and discriminants
and relate their geometry to representation theory. The underlying ring structures arise from Dubrovinās
Frobenius manifold structure which is lifted (without unit) to the space of the arrangement. We also
describe an independent approach to these structures via duality of maximal CohenāMacaulay fractional
ideals. In the process, we find 3rd order differential relations for the basic invariants of the Coxeter
group. Finally, we show that our partial normalizations give rise to new free divisors
Tuning the interactions of spin-polarized fermions using quasi-one-dimensional confinement
The behavior of ultracold atomic gases depends crucially on the two-body
scattering properties of these systems. We develop a multichannel scattering
theory for atom-atom collisions in quasi-one-dimensional (quasi-1D) geometries
such as atomic waveguides or highly elongated traps. We apply our general
framework to the low energy scattering of two spin-polarized fermions and show
that tightly-confined fermions have infinitely strong interactions at a
particular value of the 3D, free-space p-wave scattering volume. Moreover, we
describe a mapping of this strongly interacting system of two quasi-1D fermions
to a weakly interacting system of two 1D bosons.Comment: Submitted to Phys. Rev. Let
When Exercise is a Pain in the Head
Headache is one of the five most common chief complaints in the US, resulting in nearly 5 million visits to the ED (Lange, 2011). With great variance in quality, etiology, pathophysiology, and as a potential indicator of a serious underlying problem, it is critical that these headaches be accurately diagnosed, primarily for rapid identification of life threatening factors, but also to offer treatment and education specific to the particular type of headache the patient is experiencing. This will result in better outcomes for the patient through better control and will subsequently save health care dollars by reducing ED visits and unnecessary imaging
Reducing the Bias of Causality Measures
Measures of the direction and strength of the interdependence between two
time series are evaluated and modified in order to reduce the bias in the
estimation of the measures, so that they give zero values when there is no
causal effect. For this, point shuffling is employed as used in the frame of
surrogate data. This correction is not specific to a particular measure and it
is implemented here on measures based on state space reconstruction and
information measures. The performance of the causality measures and their
modifications is evaluated on simulated uncoupled and coupled dynamical systems
and for different settings of embedding dimension, time series length and noise
level. The corrected measures, and particularly the suggested corrected
transfer entropy, turn out to stabilize at the zero level in the absence of
causal effect and detect correctly the direction of information flow when it is
present. The measures are also evaluated on electroencephalograms (EEG) for the
detection of the information flow in the brain of an epileptic patient. The
performance of the measures on EEG is interpreted, in view of the results from
the simulation study.Comment: 30 pages, 12 figures, accepted to Physical Review
Feshbach Resonance Cooling of Trapped Atom Pairs
Spectroscopic studies of few-body systems at ultracold temperatures provide
valuable information that often cannot be extracted in a hot environment.
Considering a pair of atoms, we propose a cooling mechanism that makes use of a
scattering Feshbach resonance. Application of a series of time-dependent
magnetic field ramps results in the situation in which either zero, one, or two
atoms remain trapped. If two atoms remain in the trap after the field ramps are
completed, then they have been cooled. Application of the proposed cooling
mechanism to optical traps or lattices is considered.Comment: 5 pages, 3 figures; v.2: major conceptual change
Partial normalizations of coxeter arrangements and discriminants
We study natural partial normalization spaces of Coxeter arrangements and discriminants and relate their geometry to representation theory. The underlying ring structures arise from Dubrovinās Frobenius manifold structure which is lifted (without unit) to the space of the arrangement. We alsodescribe an independent approach to these structures via duality of maximal CohenāMacaulay fractional ideals. In the process, we find 3rd order differential relations for the basic invariants of the Coxeter group. Finally, we show that our partial normalizations give rise to new free divisors
On the Symmetry of b-Functions of Linear Free Divisors
We introduce the concept of a prehomogeneous determinant as a possibly nonreduced version of a linear free divisor. Both are special cases of prehomogeneous vector spaces. We show that the roots of the b-function are symmetric about ā1 for reductive prehomogeneous determinants and for regular special linear free divisors. For general prehomogeneous determinants, we describe conditions under which this symmetry persists.
Combined with Kashiwara\u27s theorem on the roots of b-functions, our symmetry result shows that ā1 is the only integer root of the b-function. This gives a positive answer to a problem posed by Castro-Jimenez and Ucha-Enrquez in the above cases.
We study the condition of strong Euler homogeneity in terms of the action of the stabilizers on the normal spaces.
As an application of our results, we show that the logarithmic comparison theorem holds for reductive linear Koszul free divisors exactly when they are strongly Euler homogeneous
Quasi-one-dimensional Bose gases with large scattering length
Bose gases confined in highly-elongated harmonic traps are investigated over
a wide range of interaction strengths using quantum Monte Carlo techniques. We
find that the properties of a Bose gas under tight transverse confinement are
well reproduced by a 1d model Hamiltonian with contact interactions. We point
out the existence of a unitary regime, where the properties of the quasi-1d
Bose gas become independent of the actual value of the 3d scattering length. In
this unitary regime, the energy of the system is well described by a hard rod
equation of state. We investigate the stability of quasi-1d Bose gases with
positive and negative 3d scattering length.Comment: 5 pages, 3 figure
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