785 research outputs found
On Eigenvalue spacings for the 1-D Anderson model with singular site distribution
We study eigenvalue spacings and local eigenvalue statistics for 1D lattice
Schrodinger operators with Holder regular potential, obtaining a version of
Minami's inequality and Poisson statistics for the local eigenvalue spacings.
The main additional new input are regular properties of the Furstenberg
measures and the density of states obtained in some of the author's earlier
work.Comment: 13 page
Detailed balance in Horava-Lifshitz gravity
We study Horava-Lifshitz gravity in the presence of a scalar field. When the
detailed balance condition is implemented, a new term in the gravitational
sector is added in order to maintain ultraviolet stability. The
four-dimensional theory is of a scalar-tensor type with a positive cosmological
constant and gravity is nonminimally coupled with the scalar and its gradient
terms. The scalar field has a double-well potential and, if required to play
the role of the inflation, can produce a scale-invariant spectrum. The total
action is rather complicated and there is no analog of the Einstein frame where
Lorentz invariance is recovered in the infrared. For these reasons it may be
necessary to abandon detailed balance. We comment on open problems and future
directions in anisotropic critical models of gravity.Comment: 10 pages. v2: discussion expanded and improved, section on
generalizations added, typos corrected, references added, conclusions
unchange
Concussion-reporting behavior in rugby: A national survey of rugby union players in the United States
Background: Rugby is the fastest growing team sport in the United States for male and female athletes. It is a contact/collision sport with an injury risk profile that includes concussions.
Purpose: To examine the prevalence of concussions in male and female rugby players in the United States and to characterize behaviors around reporting concussions that could be a target for prevention and treatment efforts.
Study Design: Cross-sectional study; Level of evidence, 3.
Methods: An online survey distributed to active members on the USA Rugby membership list was used to examine self-reported concussions in male and female athletes. Concussion-reporting behaviors and return to play after a concussion were also explored. Statistical analysis was used to compare male with female athletes and report differences, with years of experience as a dependent variable.
Results: The proportion of athletes with a history of at least 1 concussion was 61.9% in all respondents. Of those who reported a concussion, 50.8% reported the concussion during the game or practice in which it occurred, and 57.6% reported at least 1 concussion to a qualified medical provider. Overall, 27.7% of participants who reported ≥1 rugby-related concussion in our survey noted that at least 1 of these concussions was not formally reported. The most commonly cited reasons for not reporting a concussion included not thinking that it was a serious injury, not knowing that it was a concussion at the time, and not wanting to be pulled out of the game or practice. Additionally, 61.0% of athletes did not engage in recommended return-to-play protocols after their most recent rugby-related concussion.
Conclusion: US rugby union athletes may not report concussions to medical personnel or follow return-to-play protocols guided by medical advice. This could result from a lack of education on concussion recognition and the risks associated with continued play after a concussion as well as limited access to health care. Further education efforts focusing on the identification of concussions, removal from play, and return-to-play protocols are necessary in the US rugby union population
Quantum Graphs II: Some spectral properties of quantum and combinatorial graphs
The paper deals with some spectral properties of (mostly infinite) quantum
and combinatorial graphs. Quantum graphs have been intensively studied lately
due to their numerous applications to mesoscopic physics, nanotechnology,
optics, and other areas.
A Schnol type theorem is proven that allows one to detect that a point
belongs to the spectrum when a generalized eigenfunction with an subexponential
growth integral estimate is available. A theorem on spectral gap opening for
``decorated'' quantum graphs is established (its analog is known for the
combinatorial case). It is also shown that if a periodic combinatorial or
quantum graph has a point spectrum, it is generated by compactly supported
eigenfunctions (``scars'').Comment: 4 eps figures, LATEX file, 21 pages Revised form: a cut-and-paste
blooper fixe
Quantization of the Riemann Zeta-Function and Cosmology
Quantization of the Riemann zeta-function is proposed. We treat the Riemann
zeta-function as a symbol of a pseudodifferential operator and study the
corresponding classical and quantum field theories. This approach is motivated
by the theory of p-adic strings and by recent works on stringy cosmological
models. We show that the Lagrangian for the zeta-function field is equivalent
to the sum of the Klein-Gordon Lagrangians with masses defined by the zeros of
the Riemann zeta-function. Quantization of the mathematics of Fermat-Wiles and
the Langlands program is indicated. The Beilinson conjectures on the values of
L-functions of motives are interpreted as dealing with the cosmological
constant problem. Possible cosmological applications of the zeta-function field
theory are discussed.Comment: 14 pages, corrected typos, references and comments adde
Linear instability criteria for ideal fluid flows subject to two subclasses of perturbations
In this paper we examine the linear stability of equilibrium solutions to
incompressible Euler's equation in 2- and 3-dimensions. The space of
perturbations is split into two classes - those that preserve the topology of
vortex lines and those in the corresponding factor space. This classification
of perturbations arises naturally from the geometric structure of
hydrodynamics; our first class of perturbations is the tangent space to the
co-adjoint orbit. Instability criteria for equilibrium solutions are
established in the form of lower bounds for the essential spectral radius of
the linear evolution operator restricted to each class of perturbation.Comment: 29 page
On the derivation of the t-J model: electron spectrum and exchange interactions in narrow energy bands
A derivation of the t-J model of a highly-correlated solid is given starting
from the general many-electron Hamiltonian with account of the
non-orthogonality of atomic wave functions. Asymmetry of the Hubbard subbands
(i.e. of ``electron'' and ``hole''cases) for a nearly half-filled bare band is
demonstrated. The non-orthogonality corrections are shown to lead to occurrence
of indirect antiferromagnetic exchange interaction even in the limit of the
infinite on-site Coulomb repulsion. Consequences of this treatment for the
magnetism formation in narrow energy bands are discussed. Peculiarities of the
case of ``frustrated'' lattices, which contain triangles of nearest neighbors,
are considered.Comment: 4 pages, RevTe
Wavefront sets and polarizations on supermanifolds
In this paper we develop the foundations for microlocal analysis on supermanifolds. Making use of pseudodifferential operators on supermanifolds as introduced by Rempel and Schmitt, we define a suitable notion of super wavefront set for superdistributions which generalizes Dencker's polarization sets for vector-valued distributions to supergeometry. In particular, our super wavefront sets detect polarization information of the singularities of superdistributions. We prove a refined pullback theorem for superdistributions along supermanifold morphisms, which as a special case establishes criteria when two superdistributions may be multiplied. As an application of our framework, we study the singularities of distributional solutions of a supersymmetric field theory
Mixed Weyl Symbol Calculus and Spectral Line Shape Theory
A new and computationally viable full quantum version of line shape theory is
obtained in terms of a mixed Weyl symbol calculus. The basic ingredient in the
collision--broadened line shape theory is the time dependent dipole
autocorrelation function of the radiator-perturber system. The observed
spectral intensity is the Fourier transform of this correlation function. A
modified form of the Wigner--Weyl isomorphism between quantum operators and
phase space functions (Weyl symbols) is introduced in order to describe the
quantum structure of this system. This modification uses a partial Wigner
transform in which the radiator-perturber relative motion degrees of freedom
are transformed into a phase space dependence, while operators associated with
the internal molecular degrees of freedom are kept in their original Hilbert
space form. The result of this partial Wigner transform is called a mixed Weyl
symbol. The star product, Moyal bracket and asymptotic expansions native to the
mixed Weyl symbol calculus are determined. The correlation function is
represented as the phase space integral of the product of two mixed symbols:
one corresponding to the initial configuration of the system, the other being
its time evolving dynamical value. There are, in this approach, two
semiclassical expansions -- one associated with the perturber scattering
process, the other with the mixed symbol star product. These approximations are
used in combination to obtain representations of the autocorrelation that are
sufficiently simple to allow numerical calculation. The leading O(\hbar^0)
approximation recovers the standard classical path approximation for line
shapes. The higher order O(\hbar^1) corrections arise from the noncommutative
nature of the star product.Comment: 26 pages, LaTeX 2.09, 1 eps figure, submitted to 'J. Phys. B.
Cantor and band spectra for periodic quantum graphs with magnetic fields
We provide an exhaustive spectral analysis of the two-dimensional periodic
square graph lattice with a magnetic field. We show that the spectrum consists
of the Dirichlet eigenvalues of the edges and of the preimage of the spectrum
of a certain discrete operator under the discriminant (Lyapunov function) of a
suitable Kronig-Penney Hamiltonian. In particular, between any two Dirichlet
eigenvalues the spectrum is a Cantor set for an irrational flux, and is
absolutely continuous and has a band structure for a rational flux. The
Dirichlet eigenvalues can be isolated or embedded, subject to the choice of
parameters. Conditions for both possibilities are given. We show that
generically there are infinitely many gaps in the spectrum, and the
Bethe-Sommerfeld conjecture fails in this case.Comment: Misprints correcte
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