32,147 research outputs found
On Wilson Criterion
U(1) gauge theory with the Villain action on a cubic lattice approximation of
three- and four-dimensional torus is considered. The naturally chosen
correlation functions converge to the correlation functions of the R-gauge
electrodynamics on three- and four-dimensional torus as the lattice spacing
approaches zero only for the special scaling. This special scaling depends on a
choice of a correlation function system. Another scalings give the degenerate
continuum limits. The Wilson criterion for the confinement is ambiguous. The
asymptotics of the smeared Wilson loop integral for the large loop perimeters
is defined by the density of the loop smearing over a torus which is
transversal to the loop plane. When the initial torus radius tends to infinity
the correlation functions converge to the correlation functions of the R-gauge
Euclidean electrodynamics.Comment: latex, 6 page
Global well-posedness and scattering for the defocusing mass-critical Schr\"odinger equation in the three-dimensional hyperbolic space
In this paper, we prove that the initial value problem for the mass-critical
defocusing nonlinear Schr\"odinger equation on the three-dimensional hyperbolic
space is globally well-posed and scatters for data with radial
symmetry in the critical space .Comment: arXiv admin note: substantial text overlap with arXiv:1008.1237 by
other author
Modified Scattering of Cubic Nonlinear Schr\"odinger Equation on Rescaled Waveguide Manifolds
We use modified scattering theory to demonstrate that small-data solutions to
the cubic nonlinear Schr\"odinger equation on rescaled waveguide manifolds,
for , demonstrate boundedness of
Sobolev norms as well as weak instability
Masses and Majorana fermions in graphene
We review the classification of all the 36 possible gap-opening instabilities
in graphene, i.e., the 36 relativistic masses of the two-dimensional Dirac
Hamiltonian when the spin, valley, and superconducting channels are included.
We then show that in graphene it is possible to realize an odd number of
Majorana fermions attached to vortices in superconducting order parameters if a
proper hierarchy of mass scales is in place.Comment: Contribution to the Proceedings of the Nobel symposium on graphene
and quantum matte
Induced scattering of short radio pulses
Effect of the induced Compton and Raman scattering on short, bright radio
pulses is investigated. It is shown that when a single pulse propagates through
the scattering medium, the effective optical depth is determined by the
duration of the pulse but not by the scale of the medium. The induced
scattering could hinder propagation of the radio pulse only if close enough to
the source a dense enough plasma is presented. The induced scattering within
the relativistically moving source places lower limits on the Lorentz factor of
the source. The results are applied to the recently discovered short
extragalactic radio pulse.Comment: submitted to Ap
Rayleigh-Brillouin scattering in SF in the kinetic regime
Rayleigh-Brillouin spectral profiles are measured with a laser-based
scatterometry setup for a 90 degrees scattering angle at a high signal-to-noise
ratio (r.m.s. noise below 0.15 \% w.r.t. peak intensity) in
sulphur-hexafluoride gas for pressures in the range 0.2 -- 5 bar and for a
wavelength of nm. The high quality data are compared to a
number of light scattering models in order to address the effects of rotational
and vibrational relaxation. While the vibrational relaxation rate is so slow
that vibration degrees of freedom remain frozen, rotations relax on time scales
comparable to those of the density fluctuations. Therefore, the heat capacity,
the thermal conductivity and the bulk viscosity are all frequency-dependent
transport coefficients. This is relevant for the Tenti model that depends on
the values chosen for these transport coefficients. This is not the case for
the other two models considered: a kinetic model based on rough-sphere
interactions, and a model based on fluctuating hydrodynamics. The deviations
with the experiment are similar between the three different models, except for
the hydrodynamic model at pressures . As all models
are in line with the ideal gas law, we hypothesize the presence of real gas
effects in the measured spectra.Comment: 8 pages, 3 figures, Chemical Physics Letters 201
Symmetric Groups and Quotient Complexity of Boolean Operations
The quotient complexity of a regular language L is the number of left
quotients of L, which is the same as the state complexity of L. Suppose that L
and L' are binary regular languages with quotient complexities m and n, and
that the transition semigroups of the minimal deterministic automata accepting
L and L' are the symmetric groups S_m and S_n of degrees m and n, respectively.
Denote by o any binary boolean operation that is not a constant and not a
function of one argument only. For m,n >= 2 with (m,n) not in
{(2,2),(3,4),(4,3),(4,4)} we prove that the quotient complexity of LoL' is mn
if and only either (a) m is not equal to n or (b) m=n and the bases (ordered
pairs of generators) of S_m and S_n are not conjugate. For (m,n)\in
{(2,2),(3,4),(4,3),(4,4)} we give examples to show that this need not hold. In
proving these results we generalize the notion of uniform minimality to direct
products of automata. We also establish a non-trivial connection between
complexity of boolean operations and group theory
Physics of Interpulse Emission in Radio Pulsars
The magnetized induced Compton scattering off the particles of the
ultrarelativistic electron-positron plasma of pulsar is considered. The main
attention is paid to the transverse regime of the scattering, which holds in a
moderately strong magnetic field. We specifically examine the problem on
induced transverse scattering of the radio beam into the background, which
takes place in the open field line tube of a pulsar. In this case, the
radiation is predominantly scattered backwards and the scattered component may
grow considerably. Based on this effect, we for the first time suggest a
physical explanation of the interpulse emission observed in the profiles of
some pulsars. Our model can naturally account for the peculiar spectral and
polarization properties of the interpulses. Furthermore, it implies a specific
connection of the interpulse to the main pulse, which may reveal itself in the
consistent intensity fluctuations of the components at different timescales.
Diverse observational manifestations of this connection, including the moding
behavior of PSR B1822-09, the peculiar temporal and frequency structure of the
giant interpulses in the Crab pulsar, and the intrinsic phase correspondence of
the subpulse patterns in the main pulse and the interpulse of PSR B1702-19, are
discussed in detail. It is also argued that the pulse-to-pulse fluctuations of
the scattering efficiency may lead to strong variability of the interpulse,
which is yet to be studied observationally. In particular, some pulsars may
exhibit transient interpulses, i.e. the scattered component may be detectable
only occasionally.Comment: 28 pages, 2 figures. Accepted for publication in Ap
- …