60,076 research outputs found
Density of non-residues in Burgess-type intervals and applications
We show that for any fixed \eps>0, there are numbers and with the following property: for every prime and every integer
such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence
contains at least quadratic non-residues modulo . We use this
result to obtain strong upper bounds on the sizes of the least quadratic
non-residues in Beatty and Piatetski--Shapiro sequences.Comment: In the new version we use an idea of Roger Heath-Brown (who is now a
co-author) to simply the proof and improve the main results of the previous
version, 14 page
Fluctuations and massive separation in three-dimensional shock-wave/boundary-layer interactions
Shock-wave unsteadiness was observed in rapidly compressed supersonic turbulent boundary layer flows with significant separation. A Mach 2.85 shock-wave/turbulent boundary layer flow was set up over a series of cylinder-flare bodies in the High Reynolds Number Channel 1. The transition from fully attached to fully separated flow was studied using axisymmetric flares with increasing compression angles. In the second phase, the 30 deg flare was inclined relative to the cylinder axis, so that the effect on a separated flow of increasing 3 dimensionality could be observed. Two 3-D separated cases are examined. A simple conditional sampling technique is applied to the data to group them according to an associated shock position. Mean velocities and turbulent kinetic energies, computed from the conditionally samples data, are compared to those from the unsorted data and to computed values. Three basic questions were addressed: can conditional sampling be used to provide snapshots of the flow; are averaged turbulence quantities dominated by the bimodal nature of the interaction; and is the shock unsteadiness really important to computational accuracy
Anomalous diffusion in quantum Brownian motion with colored noise
Anomalous diffusion is discussed in the context of quantum Brownian motion
with colored noise. It is shown that earlier results follow simply and directly
from the fluctuation-dissipation theorem. The limits on the long-time
dependence of anomalous diffusion are shown to be a consequence of the second
law of thermodynamics. The special case of an electron interacting with the
radiation field is discussed in detail. We apply our results to wave-packet
spreading
Thermally activated escape rates of uniaxial spin systems with transverse field
Classical escape rates of uniaxial spin systems are characterized by a
prefactor differing from and much smaller than that of the particle problem,
since the maximum of the spin energy is attained everywhere on the line of
constant latitude: theta=const, 0 =< phi =< 2*pi. If a transverse field is
applied, a saddle point of the energy is formed, and high, moderate, and low
damping regimes (similar to those for particles) appear. Here we present the
first analytical and numerical study of crossovers between the uniaxial and
other regimes for spin systems. It is shown that there is one HD-Uniaxial
crossover, whereas at low damping the uniaxial and LD regimes are separated by
two crossovers.Comment: 4 PR pages, 3 figures, final published versio
Dispersion of the high-energy phonon modes in NdCeCuO
The dispersion of the high-energy phonon modes in the electron doped
high-temperature superconductor NdCeCuO has been studied
by inelastic neutron scattering. The frequencies of phonon modes with Cu-O
bond-stretching character drop abruptly when going from the Brillouin zone
center along the [100]-direction; this dispersion is qualitatively similar to
observations in the hole-doped cuprates. We also find a softening of the
bond-stretching modes along the [110]-direction but which is weaker and
exhibits a sinusoidal dispersion. The phonon anomalies are discussed in
comparison to hole-doped cuprate superconductors and other metallic
perovskites
Remarks on Conserved Quantities and Entropy of BTZ Black Hole Solutions. Part I: the General Setting
The BTZ stationary black hole solution is considered and its mass and angular
momentum are calculated by means of Noether theorem. In particular, relative
conserved quantities with respect to a suitably fixed background are discussed.
Entropy is then computed in a geometric and macroscopic framework, so that it
satisfies the first principle of thermodynamics. In order to compare this more
general framework to the prescription by Wald et al. we construct the maximal
extension of the BTZ horizon by means of Kruskal-like coordinates. A discussion
about the different features of the two methods for computing entropy is
finally developed.Comment: PlainTEX, 16 pages. Revised version 1.
Lattice dynamics and electron-phonon coupling in Sr2RuO4
The lattice dynamics in SrRuO has been studied by inelastic neutron
scattering combined with shell-model calculations. The in-plane bond-stretching
modes in SrRuO exhibit a normal dispersion in contrast to all
electronically doped perovskites studied so far. Evidence for strong electron
phonon coupling is found for c-polarized phonons suggesting a close connection
with the anomalous c-axis charge transport in SrRuO.Comment: 11 pages, 8 figures 2 table
Interaction potential in compact three-dimensional QED with mixed action
We use a variational wave function to calculate the energy of the interaction
between external charges in the compact Abelian gauge theory in 2+1 dimensions
with mixed action. Our variational wave functions preserve the compact gauge
invariance of the theory both in the vacuum and in the charged sectors. We find
that a good estimate of the interaction energy is obtained only when we allow
more variational parameters in the charged sector than in the vacuum sector.
These extra parameters are the profile of an induced electric field. We find
that the theory has a two-phase structure: When the charge-2 coupling is large
and negative there is no mass gap in the theory and no confinement, while
otherwise a mass gap is generated dynamically and the theory confines charges.
The pure Wilson theory is in the confining phase.Comment: 22 pages, Latex -- final version, minor changes from first versio
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