Density of non-residues in Burgess-type intervals and applications

We show that for any fixed \eps>0, there are numbers $\delta>0$ and $p_0\ge 2$ with the following property: for every prime $p\ge p_0$ and every integer $N$ such that p^{1/(4\sqrt{e})+\eps}\le N\le p, the sequence $1,2,...,N$ contains at least $\delta N$ quadratic non-residues modulo $p$. 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 Nd1.85_{1.85}Ce0.15_{0.15}CuO4_4

The dispersion of the high-energy phonon modes in the electron doped high-temperature superconductor Nd$_{1.85}$Ce$_{0.15}$CuO$_4$ 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 Sr$_2$RuO$_4$ has been studied by inelastic neutron scattering combined with shell-model calculations. The in-plane bond-stretching modes in Sr$_2$RuO$_4$ 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 Sr$_2$RuO$_4$.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