Harnack inequality and regularity for degenerate quasilinear elliptic equations

We prove Harnack inequality and local regularity results for weak solutions of a quasilinear degenerate equation in divergence form under natural growth conditions. The degeneracy is given by a suitable power of a strong $A_\infty$ weight. Regularity results are achieved under minimal assumptions on the coefficients and, as an application, we prove $C^{1,\alpha}$ local estimates for solutions of a degenerate equation in non divergence form

Atomic gallium laser spectroscopy with violet/blue diode lasers

We describe the operation of two GaN-based diode lasers for the laser spectroscopy of gallium at 403 nm and 417 nm. Their use in an external cavity configuration enabled the investigation of absorption spectroscopy in a gallium hollow cathode. We have analyzed the Doppler broadened profiles accounting for hyperfine and isotope structure and extracting both the temperature and densities of the neutral atomic sample produced in the glow discharge. We have also built a setup to produce a thermal atomic beam of gallium. Using the GaN-based diode lasers we have studied the laser induced fluorescence and hyperfine resolved spectra of gallium.Comment: 10 pages, 7 figure

Entanglement Content of Quantum Particle Excitations II. Disconnected Regions and Logarithmic Negativity

In this paper we study the increment of the entanglement entropy and of the (replica) logarithmic negativity in a zero-density excited state of a free massive bosonic theory, compared to the ground state. This extends the work of two previous publications by the same authors. We consider the case of two disconnected regions and find that the change in the entanglement entropy depends only on the combined size of the regions and is independent of their connectivity. We subsequently generalize this result to any number of disconnected regions. For the replica negativity we find that its increment is a polynomial with integer coefficients depending only on the sizes of the two regions. The logarithmic negativity turns out to have a more complicated functional structure than its replica version, typically involving roots of polynomials on the sizes of the regions. We obtain our results by two methods already employed in previous work: from a qubit picture and by computing four-point functions of branch point twist fields in finite volume. We test our results against numerical simulations on a harmonic chain and find excellent agreement

Detection of Tiny Mechanical Motion by Means of the Ratchet Effect

We propose a position detection scheme for a nanoelectromechanical resonator based on the ratchet effect. This scheme has an advantage of being a dc measurement. We consider a three-junction SQUID where a part of the superconducting loop can perform mechanical motion. The response of the ratchet to a dc current is sensitive to the position of the resonator and the effect can be further enhanced by biasing the SQUID with an ac current. We discuss the feasibility of the proposed scheme in existing experimental setups.Comment: 8 pages, 9 figure

Role of the target orientation angle and orbital angular momentum in the evaporation residue production

The influence of the orientation angles of the target nucleus symmetry axis relative to the beam direction on the production of the evaporation residues is investigated for the $^{48}$Ca+$^{154}$Sm reaction as a function of the beam energy. At low energies ($E_{\rm c.m.}<$137 MeV), the yield of evaporation residues is observed only for collisions with small orientation angles ($\alpha_T<45^0$). At large energies (about $E_{\rm c.m.}=$140--180 MeV) all the orientation angles $\alpha_T$ can contribute to the evaporation residue cross section $\sigma_{ER}$ in the 10--100 mb range, and at $E_{c.m.}>$180 MeV $\sigma_{ER}$ ranges around 0.1--10 mb because the fission barrier for a compound nucleus decreases by increasing its excitation energy and angular momentum.Comment: 20 pages, 10 figures, submitted to JPS

Minimal Models for a Superconductor-Insulator Conformal Quantum Phase Transition

Conformal field theories do not only classify 2D classical critical behavior but they also govern a certain class of 2D quantum critical behavior. In this latter case it is the ground state wave functional of the quantum theory that is conformally invariant, rather than the classical action. We show that the superconducting-insulating (SI) quantum phase transition in 2D Josephson junction arrays (JJAs) is a (doubled) $c=1$ Gaussian conformal quantum critical point. The quantum action describing this system is a doubled Maxwell-Chern-Simons model in the strong coupling limit. We also argue that the SI quantum transitions in frustrated JJAs realize the other possible universality classes of conformal quantum critical behavior, corresponding to the unitary minimal models at central charge $c=1-6/m(m+1)$.Comment: 4 pages, no figure

Simple scale interpolator facilitates reading of graphs

Set of cards with scale divisions and a scale finder permits accurate reading of the coordinates of points on linear or logarithmic graphs plotted on rectangular grids. The set contains 34 different scales for linear plotting and 28 single cycle scales for log plots

Sensitive methods for estimating the anchoring strength of nematic liquid crystals on Langmuir-Blodgett monolayers of fatty acids

The anchoring of the nematic liquid crystal N-(p-methoxybenzylidene)-p-butylaniline (MBBA) on Langmuir-Blodgett monolayers of fatty acids (COOHC$_{n}$H$_{2n+1}$) was studied as a function of the length of the fatty acid alkyl chains, $n$ ($n = 15, 17, 19, 21$). The monolayers were deposited onto ITO-coated glass plates which were used to assemble sandwich cells of various thickness that were filled with MBBA in the nematic phase. The mechanism of relaxation from the flow-induced quasi-planar to the surface-induced homeotropic alignment was studied for the four decreases linearly with increasing the length of the alkyl chains $n$ which suggests that the Langmuir-Blodgett film plays a role in the phenomenon. This fact was confirmed by a sensitive estimation of the anchoring strength of MBBA on the fatty acid monolayers after anchoring breaking which takes place at the transition between two electric-field--induced turbulent states, denoted as DSM1 and DSM2. It was found that the threshold electric field for the anchoring breaking, which can be considered as a measure of the anchoring strength, also decreases linearly as $n$ increases. Both methods thus possess a high sensitivity in resolving small differences in anchoring strength. In cells coated with mixed Langmuir-Blodgett monolayers of two fatty acids ($n=15$ and $n=17$) a maximum of the relaxation speed was observed when the two acids were present in equal amount. This observation homeotropic cells by changing the ratio between the components of the surfactant film.Comment: LaTeX article, 20 pages, 15 figures, 17 EPS files. 1 figure added, references moved. Submitted to Phys. Rev.