Anomalous anisotropies and field dependencies of the muon Knight shift and the relaxation rate in monocrystalline Bi

The angular dependence of the muon Knight shift,K _μ, and the muon relaxation rate in Bi at 11 K were measured in external magnetic fields up to 1 T. BothK _μ and the second moment,M ₂, are field dependent and involveP ₄ ⁰(cos θ) andP ₄ ³(cos θ) terms in the angular dependence. The Knight shift behaviour is discussed in terms of the dipole-dipole interaction and the de Haas-van Alphen effect, a consistent interpretation was not achieved in either case. The field dependence ofM ₂ is in complete contrast to the second moment calculations and points to a field dependent redistribution of the charge distribution around the interstitial site.     

Electromagnetic effects on a molecule at a metal surface: I. Effects of nonlocality and finite molecular size

The electromagnetic effects on a molecule near a metal surface are considered with the view to understanding the surface-enhanced-Raman-scattering (SERS) effect. The image enhancement effect is calculated including the nonlocal response of the metal and finite molecular size. The effect is much reduced (× 10^?5) from that for a point molecule above a local metal but can still give a gain ≈ 10³. The power emitted by a dipole above a smooth surface is also calculated. For an Ag surface the power emitted in the form of photons, surface plasmons, and electron-hole excitations are found to be in the ratio 1 : 3 : 10⁶. The numerical results are calculated using the semi-classical infinite-barrier model of the metal surface with a Lindhard dielectric function modified to take into account finite electron lifetime and core polarization.     

Some historical and technical aspects of beam quality

A survey is given on the various algorithms to describe the propagation of radiation fields in the paraxial approximation, starting with the Kirchhoff-Fresnel-Collins-integral and ending with the intensity moments and the generalizedABCD-law. The importance of characterizing beam quality for technical applications by suitable parameters is pointed out. The two competing definitions of beam parameters, intensity moments and power content values are discussed.     

Hadronic equation of state and the onset of kaon condensation

An equation of state is presented which takes the finite size of baryons and of mesons consistently into account and incorporates the contributions of both nonstrange and strange hadrons. All extensive quantities (energy, particle number, entropy) are modified by a factor taking into account the excluded volume due to baryon repulsion. Intensive quantities (pressure) are not modified. This is achieved by introducing a baryon chemical potential, _B, which is shifted from its point-like value, _B ⁰ , by a term proportional to the finite volume of a hadron,V ₀, as follows: _B= _B ⁰ + V₀[P⁰(T, _B ⁰ )–P⁰(T, 0)], whereP ⁰ is the pressure for pointlike particles. The last term is necessary to conserve baryon number at the phase transition point. The differences between the new equation of state and those considered previously in the literature are discussed. It is shown that kaon condensation sets in only in the mixed phase of the transition, where hadrons, quarks and gluons are present simultaneously in thermodynamical equilibrium.     

Connections between Romanovski and other polynomials

A connection between Romanovski polynomials and those polynomials that solve the one-dimensional Schrödinger equation with the trigonometric Rosen-Morse and hyperbolic Scarf potential is established. The map is constructed by reworking the Rodrigues formula in an elementary and natural way. The generating function is summed in closed form from which recursion relations and addition theorems follow. Relations to some classical polynomials are also given.     

Flow equations for the relevant part of the pure Yang—Mills action

Wilson’s exact renormalization group equations are derived and integrated for the relevant part of the pure Yang-Mills action. We discuss in detail how modified Slavnov—Taylor identities control the breaking of BRST invariance in the presence of a finite infrared cutoff k through relations among different parameters in the effective action. In particular they imply a nonvanishing gluon mass term for nonvanishing k. The requirement of consistency between the renormalization group flow and the modified Slavnov—Taylor identities allows to control the self—consistency of truncations of the effective action.     

Four-wave mixing in semiconductor laser amplifiers: Applications for optical communication systems

Four-wave mixing in semiconductor laser amplifiers enables various applications in photonic switching including wavelength conversion, space and time switching, optical phase conjugation, and demultiplexing. Switching times faster than 1 ps are possible.     

Supply function equilibria for uniform price auction in oligopolistic markets

We consider game-theoretic models related to the supply function auction for electricity markets. We determine the set of supply function equilibria (SFE), introduced by Klemperer and Mayer (Econometrica 57:1243–1277, 1989), for a symmetric oligopoly with linear demand, fixed marginal cost and capacity constraint. This set depends on the maximum random shock of the demand function. We also study the best response dynamics and show that in general it does not converge to any SFE. We find out sufficient conditions for the convergence and conclude on the optimal parameters of the auction.