Thermal lensing of laser beams in optically transmitting materials

Detailed numerical computations of thermal lensing in optically transmitting materials are carried out. The time evolution of the transmitted beam intensity, revealing defocusing and degradation effects, is displayed for a variety of materials, under a variety of geometrical configurations and operating conditions. While the degradation is monotonic with increasing time or incident power for materials with small induced birefringence, it may display an oscillatory character when birefringence effects are large. From the intensity degradation, criteria are formulated for rating optical performance of materials under transient and steady-state conditions. Ratings are obtained for a variety of transmitting materials at 10.6 μm. As a class, ionic materials are found to substantially outperform semiconductors and glasses at 10.6 μm.     

Critical exponents for NMR and ESR linewidths in a two-dimensional antiferromagnet

The exponent p in ΔH ∝ (T/T_N?1)^-p is derived both for NMR and ESR linewidths ΔH in a two-dimensional antiferromagnet. The approach is based on Kawasaki's dynamical equations. Comparison is made with experiments on K₂NiF₄ and K₂MnF₄.     

On the computation of electronic excitations in solids

An approximation scheme is proposed for calculating electronic excitations in solids. It is described within a projection operator formalism of the Mori-Zwanzig type. The approximation consists in successively limiting the space of dynamical variables which are treated. The selection of the variables is done by making use of the local character of the correlation hole which is surrounding an electron. The method is distinct from a perturbation expansion and can be related to a variational ansatz via the Sauermann functional. The computation of the spectral density of the Green's function is reduced to the diagonalization of matrices. Their dimension depends on the required degree of accuracy of the calculations. The present method can be considered as an extension to excited states of a previously developed. Local Approach for ground state calculations.Dedicated to Prof. S. Methfessel on the occasion of his 60th birthday     

Spectral measures and the Bade reflexivity theorem

Let $\text{B}$ be a strongly equicontinuous Boolean algebra of projections on the quasi-complete locally convex space X and assume that the space L(X) of continuous linear operators on X is sequentially complete for the strong operator topology. Methods of integration with respect to spectral measures are used to show that the closed algebra generated by $\text{B}$ in L(X) consists precisely of those continuous linear operators on X which leave invariant each closed $\text{B}$-invariant subspace of X.     

Collective cooling and self-organization of atoms in a cavity

We theoretically investigate the correlated dynamics of N coherently driven atoms coupled to a standing-wave cavity mode. For red detuning between the driving field and the cavity as well as the atomic resonance frequencies, we predict a light force induced self-organization of the atoms into one of two possible regular patterns, which maximize the cooperative scattering of light into the cavity field. Kinetic energy is extracted from the atoms by superradiant light scattering to reach a final kinetic energy related to the cavity linewidth. The self-organization starts only above a threshold of the pump strength and atom number. We find a quadratic dependence of the cavity mode intensity on the atom number, which demonstrates the cooperative effect.     

Einige ALGOL-Programme für Sortierverfahren

Blätter der DGVFM - Several ALGOL programs for sorting procedures are presented and their organization and applications are briefly discussed. Five of the programmes were checked on an IBM 650...     

Smoothed cross-validation

Summary For bandwidth selection of a kernel density estimator, a generalization of the widely studied least squares cross-validation method is considered. The essential idea is to do a particular type of presmoothing of the data. This is seen to be essentially the same as using the smoothed bootstrap estimate of the mean integrated squared error. Analysis reveals that a rather large amount of presmoothing yields excellent asymptotic performance. The rate of convergence to the optimum is known to be best possible under a wide range of smoothness conditions. The method is more appealing than other selectors with this property, because its motivation is not heavily dependent on precise asymptotic analysis, and because its form is simple and intuitive. Theory is also given for choice of the amount of presmoothing, and this is used to derive a data-based method for this choice.Research of the second author was done while on leave from the University of North Carolina. That of both the second and third was partially supported by National Science Foundation Grants DMS-8701201 and DMS-8902973     

High pressure photoluminescence and resonant Raman study of GaAs

Photoluminescence and resonant Raman scattering have been studied in GaAs under hydrostatic stress up to 72 kbar. From the pressure dependence of the photoluminescence intensity the pressure coefficient of the X₆ conduction band minimum in GaAs has been determined. The pressure dependence of zone edge phonon energies in GaAs is also reported.     

Heterolayer mobility in the Bloch-Grüneisen range

It is shown that, for two-dimensional heterolayer conduction at low temperatures, the phonon-scattering contribution to the reciprocal of the ohmic mobility has a Bloch-Grüneisen regime, for low enough temperatures T, in which the deformation coupling gives a term proportional to T⁷ and (for polar semiconductors) piezoelectric coupling gives a term proportional to T⁵. It is pointed out that there could be an intermediate temperature range with a slower T dependence.