Growth of resistance with density of scatterers in one dimensional wave propagation

We study wave propagation in a one-dimensional disordered array of scattering potentials. We consider three different ensembles of scatterer configurations: anN-ensemble with a fixed numberN of scatterers, anL-ensemble with a varying number of scatterers distributed over a fixed lengthL, and anNL-ensemble where bothN andL are fixed. The latter ensemble allows a detailed study of the mean resistance and its variance for a fixed lengthL as the number of scatterersN increases. We find that the Landauer result, which predicts an exponential increase of the mean resistance withN, is valid only in the low-density regime. At high density the mean resistance grows exponentially with N and the concept of optical potential applies. In the crossover regime we find an interesting resonance.     

On interesting walks in a graph

Notions of interesting walks and of their equivalence are introduced. A general formula for the number _l, of equivalence classes of interesting walks of lengthl in a given graphG is derived and applied forl 5 so as to express _l in terms of the adjacency matrix ofG.     

Delocalization transition of two-dimensional disordered systems in a strong magnetic field

The delocalization transition in two-dimensional systems and a strong magnetic field is investigated with respect to its dependence on the Landau band indexj and on the type of disorder. The generation of random potentials according to a given correlation functionf and for a chosen correlation lengthd is described. The spectral properties of random eigenvalue sequences are examined as measures for the extension of wavefunctions and indicate a nonuniversal delocalization behaviour in higher Landau bands for short ranged correlated potentials. The critical exponents of the localization length of wavefunctions are determined for rapidly varying potentials in the second lowest Landau band (j=1) and depend on the correlation lengthd of the disorder. This different critical behaviour compared to that in the lowest band is confirmed by calculations for the density-density correlations of wavefunctions at the centers of the Landau levels. Calculations in different geometries also show that the critical systems of delocalized states are conformal invariant in the case of the nonuniversal delocalization transition (dl ₀), whereas such local rescaling properties cannot be expected for slowly varying potentials.     

Grating tuned Ti:Sa laser for in-source spectroscopy of Rydberg and autoionizing states

Due to the large absorption cross section for optical transitions into Rydberg and autoionizing states compared to non-resonant ionization, these states are of particular interest for use in efficient laser resonance ionization excitation schemes as used in Resonant Ionization Laser Ion Sources (RILIS). In order to identify these atomic states extensive laser spectroscopy has to be performed. The lasers employed at TRIUMF’s laser ion source are birefringent filter tuned titanium:sapphire (Ti:Sa) lasers which are designed for long term frequency stability rather than continuous tuning. The design and characteristics of a grating tuned, high repetition rate, pulsed Ti:Sa laser for spectroscopy applications are presented. This laser allows fast scans of up to 40 THz with a laser linewidth of approximately 6 GHz. First tests were performed by scanning across the Rydberg series of gallium.     

Fabrication and low threshold current density CW operation of GaInAsP/InP multiple-reflector microcavity laser

We report CW operation of a GaInAsP/InP multiple-reflector microcavity (MRMC) laser operated at fairly low threshold current density. The threshold current density with broad contact (stripe widthW=240 m, cavity lengthL=60 m) under pulsed operation was 180 A cm^–2 (l _th=20 mA), and was 230 A cm^–2 under CW operation at room temperature operating at 1.52 m wavelength.     

1.55-μm non-anti-reflection-coated fiber grating laser for single-longitudinal mode operation

A 1.55-m fiber grating laser (FGL) was fabricated by optically packaging a non-anti-reflection (AR) coated Fabry–Perot (FP) laser to a lensed fiber grating. The FGL demonstrates a single-longitudinal mode operation with a side-mode suppression ratio (SMSR) of up to 40 dB. The SMSR oscillates and diminishes to <30 dB as the increase of injection current above 38 mA, and the tilt of the fiber approaches 5° away from the facet normal of the FP laser. We have performed numerical simulations on the single-longitudinal mode operation for the FGL. The SMSR for the FGL increases over 40 dB as the increase of the fiber grating reflectivity (R _g) above 0.7 with non-AR-coated FP laser facet. Our calculations also show that the strong current-dependent SMSR oscillation is from the mode selection by the fiber grating external cavity and the heating effect in the FP laser.     

Finite-size scaling for Potts models

Recently, Borgs and Kotecký developed a rigorous theory of finite-size effects near first-order phase transitions. Here we apply this theory to the ferromagneticq-state Potts model, which (forq large andd2) undergoes a first-order phase transition as the inverse temperature is varied. We prove a formula for the internal energy in a periodic cube of side lengthL which describes the rounding of the infinite-volume jumpE in terms of a hyperbolic tangent, and show that the position of the maximum of the specific heat is shifted by _m (L)=(Inq/E)L ^–d +O(L ^–2d ) with respect to the infinite-volume transition point _t . We also propose an alternative definition of the finite-volume transition temperature _t (L) which might be useful for numerical calculations because it differs only by exponentially small corrections from _t .     

Analysis of sensitivity and low-frequency intensity noise characteristics of Bragg reflector lasers induced by reflected light

An analysis of the sensitivity and low-frequency intensity noise characteristics of Bragg reflector lasers is given. It is found that Bragg reflector lasers have increased sensitivity to reflected light for low grating coupling strength (l) and is similar to that of Fabry-Perot lasers except for highl values. Also, the intensity noise can be reduced by operating the device at high injection level.     

Attractors in the fully asymmetric SK-model

The mean number of attractors of arbitrary lengthl is calculated explicitly in the fully asymmetric SK-model (<J _ij J _ij >=0) for parallel dynamics and at zero temperature. Forl=2 large finite size effects are observed with a broad maximum around a system size ofN=53 (Gaussian interactions). The basin of attraction of the metastable states for one time step increases exponentially with the system size and the exponent is 0.16.     

Group theory and kink stability equations

Starting from Schrödinger equations withSU(2) group-theoretic potentials, we consider a general family of kinks labeled by two (half-)integers (l, n) with ¦n¦l. A particular choice ofn=0,l=L (L positive integer) leads to a generalL-family, whereL=1 corresponds to sine-Gordon theory, whileL=2 represents the ( ⁴)₁₊₁ model. The ( ⁶)₁₊₁ model can also be recovered withl=3/2,n=–1/2, a particular case of theories labeled byl andn such thatl-n=2 which possess simple kink solutions. We also discuss one-loop order corrections to the kink masses in supersymmetric versions of theL-family. As a byproduct, we obtain the SUSY renormalization of the so-called parameter in sine-Gordon theory.     

First-order phase transitions in finite-size strips with interfaces

Finite-size rounding of the magnetization discontinuity at the magnetic phase transition atH=0 (T<T _c ) in 2d Ising-type strips of sizeL ×L , with ± boundary conditions alongL inducing an interface of lengthL , is studied by phenomenological considerations and transfer matrix techniques. Scaling expressions are derived forL =O(L ) and also in the infinite strip limitL . Most of the results can be extended to the 3d case.     

Physics of the Schwinger model

The Coulomb gas of massless fermions (Schwinger model) is solved in a one-dimensional space of finite lengthL using the boson representation of fermions. Special attention is paid to boundary effects and global degrees of freedom. It is shown that the mean current is not conserved, but oscillates. The theory is constructed in all charge sectors. The Wightman functions are calculated and the limitL is discussed.Work performed within the research program of the Sonderforschungsbereich 125, Aachen-Jülich-Köln     

Hypothesis of the fundamental length and quantum electrodynamics

Under the hypothesis of a fundamental lengthl ₀, the Bopp equation is considered as a basic equation of motion instead of the Klein-Gordon equation. Assuming that the mass is a function of₀, we derive a mass relationm(/2l ₀ c). The propagators obtained in the framework of the present theory have the same types as those with a simple cutoff. However, because of the mass relation, the tildon field with indefinite metric is always confined in the virtual state and never appears in real processes as a physical entity. Thus, our new version leads to a finite theory of quantum electrodynamics.     

Critical properties and finite-size effects of the five-dimensional Ising model

Monte Carlo calculations of the thermodynamic properties (energy, specific heat, magnetization suceptibility, renormalized coupling) of the nearest-neighbour Ising ferromagnet on a five-dimensional hypercubic lattice are presented and analyzed. Lattices of linear dimensionsL=3, 4, 5, 6, 7 with periodic boundary conditions are studied, and a finite size scaling analysis is performed, further confirming the recent suggestion thatL does not scale with the correlation length (the temperature variation of which near the critical temperatureT _c is |1-T/T _c |^–1/2), but rather with a thermodynamic lengthl (withl|1-T/T _c |^–2/d ,d=5 here). The susceptibility (extrapolated to the thermodynamic limit) agrees quantitatively with high temperature series extrapolations of Guttmann. The problem of fluctuation corrections to the leading (Landau-like) critical behaviour is briefly discussed, and evidence given for a specific-heat singularity of the form |1-T/T _c |^1/2, superimposed on its leading jump.Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday     

Monte Carlo renormalization of hard sphere polymer chains in two to five dimensions

A renormalization group for polymer chains with hard-core interaction is considered, where a chain ofN ₀ links of lengthl ₀ and hard-core diameterh ₀ is mapped onto a chain ofN ₁=N ₀/s links of lengthl ₁ and hard-core diameterh ₁. The lengthl ₁ is defined in terms of suitable interior distances of the original chain, andh ₁ is found from the condition that the end-to-end distance is left invariant. This renormalization group procedure is carried through by various Monte-Carlo methods (simple sampling is found advantageous for short enough chains or high dimensionalities, while dynamic methods involving kinkjumps or reptation are used else). Particular attention is paid to investigate systematic errors of the method by checking the dependence of the results on bothN ₀ ands. It is found that for dimensionalitiesd=2, 3 only the nontrivial fixed-point is stable, where upon iteration the ratio _k =h _k /l _k tends to nonzero fixed-point value ^*, while ford=4,5 the method converges to the gaussian fixed point with ^*=0. Taking both statistical and systematic errors into account, we estimate the exponentv asv=0.74±0.01 (d=2) andv =0.59±0.01 (d=3). The results are consistent with the expected crossover exponents =1/2 (d=3) and =1 (d=2), respectively.     

The Hermitian intensity matrix of a multipole transition

TheL-pole transition is described by a Hermitian (2L+1)×(2L+1) matrix. The incoherent absorption process of the nuclei in a crystal allows to sum up the matrices of all transitions at the same energy. The result is an intensity matrix of the crystal. The evaluation of the polarisation state of dipole transitions dependent on the -direction can be done by very simple tensor equations.     

Stochastic and quantum space-time metrics and the weak-field limit

In this review we present a simple method of introducing stochastic and quantum metrics into gravitational theory at short distances in terms of small fluctuations around a classical background space-time. We consider only residual effects due to the stochastic (or quantum) theory of gravity and use a perturbative stochastization (or quantization) method. By using the general covariance and correspondence principles, we reconstruct the theory of gravitational, mechanical, electromagnetic, and quantum mechanical processes and tensor algebra in the space-time with stochastic and quantum metrics. Some consequences of the theory are also considered, in particular, it indicates that the value of the fundamental lengthl lies in the interval 10^–23l10^–22 cm.     

Calculation and optimization of parameters of radiating distributed feedback structures

A simple method is suggested for calculation of reflection, radiation and transmission coefficients for the distributed feedback structure in the second diffraction order. The method is based on a slight difference between coefficients of reflectionR and radiationI of the surface wave for = (where is the light wavelength corresponding to a precise resonance for the grating length I) and those for =_l (where _l is the light wavelength corresponding to the resonance for the finite grating length). The simplicity of the method makes it possible to use it for optimization of the distributed feedback structure by a number of parameters. The technique can be used in the case of thin-film and diffused waveguides for both TE and TM modes.     

Phase-conjugate bistability and multistability in moving-grating operated orthogonally polarized pump four-wave mixing in photorefractives

We establish possible regions of bistability (BIST), multistability (MUST), hysteresis, self-oscillation (SO) and enhancement features of the phase-conjugate reflectivity (PCR) by use of moving-grating operation (MGO) in the orthogonally polarized pump four-wave mixing (OPP-FWM) geometry employing a photorefractive (PR) crystal (usually BaTiO₃). Numerical evaluation of such PCR features has been presented as a function of parameters such as coupling strength (of complex gL and real g ₀ L values), frequency-shift () owing to grating motion, the PR phase shift (ø_PR), and pump (r) and probe (q) intensity ratios. PCR results of this geometry are compared with those obtained from the regular (i.e. parallel-polarized pump) four-wave mixing (REG-FWM) geometry assuming the same set of parameters in both geometries. We find that the OPP geometry leads to a drastic PCR enhancement together with the appearance of a rich variety of multibranched solutions exhibiting BIST and MUST features of the PCR, particularly in the range 0.5 3 with values g ₀L 10, r=1 and q 0.1 that are practically realizable. Nevertheless, this geometry sometimes offers the possibility of a PCR jump (from one stable state to the other), suggesting hysteresis caused by changing only slightly. In the REG geometry, however, the PCR enhancement is less prominent, and also the BIST/MUST features rarely exist unless g ₀ L becomes sufficiently large, say 20 or more.     

Hyperfine Structure of the Configuration lll

The matrix elements for the hyperfine structure of the configuration lll in SL-Kopplung are expressed as linear combinations of the electron coupling constants α_li(10), α_li(01), α_li(12).