Fine Structure of the Optical Spectra of Bismuth Triiodide

Full sets of the optical functions of a BiI₃ crystal in the range 1–5 eV have been calculated from the experimental spectra ₁(E) and ₂(E) for the polarizations E c and E c at 300 K. The spectra of permittivity and volumetric characteristic losses have been decomposed into elementary components and their main parameters have been determined. A schematic representation of the nature of the basic maxima of transitions on the basis of the well-known theoretical calculations of the bands and spectra of reflection of the BiI₃ crystal has been suggested.     

Numerical simulation of heavy hole cyclotron resonance NEMAG inp-Ge

The cyclotron resonance of heavy holes in germanium underE ₀B ₀[001] fields is simulated by the numerical Monte-Carlo technique. Linear and non-linear regimes of hot hole interaction with high-frequency transverse electric field E [0 0 1] are considered. A new procedure for the calculation of components of the gyrotropic part of the hot hole differential mobility tensor is proposed. We concentrate mainly on negative transverse effective mass hot holes.     

Optical properties of barite in the infrared and far infrared ranges

Far infrared and infrared reflectivity was measured for barite single crystal using polarized light. Twenty six oscillators were observed. The real and imaginary parts of the complex dielectric function were obtained by a fitting procedure for three directions (E a;E b andE c). Group theory analysis has been done in detail and the number and position of experimentally observed infrared active modes were compared with the theoretical predictions.     

Random aggregation and random-walking center of mass

Two random aggregation models are used in demonstrating the properties of the random displacementsr _i of the center of mass of aggregating particles. It is found that r _i is a randomly decreasing sequence that scales with the cluster size (steps)s and _i ^=1/s r _i s ^1/D , whereD is the fractal dimension. The center-of-mass random walk is a consistent representation of the dynamics of aggregation.     

Infrared and Raman study of Si2Te3

Results of ir and Raman investigations on trigonal layer-structured Si₂Te₃ single crystals are reported. The ir reflection spectrum withEc exhibits seven reststrahl-like bands, whereas the corresponding spectrum withEc shows only one very small bump. Values for ₀ and are given. The Raman spectra are very rich in structure and can only be interpreted qualitatively as being a mixture of single phonon lines and one- and two-phonon density-of-states contributions. One-phonon density-of-states effects are disorder-induced owing to the statistical occurrence of the Si atoms within the regular hexagonal Te sublattice.     

Inequalities for the Schattenp-norm. III

We present some inequalities for the Schattenp-norm of operators on a Hilbert space. It is shown, among other things, that ifA is an operator such that ReAa0, then for any operatorX, AX+XA* _p 2aX _p . Also, for any two operatorsA andB, A–B ₂ ² +A*B* ₂ ² 2A–B ₂ ² .     

Real-space renormalization group for directed percolation system

We use the recently proposed real-space renormalization group method to study the critical behavior of directed percolation system in two dimensions. The correlation length exponents and are found to be 1.76 and 1.15. These results are in good agreements with the best known values.     

On the Existence of a Maximizer for the Strichartz Inequality

It is shown that a maximizing function u _*L ² does exist for the Strichartz inequality e ^it _x ² u _L ⁶ _t (L ⁶ _x )Su _L ², with S>0 being the sharp constant.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Renormalization group equations with several length scales and crossover scaling functions for axial anisotropy

The critical behaviour of axially anisotropicn-vector models is characterized by two distinct length scales, the correlation lengths and for the easy and hard axes. In order to handle the full range of anisotropics from to partial differential renormalization group equations are derived, depending on and . The anisotropicX-Y model is studied in detail near four dimensions. The crossover scaling functions for the susceptibilities are calculated to first order in=4–d. Two distinct crossover regions are found for weak and dominant anisotropy, respectively.     

Negative mass cyclotron resonance maser

Physical principles, design and operation characteristics of a negative mass cyclotron resonance maser inp-type germanium are considered in this paper. The formation of anisotropic inverted distributions of negative effective mass heavy holes in strong electric and magnetic fieldsE H [001], resulting in negative conductivity in the millimetre and submillimetre wavelength ranges, is discussed. The generation is observed at 0.9 to 8mm in low compensated germanium samples with the hole concentration rangeN ₀ 2×10¹² to 2×10¹⁴ cm^–3 at low temperaturesT 25 K in electric fieldsE 40 to 350Vcm^–1. The maser frequency is tuned by the magnetic field corresponding to a cyclotron resonance frequency of carriers with an effective mass ofm _c 0.4m ₀. The spectral width of the emission in single mode operation does not exceed several megahertz. A pulse duration of 1 to 200 s and a repetition rate off _rep 1 to 200 Hz has been obtained limited by sample heating. Possibilities of improving the maser characteristics inp-Ge as well as in other A_III B_v semiconductors and the perspectives of new frequency tuning methods due to the application of uniaxial stress and magnetic field are demonstrated.     

Multiatom interactions,order and stability in binary transition metal alloys

Interface delocalization or depinning transitions such as wetting or surface induced disorder are considered. At these transitions, the correlation length for transverse correlations parallel to the surface diverges. These correlations are studied in the framework of Landau theory. It is shown the t^–1/2 at all types of transitions for systems with short-range forces wheret measures the distance from bulk coexistence.     

Structure of Electron Transitions of Corundum

The integral spectra of the dielectric permeability of corundum within the region 8–40 eV in the polarizations E C and E C are decomposed into 18 Lorentz elementary oscillators. Their principal parameters, namely, the energy E _i , halfwidth H _i , band area S _i , and height of the maximum _2max, are calculated and the main features are established. An analysis of the wellknown results obtained by two models of the reproduction of the ₂ spectra with the aid of a large number of fitting parameters and theoretical calculations of the corundum bands is carried out.     

Low-temperature phase transitions in GdS,GdSe and GdTe

In the Gd monochalcogenides up to three different structural distortions have been detected in the magnetically ordered regime. Our experiments indicate that all three phases show type II antiferromagnetic order but with different orientations of the magnetic moments: A truly trigonal phase withm _k k=[1/2, 1/2, 1/2], a monoclinic phase withabc, =/2+, and the spins oriented along [110], and a pseudo-rhombohedrally compressed monoclinic phase with the spins in the (111) planes. The spin flips can be accounted for by a model including anisotropic exchange interactions.     

The influence of a surface on Ising and conjugate model spin correlations atT=T c

We calculate rigorously the two-point correlation function in the 2-d Ising model on a quasi-cylindrical lattice at the critical temperatureT _c .The scaling predictions for the surface critical exponents = 5/8, = 1 are confirmed and the change from surface to bulk behavior is studied. By a correspondence relation the results are mapped to the conjugate model, a subcase of the 8-vertex model. We find in this model = 5/4, = 2.     

Some properties of a collision term of a kinetic equation in a magnetic field

The collision term of a Fokker-Planck type kinetic equation is derived for the case of a two component magnetized plasma. It is shown that the collision processes are fully described by one symmetric two-dimensional dyadicQ. The collision term is modified for the case in which the distribution function of the field particles is Maxwellian.Conditions under which the magnetic Rosenbluth potentials can be introduced are studied. It is shown, in case that the distribution function of the field particles is Maxwellian, that the coefficients of friction and diffusion are expressible in terms of two scalar potentials only if _a = 0 or if the components D and D of the difusion coefficient are constant with respect to _a , for arbitrary _b of the field particles.     

Correlation functionals of infinite volume quantum spin systems

The existence and analyticity of the correlation functionals of a quantum lattice in the infinite volume limit is proved. The result is valid at sufficiently high temperatures and for a large class of interactions. Our method estimates the kernelK for a set of Kirkwood-Salzburg equations. While a naive estimate would indicate that K =, we take into account cancellations between different contributions toK in order to show that for sufficiently high temperatures K <1, and this estimate is independent of the volume of the system.Supported in part by the Air Force Office of Scientific Research.     

Elimination of variables in simple laser equations

The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (, ) and case 2 (, ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.     

Free carrier scattering mechanism in Bi2Se3 crystals

The single valley model proposed byKöhler andLandwehr is used for the calculation of transport parameters corresponding to pure Bi₂Se₃ crystals. From the measurements of transmission, reflectivity and the Hall constant the effective masses are determined,m _c =0·13m ₀ andm _c=0·56m ₀; using a simplification described in the paper the Fermi level is calculated to lie 0·14 eV above the bottom of the conduction band. This result allows us to conclude that a mixed mechanism of free carrier scattering exists inn-Bi₂Se₃ crystals, viz., the scattering by acoustic phonons prevails contributing about 75% and the scattering on ionized impurities contributes the remaining 25%. This result applies to pure Bi₂Se₃ crystals with free electron concentration 2×10¹⁹cm^–3.     

Long-range correlations at depinning transitions

Semi-infinite systems are considered with long-range surface fields B _z ^–(1+r) for large distancesz from the surface. The influence of such fields on the global phase diagram and on the critical singularities of depinning transitions is studied within Landau theory. For |B|0, the correlation length diverges as b ^–1/2 withb=|Bln|B^–(1+r). For finiteB, t ^v withv =(2+r)/(2+2r) wheret measures the distance from bulk coexistence. In the latter case, a Ginzburg criterion leads to the upper critical dimensiond ^*=(2+3r)/(2+r).