On the Nature of the “Low-Temperature Anomaly” in Metal–Semiconductor Schottky-Barrier Contacts

It is shown that the low-temperature anomaly of the I-V characteristics of homogeneous metal–semiconductor Schottky-barrier contacts (an increase in the ideality factor n and a decrease in the barrier height _bm, measured using the saturation current, with decreasing temperature, as well as the fact that their product _bn n_bm coincides very closely with the actual barrier height _b(V)) is a consequence of two factors: (1) the nonlinear dependence of the actual barrier height on the bias, resulting in an increase in the ideality factor with increasing bias voltage (current) and (2) measurement of the parameters n and _bm for the same current for all temperatures. A new expression for the flat-band barrier height _bf is derived.     

Asymptotic behavior of densities for two-particle annihilating random walks

Consider the system of particles on ^d where particles are of two types—A andB—and execute simple random walks in continuous time. Particles do not interact with their own type, but when anA-particle meets aB-particle, both disappear, i.e., are annihilated. This system serves as a model for the chemical reactionA+B inert. We analyze the limiting behavior of the densities _A (t) and _B (t) when the initial state is given by homogeneous Poisson random fields. We prove that for equal initial densities _A (0)= _B (0) there is a change in behavior fromd4, where _A (t)= _B (t)C/t ^d /4, tod4, where _A (t)= _B (t)C/tast. For unequal initial densities _A (0)< _B (0), _A (t)e ^–cl ind=1, _A (t)e ^–Ct/logt ind=2, and _A (t)e ^–Ct ind3. The termC depends on the initial densities and changes withd. Techniques are from interacting particle systems. The behavior for this two-particle annihilation process has similarities to those for coalescing random walks (A+AA) and annihilating random walks (A+Ainert). The analysis of the present process is made considerably more difficult by the lack of comparison with an attractive particle system.     

The contrast gain in a guest-host nematic display due to a periodic boundary condition

The mean square tilt angle of a nematic slab with finite anchoring energy and periodic boundary conditions has been theoretically investigated, as a function of the slab geometry and of the reduced extrapolation length. If the anchoring strength is free-surfacelike, the contrast is affected by a loss 10% at room temperature if the ratio between the anchoring pitch and the cell thickness is 0.5.Glossary anchoring pitch - h cell thickness - /h - ( = x/, = y/h) reduced coordinates - (, ) local tilt angle - elastic constant - w_a anchoring energy anisotropy - b=/w _a de Gennes-Kleman extrapolation length - B=b/h reduced extrapolation length - T _NI nematic-isotropic transition temperature - :=(T/T _NI ) – 1 reduced temperature - easy axis direction - _MAX - _± ² mean square tilt angle along the boundary - () absorbance coefficients of the p-dye - r /: dichroic ratio - c contrast - G contrast gain - S order parameter     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

Phase uniqueness and correlation length in diluted-field Ising models

The diluted-field Ising model, a random nonnegative field ferromagnetic model, is shown to have a unique Gibbs measure with probability I when the field mean is positive. Our methods involve comparisons with ordinary uniform field Ising models. They yield as a corollary a way of obtaining spontaneous magnetization through the application of a vanishing random magnetic field. The correlation lengths of this model defined as (lim _n-(1/n) log ₀; _n)^-1, wheren is the site on the first coordinate axis at distancen from the origin and ₀; _n is the origin ton two-point truncated correlation function, is non-random. We derive an upper bound for it in terms of the correlation length of an ordinary nonrandom model with uniform field related to the field distribution of the diluted model.     

More inequalities for critical exponents

A variety of rigorous inequalities for critical exponents is proved. Most notable is the low-temperature Josephson inequalitydv +2 2–. Others are 1 1 +v, 1 1 , 1,d 1 + 1/ (for d),dv, ₃ + (for d), ₄ , and _{2m 2m+2} (form 2). The hypotheses vary; all inequalities are true for the spin-1/2 Ising model with nearest-neighbor ferromagnetic pair interactions.NSF Predoctoral Fellow (1976–1979). Research supported in part by NSF Grant PHY 78-23952.     

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.     

Energy relaxation in aϕ 4 with long range interactions

We investigate the influence of long range interactions on the relaxation behaviour of a lattice model with an on-site potential of ⁴-type and infinite range harmonic interactions. For finite number of particlesN, it is shown that the autocorrelation functions <E _n(t)E _n > of the fluctuations of the one-particle energiesE _n(t) decays exponentially. The corresponding relaxation time is proportional toN and is given by (T, N) =N₀(T). The temperature dependent time scale ₀ can explicitly be related to the dynamics of a one-particle correlator of the noninteracting system. The results are derived using Mori-Zwanzig projection formalism. The corresponding memory kernel is calculated within a mode coupling approximation and by a perturbative approach. Both results agree in leading order in 1/N. It is speculated that any interaction of range generates a timescale .     

Light source and geometrical requirements for the optimization of optical anemometry signals

The criteria for the design of optical arrangements for laser anemometry are formulated for reference-beam, two-beam and single-beam modes of operation. The dependence of useful light intensity upon optical path-length difference and number of axial laser modes is calculated. Laser power requirements are evaluated and the dependence upon band-pass filtering is quantitatively assessed. A new two-channel integrated-optical unit, with light-path compensation, and embodying the proposed design criteria, is described.Nomenclature c velocity of light - D _1/e diameter of laser beam at 1/e-point - d half distance separating the beams leaving the lens - d _m effective diameter of measuring control volume - d _ph diameter of aperture in front of photo-multiplier - d _r waist diameter of focused reference beam - d _s waist diameter of scattering light beam - d _l waist diameter of fucused light beam - F f-number of lens - scattering function introduced in Mie's theory - f signal frequency - f bandwidth of filter - f _D Doppler line width of laser radiation - f _G effective bandwidth of gain envelope of a laser - f _M frequency difference between two adjacent axial modes - h Planck constant (6.6256×10^–34J sec) - K 2/ wave number - L cavity length of laser - l _m length of measuring control volume - m total number of axial modes of laser - M magnification (a/b) - N _fr number of fringes in crossing region of the two light beams - N _ph number of fringes seen by photomultiplier - N _s number of photons scattered per particle passage - N _e number of electrons leaving photo cathode per unit time - P _l total light power emitted by laser - P _s total light power scattered by particle - Q _scat scattering coefficient - R distance from particle centre to point on plane of observation - r _p radius of scattering particle - u velocity component perpendicular to fringe pattern - _fr distance between fringes inside measuring control volume - _c efficiency of light collecting system - _q overall quantum efficiency of photodetector - g _q coordinate measuring angle from the optical axis - half angle between wave fronts - wave length of light - frequency of incident light wave - _e standard deviation of electron flux - transit time of scattering particle - solid angle - d solid angle element This paper was presented at the Conference on Electro-optic Systems in Flow Measurement, Southampton, September 1972.     

High resolution measurement of absorption μ(E) and anomalous dispersion f′(E) at theK-edge of copper

The variation with energyE of the X-ray absorption coefficient (E) and that of the anomalous dispersion correctionf(E) at the Cu-K-edge have been measured under identical experimental conditions using the X-ray interferometer installed in the Hamburger Synchrotronstrahlungslabor (HASYLAB) at the storage ring DORIS of DESY. The energy resolution achieved is E2 eV atE=9 keV. As a result of the extreme energy resolution in the near edge region up to about 60 eV above the edge, very detailed fine structures are observed in both (E) andf(E) which are tentatively attributed to multiple scattering resonances occuring in the scattering of the low energy photoelectron by neighbour atoms.The simultaneous measurement of (E) andf(E) opens the possibility to cross-correlate the experimental results with the help of Kramers-Kronig relations.     

Some properties of topological geons

We investigate the Finkelstein-Misner geons for a non-simply-connected space-time manifold (M, g ₀). We use relations between different Lorentzian structures unequivalent tog ₀ and topological properties ofM given by the Morse theory. It implies that to some pieces of geons we have to associate Wheeler's worm-holes. Geons that correspond to time-orientable Lorentz structures are related tog ₀ by Morse functions that describe the attaching of a handle of index one. In the case of geons associated to time-nonorientable Lorentzian structures, appropriate handles are related to loops along which the notion of time reverses. If we assume electromagnetic properties of geons, then only four species, v, e, p, m, of different geons can exist and geon m has to decay according to mv+p+e.     

On Convergence to Equilibrium Distribution, II. The Wave Equation in Odd Dimensions, with Mixing

The paper considers the wave equation, with constant or variable coefficients in ⁿ , with odd n3. We study the asymptotics of the distribution _t of the random solution at time t as t . It is assumed that the initial measure ₀ has zero mean, translation-invariant covariance matrices, and finite expected energy density. We also assume that ₀ satisfies a Rosenblatt- or Ibragimov–Linnik-type space mixing condition. The main result is the convergence of _t to a Gaussian measure as t , which gives a Central Limit Theorem (CLT) for the wave equation. The proof for the case of constant coefficients is based on an analysis of long-time asymptotics of the solution in the Fourier representation and Bernstein's room-corridor argument. The case of variable coefficients is treated by using a version of the scattering theory for infinite energy solutions, based on Vainberg's results on local energy decay.     

Magnetic moments of proton drip-line nuclei13O and9C

The magnetic moments of the proton drip-line nuclei¹³O(I = 3/2^–,T _1/2 = 8.6 ms) and 9C(I = 3/2^–,T _1/2 = 126 ms) have been determined for the first time through the combined techniques of polarized radioactive nuclear beams and-NMR detection. The observed magnetic moments are ¦(¹³O)¦ = 1.3891 ±0.0003 _N and ¦(⁹C)¦ = 1.3914 ±0.0005 _N. Spin expectation values are deduced to be 0.76 and 1.44 for¹³O and⁹C, respectively. While the of¹³O is consistent with the systematics from isospinT= 1/2 mirror pairs, the of⁹C is unusually large, even far larger than the single particle value, = 1.     

Thes-f model with Coulomb repulsion: Thermodynamics of two atomic cluster. Spin 1/2

A cluster of two atoms described by thes-f model with Coulomb repulsion has been considered. The interaction between localized 4f electrons (S=1/2) is taken in the molecular field approximation. The thermodynamic quantities like magnetization, specific heat and correlation functions n , n , S ^z n , S ^z n , S ^z (n –n ), n n and S ⁺ a ⁺ a as functions of temperature are presented for different band fillingN=0, 0.5, 1, 1.5, 2. The dependence of Curie temperature onN is calculated. The phase diagram forN=1 (T=0K) shows the possibility of existence of two phases: paramagnetic and ferromagnetic.The Curie temperature and the specific heat as functions ofN exhibit similar trends as found in experiments on doped magnetic semiconductors.     

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.     

Correlation inequalities for two-component hypercubicϕ 4 models

A collection of new and already known correlation inequalities is found for a family of two-component hypercubic ⁴ models, using techniques of duplicated variables, rotated correlation inequalities, and random walk representation. Among the interesting new inequalities are: rotated very special Dunlop-Newman inequality _1,x ² ; _1,z ² + _2g ² 0, rotated Griffiths I inequality _{1,x 1,y} ; _1z ² 0, and anti-Lebowitz inequalityu ₄ ¹¹¹¹ >-0.     

Strict inequalities for some critical exponents in two-dimensional percolation

For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL():={(x, y):x=r cos, y=r sin for some r0, or} and():=limpp _c [log(p–p _c )]^–1 log P_cr {itO is connected to by an occupied path inL()}, then() is strictly decreasing in on [0, 2]. Similarly, lim_n [–logn]^–1 logP _cr {itO is connected by an occupied path inL()() to the exterior of [–n, n]×[–n, n] is strictly decreasing in on [0, 2].     

Symmetry conservation and integrals over local charge densities in quantum field theory

For conserved local currents ^µ j ^µ (x)=0 in quantum field theory it is shown that anR-dependence of _R (x ₀) inj ₀(f _R(x)· _R (x ₀)) leads to nicer properties than a fixed (x ₀). The behaviour of j ₀(f _R(x)·_R(x ₀) is discussed under this aspect.     

Magnetic susceptibility of layered 2H-WSe2 semiconductors

Magnetic susceptibility and anisotropy in magnetic susceptibility _L are studied in 2H-WSe₂ layered semiconductor crystals over the temperature interval 77–300 K and magnetic fields 1–10 kOe.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 20–23, November, 1989.The authors are indebted to L. P. Strakhov for his kind evaluation of the results of the study.     

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.