Magnetoresistance in two-dimensional magnesium films of various thicknesses

The magnetoresistance of thin magnesium films in the weakly localized regime has been measured at 4.2 K as a function of film thickness. The results are analysed in a new and simple way based on the theory of Hikami et al. [1]. We use only two adjustable parameters, the inelastic relaxation time _i and the spin-orbit scattering time _so. Whereas _so is found to be almost independent of thickness, _i changes significantly. The variation of _i with thickness is discussed in the light of the theories for the enhanced electron-electron interaction, but it does not seem to tie up with any of the existing theories.     

A matrix method for estimating the Liapunov exponent of one-dimensional systems

Let : [0, 1][0, 1] be a piecewise monotonie expanding map. Then admits an absolutely continuous invariant measure. A result of Kosyakin and Sandler shows that can be approximated by a sequence of absolutely continuous measures _n invariant under piecewise linear Markov maps _itn. Each _itn is constructed on the inverse images of the turning points of . The easily computable measures _n are used to estimate the Liapunov exponent of . The idea of using Markov maps for estimating the Liapunov exponent is applied to both expanding and nonexpanding maps.     

Is the electron a composite particle? An experiment

The crucial problem of physics was first formulated by Democritus in the 5th century BC: to find the or smallest uncuttable bits of matter. That has not changed ever since. Among the current candidates are electron and positron, the least expensive of today's bona fide . Experimental tests of their non-compositeness by precisely measuring the gyromagnetic ratios of the individual trapped particles are reviewed.You know, it would be sufficient to really understand the electron.Albert Einstein     

Spannungsverläufe Nach Wechseln der Verformungsgeschwindigkeit an Metalleinkristallen

The theoretical relations between _v and measured stress changes are discussed and compared with experimental results. For instantaneous change in the strain rate, the first deviation of the stress increase from the linearity ( _C ) can be used as a measure of _v for small deformation only. The comparison of _C with the extrapolated value _A enables to reveal the presence of recovery. The comparison of stress changes measured after a given rate change at the same strain on unrecovering (low temperatures) and recovering (higher temperatures) samples enables to differentiate between various types of recovery.     

Macroscopic short-time electrodynamics for conductors

In the macroscopic electrodynamics (MED) of good conductors (metals) based on Ohm's law j=E, the momentum relaxation time =m/ne² of the electrons limits the application to electromagnetic (EM) processes with characteristic timest. An interesting physical difficulty occurs in MED since the EM field damping time _R=/ of metals is very small compared with the minimum macroscopic time scale, _R. Consequently, the damping and propagation of EM waves and pulses in good conductors cannot be correctly described within the frame of conventional MED. New hyperbolic EM wave equations with relaxation and memory are proposed, which no longer exhibit the _R deficiency. The latter is caused by Ohm's law, which breaks down for short-time processes, due to neglect of electron inertia. The advantages of the proposed and the disadvantages of the conventional EM wave equations for good conductors are discussed in applications.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Laser damage in silicon photodiodes

Thermal damage of silicon photodiodes exposed to intense optical radiation is investigated. Damage thresholds of Si photodiodes irradiated by 1.06m laser pulses are reported for values of irradiation time,, ranging from 10^–8 to 1s. Threshold laser irradiation produces visible microscopic damage and a permanent degradation in photoresponse. The loss of responsivity is associated with degradation of the detector diode characteristics due to laser-induced heating. The time and wavelength dependence agree with the predictions of a thermal model which treats a semi-infinite material irradiated by a Gaussian laser beam. The energy density thresholds are independent of for short irradiation times and asymptotically approach a limiting behaviour which increases as for long times. They are given by the empirical relationE ₀=65[1+217/tan^–1(258)^1/2] J cm^–2 for 1.06m radiation. The thresholds at short irradiation times of detectors damaged by 1.06m radiation are about 25 times larger than those of detectors exposed to 0.6943m radiation. The greater susceptibility at 0.6943m is attributed to a larger optical absorption coefficient.     

Tree graph inequalities and critical behavior in percolation models

Various inequalities are derived and used for the study of the critical behavior in independent percolation models. In particular, we consider the critical exponent associated with the expected cluster sizex and the structure of then-site connection probabilities =_n(x₁,..., x_n). It is shown that quite generally 1. The upper critical dimension, above which attains the Bethe lattice value 1, is characterized both in terms of the geometry of incipient clusters and a diagramatic convergence condition. For homogeneousd-dimensional lattices with (x, y)=O(¦x -y¦^–(d–2+), atp=p _c, our criterion shows that =1 if > (6-d)/3. The connectivity functions _n are generally bounded by tree diagrams which involve the two-point function. We conjecture that above the critical dimension the asymptotic behavior of _n, in the critical regime, is actually given by such tree diagrams modified by a nonsingular vertex factor. Other results deal with the exponential decay of the cluster-size distribution and the function ₂ (x, y). A. P. Sloan Foundation Research Fellow. Research supported in part by the National Science Foundation Grant No. PHY-8301493.Research supported in part by the National Science Foundation Grant No. MCS80-19384.     

A two-level Kaluza-Klein theory

Let the Lie groups G and H act on the manifold P in such a way that P fibres as a principal G-bundle over P/G and as an H-bundle over P/H. We find that every pair (,) where is an H-invariant connection form in PP/G and is a G-invariant connection form in PP/H corresponds uniquely to a connection form in PP/(H×G) and a cross-section of a vector bundle with base P/(H×G).     

Studies on the microstructure of phase transitions in two kinds of liquid crystals by PAT and DSC

The positron lifetime and DSC measerments for EBBA and DOBAMBC have been made with heating and cooling clycles. The experimental results show that a shorter lifetime (₁) is essentially independent of temperature while the longer lifetime (₂) and the intensity (I ₂) change abruptly double or triple with temperature. Consequently, the EBBA has only nematic phases while the DOBAMBC has two liquid-crystalline phases (smectic C* and smectic A) with transition temperatures as follows: for EBBA, solid nematic (304.5 K), nematic isotropic (356.5 K), isotropic nematic (356.5 K), nematic solid (301 K); and for DOBAMBC, solid smectic C* (346 K), smectic C* smectic A (357.5 K), smectic A isotropic (389 K). These critical temperatures are in accordance with the transition temperatures measured by DSC. In addition, the difference in the solid-nematic transition temperature in the heating and cooling cycles was also observed. A discussion about the correlation of the observed changes in lifetime (₂) with the changes in molecular orientational order (S) and dielectric anisotropy () is presented.     

Colored noise in activated rate processes

We consider bistable systems driven by stationary wideband Gaussian colored noise. We construct uniform asymptotic expansions of the stationary probability density function and of the activation rate, for small intensity and short correlation time of the noise. We find that for different values of the total power output / of the noise, different terms in the asymptotic expansions become dominant. For we recover previously derived results, while for =O() and new results are obtained.     

Kinetic equation in the kinetic region of the dilute and nonuniform electron plasma

Mori's scaling method is used to derive the kinetic equation for a dilute, nonuniform electron plasma in the kinetic region where the space-time cutoff (b, t _c) satisfies _Dbl _f , _D t _{c f} , with _D the Debye length, _D ^–1= _p the plasma frequency, andl _f and _f the mean free path and time, respectively. The kinetic equation takes account of the nonuniformity of the order ofl _f and _D for the single-and the two-particle distribution function, respectively. Thus the Vlasov term associated with the two-particle distribution function is retained. This kinetic equation is deduced from the kinetic equation in the coherent region obtained by Morita, Mori, and Tokuyama, where the space-time cutoff of the coherent region satisfies _Dbr ₀, _Dt _{c 0}, withr ₀ the Landau length and ₀ the corresponding time scale.     

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 .     

Microscopic theory of gas-surface interaction

A kinetic theory for inelastic scattering, trapping and desorption of gas molecules by surfaces is described. The theory is valid if the time scale _l = 1/r introduced by the relaxation ratesr in the kinetic equations (which is of the order of the life time of vibrational states of adsorbates) is sufficiently large compared to the vibrational period ₀. For sufficiently large activation energies of the adsorbates another time constant _res, the residence time of adsorbed particles, can be determined from the theory. One thus may distinguish four different partly overlapping regimes defined by the time scalest _{I l} , ₀t_II, _l t_III and _rest_IV. Regime I is governed by the Schrödinger equation regime II by the kinetic equations. In the region where both regimes overlap the kinetic coefficients can be expressed in terms of microscopic quantities which have been calculated previously. The relevant quantities in the other regimes are introduced and discussed from a unified point of view thus providing a link between the regimes I and IV which have been treated in detail before.     

Der Einfluss der positiven Ionen auf die Exoelektronenemission

Zusammenfassung Es werden die Ergebnisse der Messung des Einflusses der auf den Emitter bei der Messung der Exoelektronenemission mittels Geiger-Müller-ZÄhlers auffallenden positiven Ionen beschrieben und die möglichen Mechanismen der Beeinflussung der Emission diskutiert.

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From the eden model to the kinetic growth walk: A generalized growth model with a finite lifetime of growth sites

We propose a new class of cluster growth models where growth sites have a finite lifetime , which contains as special cases the Eden model ( = ) and the kinetic growth walk ( = 1). For finite but large values the growth process can be characterized by a crossover timet _X; for times belowt _X an Eden-type cluster is formed, while for times abovet _X the growth process belongs to the universality class of the self-avoiding random walk. The crossover time increases monotonically with . We develop a scaling theory for the time evolution of the mean end-to-end distance between the seed and the last-added site, and for the average number of growth sites by which the kinetics of the growth process can be characterized. We test this scaling theory by extensive Monte Carlo simulations. We also extend our results to inhomogeneous media (percolation systems).     

Perturbed periodic Hamiltonians: Essential Spectrum and exponential decay of eigenfunctions

Spectral properties of – +V(x), whereV(x) lies in a neighbourhood of the periodic case and describes various models of disorder, are studied. We prove the exponential decay of generalized eigenfunctions corresponding to energies in the resolvent set of the unperturbed periodic Hamiltonian, as well as the stability of the essential spectrum for the dislocation disorder in two dimensions.     

Free Bosons and Tau-Functions for Compact Riemann Surfaces and Closed Smooth Jordan Curves. Current Correlation Functions

We study families of quantum field theories of free bosons on a compact Riemann surface of genus g. For the case g > 0, these theories are parameterized by holomorphic line bundles of degree g – 1, and for the case g = 0 — by smooth closed Jordan curves on the complex plane. In both cases we define a notion of -function as a partition function of the theory and evaluate it explicitly. For the case g > 0 the -function is an analytic torsion, and for the case g = 0, the regularized energy of a certain natural pseudo-measure on the interior domain of a closed curve. For these cases we rigorously prove the Ward identities for the current correlation functions and determine them explicitly. For the case g > 0, these functions coincide with those obtained by using bosonization. For the case g = 0, the -function we have defined coincides with the -function introduced as a dispersionless limit of the Sato's -function for the two-dimensional Toda hierarchy. As a corollary of the Ward identities, we note some recent results on relations between conformal maps of exterior domains and -functions. For this case, we also define a Hermitian metric on the space of all contours of given area. As another corollary of the Ward identities, we prove that the introduced metric is Kähler and the logarithm of the -function is its Kähler potential.     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

Electron (muon) decay of a heavy lepton

Expressions are derived for the differential probability for the decay e(). The possibly nonzero mass of and the polarizations of both the decaying lepton and the charged lepton which is produced are all taken into account. A quantitative analysis is carried out for various masses of the neutrino and for various energies of the lepton emitted during the decay.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 97–100, June 1981.