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.     

Colored noise driven systems with inertia

We present a novel approximation scheme, termed unified colored noise approximation (UCNA), for colored Gaussian noise driven nonlinear systems with inertia. This approximation allows one to evaluate static (stationary distributions, moments) as well as dynamical quantities (correlation functions) for small-to-moderate-to-large values of the correlation time. The approximation replaces a three-dimensional Markovian process by a reduced, two-dimensional Markovian dynamics with new drift and diffusion coefficients. For a harmonic potential the stationary moments are reproduced exactly. Most importantly, we present a criterion involving the noise strengthD, the friction strength and the noise color , which describes the region of validity of UCNA in the parameter space given by (D, , ). At small -values we contrast the UCNA with the well-known small approximation. In order to have a comparison onanalytical grounds, we test the static and dynamical predictions of UCNA versus the well-known analytical results obtained from a three-dimensional Ornstein-Uhlenbeck process.     

Dispersion of the permittivity of high-resistance semiconductors

We consider the mechanism of macroscopic polarization of semiconducting plates owing to the interaction of free carriers with an impurity level, in which role the level of the residual impurity of compensated semiconductors may appear. This mechanism, in combination with the diffusion-drift mechanism of polarization, results in additional dispersion of the real () and imaginary () parts of the dielectric permittivity, this being particularly significant for semiconductors of thickness smaller than the screening length L_s of free carriers. The character of the behavior of and depends on the relation between the Maxwell relation time _M and the times of carrier capture: _c and ejection _e by an impurity center. For _cetm and (/L_s) _e/_c1 the dispersion of and is the same as for thick plates (/L_s1). For _{c m e} and (/L_s)_e/_c1 the () curve has a characteristic kink in the region 1/_e, indicating additional absorption associated with the ejection of carriers into the surface region.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 11–13, October, 1981.     

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.     

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.     

How to measure the magnetic moment of the tau lepton

We present a method for obtaining bounds on the magnetic moment of the lepton. In order to do this, we study the radiative decayW as a function of the anomalous magnetic moment of the ,a . One can obtain bounds as good asa < 4.05×10^–2, 2.25×10^–2, 4.5×10^–3, and 2.5×10^–3 at the present Fermilab, future Fermilab, SSC, and LHC, respectively.     

The paramagnetic state (μ+e−) in silicon and tellurium at high temperature

The paramagnetic state (⁺e^–) in Si and Te was observed in a longitudinal magnetic field. The mean lifetimes of these states were obtained: _Si = 1.45(3) s, _Te = 12.5(8) s at 290 K, _Te = 12(2) s at 250 K.     

A frequency response model in multiquantum well lasers with unequilibrium carrier transport

A carrier transport model to explain the high-frequency response in high-speed MQW lasers is described. The ambipolar approximation, which is unsuitable for dealing with the high-speed carrier dynamics in MQW structures, was not adopted for small-signal analysis. The carrier transport effect can be characterized by four time constants: the electron transport time, _bmn; the hole transport time, _bmp; the electron escape time, _wbn; and the hole escape time, _wbp. The frequency response was interpreted as the sum of the constant response term due to the fast electron current and the roll-off term due to the slow hole transport time. The ratio of the electron contribution to the total response was proportional to the ratio of electron contribution to the total differential gain, , and reciprocally proportional to _n0 = 1 + _bmn/_wbn. The value of was calculated to be about 0.5 for typical MQW lasers. The roll-off frequency is mainly determined by . The ratio _p0 = 1 + _bmp/_wbp affects the resonant frequency and the damping rate in the high-bias condition.     

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.     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

External non-white noise and nonequilibrium phase transitions

Langevin equations with external non-white noise are considered. A Fokker Planck equation valid in general in first order of the correlation time of the noise is derived. In some cases its validity can be extended to any value of. The effect of a finite in the nonequilibrium phase transitions induced by the noise is analyzed, by means of such Fokker Planck equation, in general, for the Verhulst equation under two different kind of fluctuations, and for a genetic model. It is shown that new transitions can appear and that the threshold value of the parameter can be changed.     

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).     

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.     

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.     

Population growth in random media

In this second part of a two-part presentation, we continue with the model introduced in Part I. In this part, the initial configuration has one particle at each site to the left of 0 and no particle elsewhere. The expected number of particles observed at a site moving at speed has an exponential growth rate (speed- growth rate) that is computed explicitly. The result reveals two characteristic wavefront speeds: ₁, the speed of the front of zero growth (rightmost particle), and ₂, the speed of the front of maximal growth. The latter speed exhibits a phase transition, changing from zero to positive as the drift in the migration crosses a threshold. The qualitative shape of the growth rate as a function of changes as well. In particular, below the threshold there appears a linear piece, which corresponds to the system exhibiting an intermittency effect.     

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.     

Generalization of the relativistic string model in the geometrical approach

We present a model of a one-dimensional extended relativistic object, whose motion is defined by the requirement that its time track in Minkowski space is a surface of the constant mean curvature H. The world surface of the relativistic string is a particular case of such surfaces, namely, a minimal surface with H=0. By differential-geometry methods the theory of the proposed object moving in three-dimensional space-time is reduced to one nonlinear equation – = Hsh. In the theory under consideration, there naturally arises the pair of Lax's operators needed to solve this nonlinear equation by the inverse scattering method.     

Role of Activator and Vacancy Centers in the Decay of the Gamma Scintillators of CsI–Na Crystals

The influence of the concentration of an activator (C _NaI) and of plastic deformation on a change in the contribution of a slow component to the decay of the -scintillations of CsI–Na crystals was investigated, as well as the influence of C _NaI on a change in the shape of the luminescence excitation spectrum in the region of absorption of activator centers (AC) and of vacancy-related centers (VRC) and also on a change in the intercenter time of deexcitation of the centers indicated. It is shown that AC and VRC participate in the photoluminescence and -scintillations of CsI–Na crystals. In the -scintillations, AC are responsible for the component ₁ = 370 nsec, whereas the components ₁ = 460 nsec and ₂ 2 sec are associated with VRC. The reduction of ₁ from 770 to 560 nsec with an increase in C _NaI from 2·10^–3 to 3·10^–2 mole% and from 570 to 470 nsec after plastic deformation of the crystals ( = 5%) along the 111 axis is caused by a decrease in the number of VRC. The mechanisms underlying the -scintillations of the CaI–Na crystals containing AC and VRC and also the decrease in the number of VRC are discussed.     

Holes in the probability density of strongly colored noise driven systems

A qualitative change in the topology of the joint probability densityP(,x), which occurs for strongly colored noise in multistable systems, has recently been observed first by analog simulation (F. Moss and F. Marchesoni,Phys. Lett. A 131:322 (1988)) and confirmed by matrix continued fraction methods (Th. Leiber and H. Riskin, unpublished), and by analytic theory (P. Hänggi, P. Jung, and F. Marchesoni,J. Stat. Phys., this issue). Systems studied were of the classx=–U(x)/x+(t,), whereU(x) is a multistable potential and (t, ) is a colored, Gaussian noise of intensityD, for which =0, and (t) (s)=(D/)exp(–t–s/). When the noise correlation time is smaller than some critical value ₀, which depends onD, the two-dimensional densityP(,x) has the usual topology [P. Jung and H. Risken,Z. Phys. B 61:367 (1985); F. Moss and P. V. E. McClintock,Z. Phys. B 61:381 (1985)]: a pair of local maxima ofP(,x), which correspond to a pair of adjacent local minima ofU(x), are connected by a single saddle point which lies on thex axis. When >₀, however,the single saddle disappears and is replaced by a pair of off-axis saddles. A depression, or hole, which is bounded by the saddles and the local maxima thus appears. The most probable trajectory connecting the two potential wells therefore does not pass through the origin for >₀, but instead must detour around the local barrier. This observation implies that successful mean-first-passage-time theories of strongly colored noise driven systems must necessarily be two dimensional (Hänggiet al.). We have observed these holes for several potentialsU(x): (1)a soft, bistable potential by analog simulation (Moss and Marchesoni); (2) a periodic potential [Th. Leiber, F. Marchesoni, and H. Risken,Phys. Rev. Lett. 59:1381 (1987)] by matrix continued fractions; (3) the usual hard, bistable potential,U(x)=–ax ²/2+bx ⁴/4, by analog simulations only; and (4) a random potential for which the forcingf(x)=–U(x)/x is an approximate Gaussian with nonzero correlation length, i.e., colored spatiotemporal noise, by analog simulation. There is a critical curve ₀(D) in the versusD plane which divides the two topological behaviors. For a fixed value ofD, this curve is shifted toward larger values of ₀ for progressively weaker barriers between the wells. Therefore, strong barriers favor the observation of this topological transformation at smaller values of . Recently, an analytic expression for the critical curve, valid asymptotically in the small-D limit, has been obtained (Hänggiet al.).This paper will appear in a forthcoming issue of theJournal of Statistical Physics.     

Representations of state space transformations by Markov kernels

Every convex subset of a locally convex Hausdorff space (X, ) is equipped with the (-algebra generated by its-relatively open subsets. Within the set () of probability measures on two particular convex subsets are considered: (a) the set ^s () of probability measures with a separable support, and (b) the set ^c () of probability measures with a compact convex support. If is the base of a cone inX, then there exists an affine barycenter map from ^c () onto whose composition with the natural embedding of in ^c () yields the identity map on , and every-continuous affine transformation of can be represented by an affine transformation of ^c () that is induced by a Markov kernel. If (X, ) is a Banach space and is a closed, bounded, generating cone base inX that is contained in a hyperplane, then analogous results are obtained with respect to ^s (). Since the state spaces considered in noncommutative measure theory are cone bases and every change in time of an empirical system can be thought of as an affine transformation of the associated state space (Schrödinger picture), the existence of these representation theorems implies that the time evolution of general empirical systems can be described by dynamical concepts borrowed from classical probability theory.