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.     

An Equilibrium Lattice Model of Wetting on Rough Substrates

We consider a semi-infinite 3-dimensional Ising system with a rough wall to describe the effect of the roughness r of the substrate on wetting. We show that the difference of wall free energies (r)= _AW(r)– _BW(r) of the two phases behaves like (r)r(1), where r=1 characterizes a purely flat surface, confirming at low enough temperature and small roughness the validity of Wenzel's law, cos (r)r cos (1), which relates the contact angle of a sessile droplet to the roughness of the substrate     

Enhancement of conductance fluctuations in two-dimensional mesoscopic electron systems with valley structures

Conductance fluctuations are studied in twodimensional mesoscopic electron system with a two-hold valley degeneracy (n _v =2), which corresponds to the inversion layer of Si-MOSFET formed in (1,0,0) plane. It is shown that the intervalley scattering modifies conductance fluctuations depending on the ratio, Min { _c , _T }/ _v , where _v = ( – 2)/2 and _c , _T , and are, respectively, system traversal time, thermal diffusion time, intervalley scattering time and total life time of electrons. Conductance fluctuations are no longer universal and vary from G _univ 0.862·e ²/h to {ie223-5} at low temperatures even for isotropic systems. The conductance fluctuations increase with decreasing system size, increasing electron density and increasing intervalley scattering time. The effect of intervalley scattering is essentially the same as that of intersubband scattering as previously reported. At finite temperatures where _{T c} , the intervalley scattering modifies the fluctuations through the change in the energy correlation range to results in the reduction of the conductance fluctuations. In Si-MOSFET formed in (1, 1, 1) plane, wheren _v =6, more enhanced fluctuations are expected. Experimental studies are desired on theoretically predicted points.     

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.     

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).     

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.     

The physical nature of the production of moving striations in a d-c discharge plasma

The physical nature of the stratification of the d-c discharge plasma is found and physically interpreted. The interpretation is based on the mathematical expression of the production of periodic structure in plasma after an aperiodic disturbance, derived from an extremely simplified system of equations. Only three basic phenomena occurring in the plasma of each d-c discharge are included: a) the dependence of the rate of ionization on the electron temperature and hence on the electric field, b) the production of space charges due to the different rates of diffusion of the electrons and ions, c) the creation of additional electric fields due to the creation of space charges. The interactions of these phenomena gives rise to a chain, expanded in time and space, which leads to the production of moving striations. In agreement with experiment this structure is developed only on the side towards the anode from the place where the equilibrium state is disturbed.

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. (9, 10) (4, ), . , , : ) , , ; ) , ; ) , . , , — — . , .

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In conclusion the authors thank J. Fousek, J. Kaczér and M. Novák for carefully reading this paper and for valuable remarks, and J. Holub for carrying out the numerical and graphical work.     

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 .     

Transport of light radiation in a spatially finite three-dimensional scattering medium

We propose a new method for solving radiation transport problems, which permits including in analytic form for the case of normal incidence the effect of spatial finiteness of the scattering medium. The formation of the light field accompanying changes in the optical parameters and optical dimensions of the medium is analyzed.this paper, we examine the simplest case of a geometry of a scattering medium in the form of a parallelipiped with optical length _x, height _y, and width _z. The analysis is performed for the case =1, _y = _z with the latter varying in the range 0.1 to . The results obtained show that the light field depends strongly on the optical dimensions of the medium. The limiting values of the optical dimensions (_y = _z), beginning with which the spatial finiteness of the medium can be neglected, are determined.Translated from Izvestiya Vysshikh Uchebnykh Zavednii, Fizika, No. 8, pp. 82–85, August, 1982.     

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.     

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 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.     

К КИНЕТИКЕ ФОТОПРОВОДИМОСТИ СЕ ЛЕНА

- 65 –150 °. 0,2 . - , .     

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.     

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.     

Effect of electron irradiation on the parameters of gallium arsenide pulsed diodes

It is shown that the current-voltage characteristics of diodes produced by various methods vary in approximately the same manner. The behavior of the capacitance C(U) during irradiation can be explained on the basis of the theories developed for planar p-n junctions and Schottky barriers. The recovery time of diodes always increases during irradiation with large doses ( 10¹⁶ electrons/cm²). At smaller doses for diodes of the Schottkybarrier type (weakly formed), _recov always increases with irradiation, perhaps due to a decrease in the concentration n; for strongly formed diodes (having parameters approximating those of diffused diodes), the _recov behavior is governed by the nature of the impurity distribution and by the ratio of the lifetime of the minority carriers to the diode time constant ¯R¯C. With > RC, a decrease in _recov may be observed as a result of a decrease in .Translated from Izvestia VUZ. Fizika, No. 4, pp. 109–113, April, 1970.     

Stationary states of an electron in the field of a hole in an ionic crystal

An approximate solution is given of the Schrödinger equation for S-states of an electron in the field of a hole, when the potential energy of the electron has the form — e²/r [1+exp (–qr].

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s- , –e²/r [1+exp (–qr].

     

Langevin dynamic simulation of hysteresis in a field-swept Landau potential

Numerical simulations are done of Langevin dynamics for a uniform-orderparameter, field-swept Landau model,= –|a/2|m ²+|b/4|m ⁴–mh(t) , to study hysteresis effects. The field is swept at a constant rateh(t)=h(0)+ht. The stochastic jump values of the field {h_J from an initially prepared metastable minimumm(0) are recorded, on passage to a global minimum m(). The results are: (a) The mean jump¯h _J(h) increases (hysteresis loop widens) with h, confirming a previous theoretical criterion based on rate competition between field-sweep and inverse mean first-passage time (FPT); (b) The broad jump distribution(h _J,h) is related to intrinsically large FPT fluctuations ( ²–²)/ ² O(1), and can be quantitatively understood. Possible experimental tests of the ideas are indicated.     

Recombination of nonequilibrium current carriers in n-InAs1−x−ySbxPy

The stationary photoconductivity, the photomagnetic effect, and the relaxation kinetics of photoconductivity in n-InAs_1–x–ySb_xP_y crystals (x=0.06, y=0.11) with n₀ = 8·10¹⁵ and 3·10¹⁶ cm^–3 were measured and the lifetimes of nonequilibrium current carriers in the temperature interval T=78–295 K were determined. The possible mechanisms of recombination, which limit the lifetimes (radiative _R, Auger recombination _A, and recombination through centers with E_f=0.13 eV), which, as is demonstrated, are determined by interband recombination processes with _RA = _RA/(_R + _A), are calculated theoretically. The contribution of the 0.13 eV recombination centers can be significant when n₀10¹⁴ cm^–3.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 52–54, April, 1991.     

On the theory of amplification of meso-ultrasound in anisotropic monopolar semiconductors

The electronic absorption coefficient (_e) of meso-ultrasound (_p ^–1 _en, _t, _ee; ql 1, where _p, _en, _t are the times of pulse relaxation, energy, and current carrier traps; _ee ^–1 is the frequency of intraelectron collisions; , q are the frequency and wave vector of sound; l is the carrier mean free path) in the presence of a permanent external field E₀ e ₀ ^–1 q₀T is calculated for anisotropic single-valley semiconductors with piezoelectrical and potential-deformation acoustoelectronic interaction. Considered arbitrary are: 1) the anisotropy of the tensors * and _p (and other crystal parameters); 2) the degree of Fermi degeneration of the carriers; 3) the dependence of _p on the carrier energy . The acoustoheat nonlinearity is neglected. The possibility of meso-ultrasound amplification by the transverse field (E₀ - q) is predicted. By changing the orientation of the vector q relative to the crystal axes, the transverse threshold field (E ^thr ) can be controlled smoothly and within broad limits, This permits the production of a mechanical sound-amplification regulator or a modulator of its intensity. The ratio between E ^thr and E ^thr yields a measure of the relative anisotropy of the mobility.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 87–92, February, 1977.