Замечание К теории по степенного возникновения подви жных слоев в плазме инертных газов

[1] t _B , t _B . , t _B , . .

---

A note on the theory of the successive production of moving striations in the plasma of inert gases

Approximate expressions are derived on the basis of Pekárek's theoretical paper [1] for the period of the maximum t_B of a wave packet produced by the passage of a wave of stratification before the aperture of a photomultiplier, and for its time width in the half-height t_B. The relaxation time of a wave of stratification, following from the theory [1], can thus be calculated by means of the experimentally measured velocity of motion of the maximum of a wave packet u and its width t_B. The calculation is supplemented by numerical data on the magnitude of errors committed by using approximate expressions.

     

Geometry ofSU(2) gauge fields

We studySU(2) Yang-Mills theory onS ³× from the canonical view-point. We use topological and differential geometric techniques, identifying the true configuration space as the base-space of a principal bundle with the gauge-group as structure group.     

Muon catalyzed fusion: old and new aspects of energy production

Muon catalyzed fusion of deuterium and tritium (CF) yields the same energy gain per reaction as fusion with magnetic or inertial confinement (17.6 MeV). The crucial points of Cf are, however, very different, namely (a) the energy costW ₍₎ for production of one ^– and (b) the numbern of reactions a single muon can catalyze on the average. (b) is ultimately limited by theeffective sticking probability _f :n1/ _f. With standard methods one hasW ₍₎5 GeV, _f=0.5%. Hence a standard CF reactor can never reach a net energy gain. To solve this problem, ways discussed since about a decade are to increase the efficiency by both (i) energy multiplication using a fissionable blanket and (ii) breeding. A new way to increase the safety of fission devices mostly due to Yu. Petrov is outlined. On the other hand there is a hope to lowerW ₍₎ slightly and _f drastically, the latter by artificial reactivation. New theoretical results for beam cooling in an omegatron type driven integrated CF reactor, important forW ₍₎ and, in particular, _f, is presented.     

Construction and Borel summability of planar 4-dimensional euclidean field theory

We use the methods of [1] to show that the planar part of the renormalized perturbation theory for ₄ ⁴ -euclidean field theory is Borel-summable on the asymptotically free side of the theory. The Borel sum can therefore be taken as a rigorous definition of theN limit of a massiveN×N matrix model with a +trg ⁴ interaction, hence with wrong sign ofg. Our construction is relevant for a solution of the ultra-violet problem for planar QCD. We also propose a program for studying the structure of the renormalons singularities within the planar world.     

Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

Влияние катодной обл асти на динамические свойства тлеющего разряда в во дороде

. . , , I-om 1957 .     

Spectral response of CdS with Ag,Cu, and in impurities

High-resistance (dark 10⁸ · cm) photosensitive CdS samples (light 10²–10³ · cm at saturation) were obtained from low-resistance ( 0.1 · cm) nonphotosensitive CdS single crystals by thermal diffusion of Cu, Ag, and In in vacuum at 2 · 10^–5 torr. The spectral response of impurity and pure high-resistance photosensitive single-crystal CdS samples was studied in the wavelength range from 0.35 to 3. The short-wave and long-wave limits of the spectral curves, the wavelength range of maximum photoconductivity and the forbidden band width, the depth of impurity levels, the upper edge of the impurity band, and the depth of maximum-density activation centers have been determined from the spectral curves. The results are discussed and compared with published data.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 117–121, June, 1972.     

Shockley surface states for a graphite and diamond model with a delta function potential

The Shockley surface states problem was formulated for the Coulson graphite model and Hoerni diamond model with delta function potentials. It was shown that the solution of these problems can be reduced to the solution of analogous problems in the MO-LCAO method. A solution is given for one type of models. The analogy of both methods shows that the qualitative properties of Shockley surface states depend primarily on the geometry of the lattices.

---

. , MO-LCAO. . , .

     

The number of bound states of singular oscillating potentials

For a spherically symmetric potential such that rVL ¹(a, ), a>0, and is such that, if we define W=– _r V(t) d(t), W belongs to L ¹ (0, ) and rW0 as r0, we show that the number of bound states in any partial-wave satisfies the bound n2 ₀ r W ² dr. It was shown in a previous paper [1] that this class of potentials is regular from the point of view of abstract scattering theory as well as from the time-independent theory and the Jost function approach. We show also that, for large values of the coupling constant, n(gV) has the asymptotic behaviour C _±g ₀ W(r) dr as g±.     

Geometrical interpretation of the bilinear equations for the KP hierarchy

The Grassmann manifold approach to the KP hierarchy, in the spirit of Segal and Wilson, is used to define the wavefunction _W and its adjoint _W. From the fact that _W and _W are the orthogonal, we derive the bilinear equations. The modified equations are treated at the same time.     

Wave chaos in quantum systems with point interaction

We study perturbations of the quantized version ₀ of integrable Hamiltonian systems by point interactions. We relate the eigenvalues of to the zeros of a certain meromorphic function . Assuming the eigenvalues of ₀ are Poisson distributed, we get detailed information on the joint distribution of the zeros of and give bounds on the probability density for the spacings of eigenvalues of . Our results confirm the wave chaos phenomenon, as different from the quantum chaos phenomenon predicted by random matrix theory.SFB 237 Essen-Bochum-Düsseldorf     

Lattice vibrations in ordered and disordered thiourea

The critical dynamics of the Syozi model for dilute ferromagnetism is considered by the use of master equations. The dynamics is soluble as it is assumed that the time scale of motion on the sublattice on which the impurities move is so much faster than on the other sublattice that fast relaxing variables may be adiabatically eliminated, leaving a new soluble master equation. It is found that the linear and non-linear relaxation of magnetization exponents ^(l) and ^(nl) increase on dilution to ^(l)/(1–) and ^(nl)/(1–) respectively ( is the specific heat exponent for the pure system, which itself changes on dilution to –/(1–)). Thus if the exponents for the pure system obey the scaling law of Rácz and Fisher ^(nl)= ^(l)– ( is the magnetization exponent which changes on dilution to /(1–)) then so do the exponents for the diluted system. Similarly the exponent for spin diffusion changes on dilution to /(1–).     

Some consequences of the nonlocalizability of space-time events

Space-time events are characterized by their coordinatesx from the classical point of view. The same events from the quantum-mechanical point of view should be described rather by the expectation value of coordinates X. The expectation value could be evaluated by introducing a density operator(x,x) associated with the event. In the case where(x,x) cannot be described by delta functions strictly monochromatic radiation does not exist. If localizability is limited by Planck's length there are no narrower spectral lines than 2× 10^–29 E ² (eV) whereE stands for the photon energy.On leave from the Institute of Nuclear Physics, Kraków, ul. Radzikowskiego 152, Poland.     

The transverse correlation length for randomly rough surfaces

It is shown by numerical simulations for a random, one-dimensional surface defined by the equationx ₃=(x ₁), where the surface profile function (x ₁) is a stationary, stochastic, Gaussian process, that the transverse correlation lengtha of the surface roughness is a good measure of the mean distance d between consecutive peaks and valleys on the surface. In the case that the surface height correlation function (x ₁)(x ₁)/²(x ₁)=W (|x ₁–x ₁|) has the Lorentzian formW(|x ₁|)=a ²/(x ₁ ² +a ²) we find that d=0.9080a; when it has the Gaussian formW(|x ₁|)=exp(–x ₁ ² /a ²), we find that d=1.2837a; and when it has the nonmonotonic formW(|x ₁|)=sin(x ₁/a)/(x ₁/a), we find that d=1.2883a. These results suggest that d is larger, the faster the surface structure factorg(|Q|) [the Fourier transform ofW(|x ₁|)] decays to zero with increasing |Q|. We also obtain the functionP(itx ₁), which is defined in such a way that, ifx ₁=0 is a zero of (x ₁),P(x ₁)dx ₁ is the probability that the nearest zero of (x ₁) for positivex ₁ lies betweenx ₁ andx ₁+dx ₁.     

Gravitational (dynamic) time dilation according to absolute space-time theory

Proceeding from our absolute space-time conceptions, we obtain the formula for the gravitational frequency shift in an extremely simple way. Using our burst model for photons, we show that the different rates of clocks placed in spatial regions with different gravitational potentials appear as a direct result of the gravitational frequency shift and the axiomatic assumption that at any space point the time unit is to be defined by light clocks with equal arms, i.e., that at any space point the light velocity (in moving frames the there-and-back velocity) has the same numerical valuec. Considering the principle of equivalence, we come to the logical conclusion that the kinematic (Einstein-Lorentz) time dilation is an absolute phenomenon.     

Parametric upconversion of TM and Trivelpiece-Gould (TG) modes to high frequency free electron laser (FEL)

A backward wave oscillator (BWO) filled with a strongly magnetized plasma supports TM and Trivelpiece-Gould (TG) modes. At large amplitudes these modes may act as wigglers for generating millimeter waves via free electron laser instability. The nonlinear coupling between the wiggler, the beam space charge mode, and the high frequency free electron laser wave is dominated by parallel motions. In the Raman regime the growth rate of instability goes as _pb ^1/2 / ₀ ^9/4 , where _pb is the beam plasma frequency and ₀ is the relativistic gamma factor.Department of Physics, Indian Institute of Technology, India. Published in Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 37, No. 6, pp. 748–753, June, 1994.     

Novel perturbation expansion for the Langevin equation

We discuss the randomly driven systemdx/dt= -W(x) +f(t), wheref(t) is a Gaussian random function or stirring force withf(t)f(t)=2(t–t), andW(x) is of the formgx ¹⁺². The parameter is a measure of the nonlinearity of the equation. We show how to obtain the correlation functionsx(t)f(t)···x(t( n)) _f as a power series in. We obtain three terms in the expansion and show how to use Padé approximants to analytically continue the answer in the variable. By using scaling relations, we show how to get a uniform approximation to the equal-time correlation functions valid for allg and.     

Spectral broadening of picosecond laser pulses in optical fibres

Picosecond light pulses of a passively mode-locked ruby laser (pulse duration t _L35 ps) are spectrally broadened in optical fibres of core diameters from 4 m to 600 m. Combining the effects of self-phase modulation, stimulated Raman scattering, and parametric four-photon interaction in an 8-m core fibre of 4 m length with the effect of selective spectral attenuation in a ruby rod resulted in rather smooth spectra extending from 685 nm to 830 nm (spectral width 2300 cm^-1).     

Rate equations in the hopping transport

The usual kinetic equations for the site occupation probabilities in an external field are solved exactly in a simple one-dimensional periodic model with two kinds of atoms using a) free boundary conditions and order of limitsN, 0 needed for a proper treatment of the dc conductivity here b) boundary conditions with metallic contacts and order of limitsN, 0 and c) the same boundary conditions but reversed order of limiting processes 0,N typical of e.g. numerical and percolation treatments. (N and are the number of sites and frequency.) It is demonstrated that though the bulk dc conductivity is the same in all three cases, local bulk properties of the material are strongly dependent on the régime used. The role of the order of all three limiting processes 0,N+ andn+ (N–n+) for local shifts of the chemical potential _n in the dc limit is examined (n is the number of the relevant site calculated from a boundary of the chain). It is shown especially that the rate equation treatment (régime a) on the one hand and numerical or percolation treatments (régime c) on the other hand never yield the same bulk values of _r.     

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

The [, , ]-Langevin equation describes the time evolution of a real stationary process withT-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [, , ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics.