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.     

Vacuum Einstein spaces with axial symmetry

Four classes of solutions are found to the equations R=–2_{; ;} and g _;=0 in three-dimensional space with metric gdxdx and signature (+ ––), equivalent to the Einstein equations R_ij=0 in a vacuum for the metric . The metric ds² assumes axial symmetry and symmetry with respect to the reflection .Translated from Izvestiya Uchebnykh Zavedenii, Fizika, No. 9, pp. 43–45, September, 1976.     

Multiple coherent scattering of γ-radiation

Conclusions Multiplying (5) by 2d and integrating over angle, we get the relationship between the total flux and depth in the form , where .A similar result is obtained from integration of (11) over the angles and integration of (12) over the plane z = const. It thus follows that if we are interested in the angular distribution for in the first two cases and in the radial distribution for z in the third case, we can make an approximate estimate of the coherent scattering by eliminating the appropriate term from. This approach has been used in [15 etc.] but no indications were given of the conditions under which this is permissible.For problems in which small angles or small distances from the axis of a collimated source are important, allowance for the coherent scattering can change the result by an order of magnitude or more. For angles and it is possible to consider only the coherent scattering and to use (5), (11), and (12). For angles >gh and scattering >z, the contribution from coherent and incoherent scattering can be comparable. The kinetic equation must then be solved with allowance for both effects.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 129–132, May, 1973.     

TypeN vacuum space-times as special functions in ℂ2

The members of one explicit class of functions in ² are identified with the geodetic shear-free null congruences in Minkowski's space-time. Members of a second explicit class are identified with the type-N vacuum space-times with twist-free rays. These two classes are special subclasses from a larger class of functions associated with the type-N space-times. This larger class is characterized in the following way: If and are holomorphic variables in ², thenu (, , ), a function holomorphic in, belongs to the class provided the function u/ u satisfies the tangential Cauchy-Riemann equation for an antiholomorphic function on the 3-surface whereu (, , ) has real values.This work was supported in part by NSF grant No. MPS74-14191-A01.     

Effective Potential for \mathcal{P}\mathcal{T}-Symmetric Quantum Field Theories

Recently, a class of -invariant scalar quantum field theories described by the non-Hermitian Lagrangian = () ² +g ² (i) was studied. It was found that there are two regions of . For <0 the -invariance of the Lagrangian is spontaneously broken, and as a consequence, all but the lowest-lying energy levels are complex. For 0 the -invariance of the Lagrangian is unbroken, and the entire energy spectrum is real and positive. The subtle transition at =0 is not well understood. In this paper we initiate an investigation of this transition by carrying out a detailed numerical study of the effective potential V _eff (_c) in zero-dimensional spacetime. Although this numerical work reveals some differences between the <0 and the >0 regimes, we cannot yet see convincing evidence of the transition at =0 in the structure of the effective potential for -symmetric quantum field theories.     

A spectral characterization of KMS states

Let be a state on aC*-dynamical system . For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O.     

Hyperbolic initial-boundary-value problem for magnetic flux compression by plane liners

Based on the (relativistic) Maxwell equations with displacement current E/t, the initial-boundary-value problem for the compression of an initially homogeneous magnetic fieldB={0,B(x,t),0} between a fixed liner atx=0 and a detonation-driven liner atx=s(t) is solved analytically. By homogenizing the boundary conditions at the moving boundary, the transient electromagnetic fields are shown to be a superposition of quasistatic elliptic (E/t=0) and hyperbolic (E/t0) wave solutions. The wave equation is solved by a Fourier expansion in time-dependent eigenfunctionsf _n =f _n [nx/s(t)] for the variable region 0xs(t), where the Fourier amplitudes _n (t) are determined by coupled differential equations of second order. It is concluded that the conventional elliptic flux compression theories (E/t=0) hold approximately for nonrelativistic liner speeds , whereas the hyperbolic theory (E/t0) is valid for arbitrary liner speeds .     

Spectral distribution and kinetics of the high-voltage photoelectromotive force of PbS layers

The spectral dependences of the short-circuit current Iph and the photoconductivity _ph of photovoltaic PbS layers are similar in shape and in the position of the long-wavelength threshold. As the temperature is reduced, the spectral curves shift toward longer wavelengths. Several samples show a photoemf of different sign in different parts of the spectrum. The relaxation of the photoemf V_ph, the current I_ph, and the photoconductivity _ph is characterized by times , respectively, where > \tau \sigma > > \tau I$$ " align="middle" border="0"> . The temperature dependences of these times and of the layer resistance have been studied. The results are interpreted on the basis of a barrier model for the high-voltage photoemf in PbS layers.     

Sharpness of the phase transition in percolation models

The equality of two critical points — the percolation thresholdp _H and the pointp _T where the cluster size distribution ceases to decay exponentially — is proven for all translation invariant independent percolation models on homogeneousd-dimensional lattices (d1). The analysis is based on a pair of new nonlinear partial differential inequalities for an order parameterM(,h), which forh=0 reduces to the percolation densityP — at the bond densityp=1–e ^– in the single parameter case. These are: (1)MhM/h+M ²+MM/, and (2) M/|J|MM/h. Inequality (1) is intriguing in that its derivation provides yet another hint of a ³ structure in percolation models. Moreover, through the elimination of one of its derivatives, (1) yields a pair of ordinary differential inequalities which provide information on the critical exponents and . One of these resembles an Ising model inequality of Fröhlich and Sokal and yields the mean field bound 2, and the other implies the result of Chayes and Chayes that . An inequality identical to (2) is known for Ising models, where it provides the basis for Newman's universal relation and for certain extrapolation principles, which are now made applicable also to independent percolation. These results apply to both finite and long range models, with or without orientation, and extend to periodic and weakly inhomogeneous systems.Research supported in part by the NSF Grant PHY-8605164Also in the Physics Department     

Distribution of the error term for the number of lattice points inside a shifted circle

We investigate the fluctuations inN (R), the number of lattice pointsnZ ² inside a circle of radiusR centered at a fixed point [0, 1)². Assuming thatR is smoothly (e.g., uniformly) distributed on a segment 0RT, we prove that the random variable has a limit distribution asT (independent of the distribution ofR), which is absolutely continuous with respect to Lebesgue measure. The densityp (x) is an entire function ofx which decays, for realx, faster than exp(–|x|^4–). We also obtain a lower bound on the distribution function which shows thatP (–x) and 1–P (x) decay whenx not faster than exp(–x ⁴⁺). Numerical studies show that the profile of the densityp (x) can be very different for different . For instance, it can be both unimodal and bimodal. We show that , and the variance depends continuously on . However, the partial derivatives ofD are infinite at every rational point Q ², soD is analytic nowhere.     

Von neumann entropy as information rate

Recently it has been shown that quantum theory can be viewed as a classical probability theory by treating Hilbert space as a measure space (H, B(H)) of events or hidden states. Each density operator defines a set of probability measures such that(E _n )=w _n (alln). Coding elements H by subspacesE _n entails distortion. We show that the von Neumann entropyS() = -trInequals the effective rate at which the Hilbert space produces information with zero expected distortion, and comment on the meaning of this.     

Unified fields of analytic space-time-energy

An analytic gravitational fieldZ (Z ^y ) is shown to include electromagnetic phenomena. In an almost flat and almost static complex geometryds ² =zdzdz of four complex variables z=t, x, y, x the field equationsR Rz = –(U U – Z ) imply the conventional equations of motion and the conventional electromagnetic field equations to first order if =(Z ^v) and =(z ) are expressed in terms of the conventional mass density function , the conventional charge density function , and a pressurep as follows: v=const=p/c ²–10^–29 gm/cm³.     

Bounded Fluctuations and Translation Symmetry Breaking: A Solvable Model

The variance of the particle number (equivalently the total charge) in a domain of length of a one-component plasma (OCP) on a cylinder of circumference W at the reciprocal temperature =2, is shown to remain bounded as . This exactly solvable system with average density has a density profile which is periodic with period (W)^–1 along the axis of the infinitely long cylinder. This illustrates the connection between bounded variance and periodicity in (quasi) one-dimensional systems.⁽¹⁾ When W the system approaches the two-dimensional OCP and the variance in a domain grows like its perimeter ||. In this limit, the system is translation invariant with rapid decay of correlations.     

On the measure of the spectrum for the almost Mathieu operator

We obtain partial results on the conjecture that for the almost Mathieu operator at irrational frequency, , the measure of the spectrum,S(, , )=|4–2|. For ||2 we show that if _n is rational and irrational, then .Dedicated to Res Jost and Arthur WightmanResearch partially supported by U.S. NSF grant number DMS-8801918 and by BSF under grant number 88-00325     

Ergodic states in a non commutative ergodic theory

Using the Godement mean of positive-type functions over a groupG, we study -abelian systems { , } of aC*-algebra and a homomorphic mapping of a groupG into the homomorphism group of . Consideration of the Godement mean off(g)U _g withf a positive-type function overG andU a unitary representation ofG first yields a generalized mean-ergodic theorem. We then define the Godement mean off(g) ( _g (A)) withA and a covariant representation of the system { , } for which theG-invariant Hilbert space vectors are cyclic and study its properties, notably in relation with ergodic and weakly mixing states over . Finally we investigate the discrete spectrum of covariant representations of { , } (i.e. the direct sum of the finite-dimensional subrepresentations of the associated representations ofG).On leave of absence from Istituto di Fisica G. Marconi Piazzale delle Scienze 5 — Roma.     

Higher spin BRS cohomology of supersymmetric chiral matter inD=4

We examine the BRS cohomology of chiral matter inN=1,D=4 supersymmetry to determine a general form of composite superfield operators which can suffer from supersymmetry anomalies. Composite superfield operators _{(a, b)} are products of the elementary chiral superfieldsS and and the derivative operatorsD , and . Such superfields _{(a, b)} can be chosen to have a symmetrized undotted indices _i and b symmetrized dotted indices . The result derived here is that each composite superfield _(a,b) is subject to potential supersymmetry anomalies ifa–b is an odd number, which means that _(a,b) is a fermionic superfield.     

ВЛИЯНИЕ ПОЛНОГО ОТРА ЖЕНИЯ НА ДИАФРАГМЕ СОЛЛЕРА НА РАЗРЕШАЮШ УЮ СИЛУ РЕНТГЕНОВСКО ГО СПЕКТРОГРАФА

- - , , , . - , -.     

On the Davey–Stewartson and Ishimori Systems

We study the initial value problem for the two-dimensional nonlinear nonlocal Schrödinger equations i u_t + u = N(v), (t, x, y) R³, u(0, x, y) = u₀(x, y), (x, y) R² (A), where the Laplacian = ² _x + ² _y, the solution u is a complex valued function, the nonlinear term N = N₁ + N₂ consists of the local nonlinear part N₁(v) which is cubic with respect to the vector v=(u,u_x,u_y,\overline{u},\overline{u}_{x},\overline{u}_{y}) in the neighborhood of the origin, and the nonlocal nonlinear part N₂(v) =(v, ^{– 1} _x K_x(v)) + (v, ^{– 1} _y K_y(v)), where (, ) denotes the inner product, and the vectors K_x (C⁴(C⁶; C))⁶ and K_y (C⁴(C⁶; C))⁶ are quadratic with respect to the vector v in the neighborhood of the origin. We assume that the components K⁽²⁾ _x = K⁽⁴⁾ _x 0, K⁽³⁾ _y = K⁽⁶⁾ _y 0. In particular, Equation (A) includes two physical examples appearing in fluid dynamics. The elliptic–hyperbolic Davey–Stewartson system can be reduced to Equation (A) with , and all the rest components of the vectors K_x and K_y are equal to zero. The elliptic–hyperbolic Ishimori system is involved in Equation (A), when , and . Our purpose in this paper is to prove the local existence in time of small solutions to the Cauchy problem (A) in the usual Sobolev space, and the global-in-time existence of small solutions to the Cauchy problem (A) in the weighted Sobolev space under some conditions on the complex conjugate structure of the nonlinear terms, namely if N(eⁱ v) = eⁱ N(v) for all R.     

On X-ray measurements of residual stresses in materials with lattice strain gradient

The non-linear distribution of lattice strain ³¹⁰vs sin² observed on the surface of a polished steel specimen can be interpreted by tri-axial stress state with surface components of stress tensor ₁₁(0)= ₂₂(0) and gradientsg ₁₁= ₁₁/T, g ₃₃= ₃₃/T. The distribution of experimental values is duscussed from the viewpoint of various ways of calculating ₁₁.The authors would like to thank Dr. J. Musil, D. Sc. of the Institute of Physics of Czechoslovak Academy of Sciences for kindly providing the samples which made possible this study.     

Decay π → + ν in the field of a plane electromagnetic wave with allowance for the polarizability of the pion

The process + in the field of a plane electromagnetic wave is investigated with allowance for the complex structure of the pion. Exact values are obtained for the probability of pion decay in circularly and elliptically polarized fields. Pion structure effects become observable for 5, where .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 65–68, December, 1991.