LETTER: A Simple Quantum Cosmology

A simple and surprisingly realistic model of the origin of the universe can be developed using the Friedmann equation from general relativity, elementary quantum mechanics, and the experimental values of , c, G and the proton mass m _p. The model assumes there are N space dimensions (with N > 6), and the potential constraining the radius r of the invisible N – 3 compact dimensions varies as r ⁴. In this model, the universe has zero total energy and is created from nothing. There is no initial singularity. If space-time is eleven dimensional, as required by M theory, the scalar field corresponding to the size of the compact dimensions inflates the universe by about 26 orders of magnitude (60 e-folds). If H ₀ = 65 km sec^–1 Mpc^–1, the energy density of the scalar field after inflation results in = 0.68, in agreement with recent COBE and Type SNe Ia supernova data.     

Influence of magnetic field on cesium thermionic energy converter

This article deals with the calculation of the influence of the magnetic field upon the electric current of a thermionic converter presupposing the approach to conditions in a low-pressure cesium converter. The distribution of the starting velocities of the emitted electrons is considered firstly as independent of the angle from the perpendicular to the emitter plane, and secondly according to the cosine law.The magnetic field effect from the converter current is calculated and compared with the calculations in the papers by Schock [1] and Block [2]; the effect of the external magnetic field is verified by measurements on a solar thermionic converter prototype.Symbols F=I/I ₀ factor of current reduction from magnetic field effect - ¯F value of factorF (when the magnetic field is not constant) - I [A/m²] density of collector current (real current influenced by magnetic field) - I ₀ [A/m²] theoretical density of collector current (in ideal case equals electron emission current) - T _e [°K] electron gas temperature; assumed equal to emitter temperatureT _E [°K] - B[Wb/m²] magnetic induction (field) - D[m] distance from emitter to collector - R[m] radius of electrodes, emitter and collector - r[m] variable radius in the limits 0 toR - V [m/s] random velocity of electron - v _xz [m/s] component of the vectorV inx-z plane - v _m =2kT _E /m most probable velocity in the velocity distribution according to Maxwell and Boltzmann - w-v _xz /v _m relatively expressed electron velocityv _xz - the angle of any vectorV - [m] radius of circular electron path - n [m^–3] number (density) of electrons with certain value of random velocity - n ₀ [m^–3] total electron number (density) - n ₁ [m^–3] number of electrons returned to emitter by means of magnetic field - N ₀ [m^–2s^–1] total flow of thermionic electrons emitted from a unit surface - N ₁ [m^–2s^–1] partial flow of electrons returned to emitter - P=N ₁/N₀ relatively expressed flow of electrons returned to emitter (whenB = const.) - ¯P mean value ofP (whenB const.) - F _cos, ,P _cos, values asF,¯F,P,¯P in case of velocity distribution according to cosine law - m=9·107×10^–31 [gk] electron mass - e=1·60×10^–19 [C] electron charge - k×1·38×10^–23 [J/grad] Boltzmann's constant - ₀ 1·257×10^–6 [H/Vs] permeability of vacuum     

Painlevé test of the McKean and Carleman models

The Painlevé test of the system of nonlinear partial differential first-order equations u₁+u_k=k₁v²+k₂u²+k₃uv, v₁–v_x=–k₁v²–k₂u²–k₃uv is performed. The system includes the Carleman and McKean models which are caricatures of the Boltzmann equation. For k ₁=k ₂=0 the system describes the interaction of two waves u and v. The results of the Painlevé test are discussed in connection with whether or not the system is integrable. We also study in detail the constraint on (whose vanishing defines a noncharacteristic hypersurface S) which arises at the resonance.     

Narrow-band extreme-ultraviolet laser radiation tunable in the range 90.5–95 nm

Tunable, narrowband extreme ultraviolet radiation in the range 90.5–95 nm with only limited intensity variations is produced by frequency-tripling ultraviolet light from a frequency-doubled dye laser in a gas-jet of xenon. Acetylene gas is found to be an efficient medium for third-harmonic generation in this wavelength range as well. The extreme-ultraviolet radiation is applied in a spectroscopic study of the b ¹ II _u , v=6–8 and v=10–12, o ¹ II _u , v=0 and b¹ _u ⁺ , v=9 states of molecular nitrogen. From linewidth measurements a value k _p=6×10¹⁰ s^–1 for the predissociation rate of the b ¹ II _u , v=11 state is deduced.     

Drift theory of charged-particle motion for a strong electric field in a weakly relativistic approximation

Drift equations of motion are derived for a charged particle in the case of a strong electric field with allowance for relativistic effects of order v²/c². The role of these effects is discussed along with the effects of a high-frequency field. The cases of weak and strong electric fields are distinguished [2] in the drift theory of the motion of charged particles in weakly inhomogeneous magnetic and electric fields. In the case of a weak electric field, the electric-drift velocity is v_E v, where v is the characteristic velocity of the particle. For a strong electric field,v _Ev.The drift theory has now been reasonably well developed for the case of weak electric fields in the classical and relativistic cases, for the absence of high-frequency fields and for the presence of these [1–3], Extension of the theory to strong electric fields involves considerable mathematical difficulties, and this has been done only in the classical approximation with and without hf fields [2–4], Here we consider the drift theory of charged-particle motion for the case of a strong electric field in the weakly relativistic approximation, incorporating terms of order v²/c², where c is the velocity of light. Also hf fields may be present.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 9, pp. 7–9, September, 1981.     

Determination of the isotopic composition of hydrogentritium mixtures by emission spectroscopy

Absolute effective cross sections for collisions of the second kind are evaluated by studying the dependence of line or molecular band intensification on the partial pressures of mixture components in a glow discharge. Determination of the cross sections is based on measurement of the relative intensities of the corresponding bands in mixtures of different percentage composition. The resulting values for the effective cross sections Q are as follows: N₂(C³ II)_v=3 and Ar(³P_o) 3.10^–15 cm², N₂(C³ II)_v=2 and Ar(³P₂) 0.8.10^–15 cm, N₂(C³ II)_v=0 and CO 2.10^–15 cm, CO(C³ II)_v=0 and Ar(³P₂) 0.3.10^–15 cm².In conclusion, the authors wish to thank V. S. Mel'chenko for discussing the results of the present study.     

Monte Carlo renormalization of hard sphere polymer chains in two to five dimensions

A renormalization group for polymer chains with hard-core interaction is considered, where a chain ofN ₀ links of lengthl ₀ and hard-core diameterh ₀ is mapped onto a chain ofN ₁=N ₀/s links of lengthl ₁ and hard-core diameterh ₁. The lengthl ₁ is defined in terms of suitable interior distances of the original chain, andh ₁ is found from the condition that the end-to-end distance is left invariant. This renormalization group procedure is carried through by various Monte-Carlo methods (simple sampling is found advantageous for short enough chains or high dimensionalities, while dynamic methods involving kinkjumps or reptation are used else). Particular attention is paid to investigate systematic errors of the method by checking the dependence of the results on bothN ₀ ands. It is found that for dimensionalitiesd=2, 3 only the nontrivial fixed-point is stable, where upon iteration the ratio _k =h _k /l _k tends to nonzero fixed-point value ^*, while ford=4,5 the method converges to the gaussian fixed point with ^*=0. Taking both statistical and systematic errors into account, we estimate the exponentv asv=0.74±0.01 (d=2) andv =0.59±0.01 (d=3). The results are consistent with the expected crossover exponents =1/2 (d=3) and =1 (d=2), respectively.     

A μSR study of spin density wave condensation in Cr85Mo15

Zero field SR spectra from Cr₈₅Mo₁₅ are well described by the sum of a lightly damped (0.02s^–1<₁<0.2s^–1) and a heavily damped (2s^–1<₂<15s^–1) exponential. The temperature dependence of these components is discussed in relation to the condensation of the incommensurate spin density wave and the onset of the antiferromagnetic state in this Cr-like alloy below T_N=120K. Evidence is presented for the nucleation of the spin density wave at temperatures greater than 1.5T_N.     

Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2^– state in¹⁴⁵Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency _L=g_NN¹ (T)B_ext. The paramagnetic correction factor strictly follows the Curie-Weiss relation =1+C/(T-), withC=–50(2) K and =–29(5) K. This is compatible with a hyperfine field ofB _int(0)=–25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.The temperature dependence of the electric quandrupole coupling constant v_Q, investigated between 100 K and 400 K, can be reproduced by a linear temperature variation v_Q(T)=v_Q(0) (1-AT), with v_Q(0)=16.2(4) MHz andA=7.2(8)·10^–4 K^–1.The paramagnetic relaxation time _rel of the nuclear alignment is proportional to the temperature of the sample, with _rel T^–1=3.7(2) ·10^–9s K^–1.This leads to the Korringa relation _J T=const=5.1(5)·10^–11s K for the relaxation time of the 4f electronic spinJ. Assuming that the relaxation ofJ is mainly caused by exchange interaction between conduction electrons and localized 4f electrons at the Eu site, an exchange integral of |J _eff|=0.10(2) eV can be deduced.     

Generalized Position and Momentum Tsallis Entropies

We use the generalized Tsallis entropy S _v(q = (1 –( ^w _i=1 p ^q _i )/(q – 1) to studythe information measurement in position and momentum space for simple quantummechanical systems. We consider here the hydrogen atom in three dimensions andthe D-dimensional harmonic oscillator to calculate the position and momentumentropies analytically for ground and excited states which involve classicalorthognal polynomials. In both the cases we verify the generalized entropicuncertainty relation and pseudoadditivity relation. We also study the effect ofscreening on the entropies. We compare the present results with the correspondingresults of the Shannon formalism.     

Bianchi-I Cosmologies with Electromagnetic and Spinor Fields. Isotropization Problem

We consider Bianchi type I cosmologies with unidirectional magnetic and electric fields, assuming as well the existence of a global spinor field ψ(t) as one more possible source of gravity able to suppress the inevitable anisotropy accompanying a nonzero vector field. The field ψ(t) is assumed to contain a nonlinearity in the form s ⁿ , where and n=const (the special case n=1 corresponds to a Dirac massive field). The structure of the stress-energy tensor of the spinor field is shown to be the same as that of a perfect fluid with the equation of state p=w ρ where w=n−1. The Dirac massive spinor field and nonlinear fields with n<4/3 are shown to be able to provide isotropization. A numerical estimate shows that this isotropization could occur early enough to be compatible with observations.     

Volume and grain boundary diffusion of implanted 113Sn in aluminium

Volume and grain boundary diffusion of ¹¹³Sn in aluminium was investigated with the radiotracer method. The implantation technique was used for tracer deposition to avoid problems of tracer hold-up caused by the oxide layer always present on aluminium. The diffusion penetration was chosen large enough to permit serial sectioning of samples with the aid of a microtome.The temperature dependence of the volume diffusivity was determined as D(T)=4.54×10^–5×exp[–(114.5±1.2)kJmol^–1/RT] m ² s ^–1. This confirms previous measurements from our group which already showed that Sn is the fastest foreign metal diffusor so far investigated in aluminium.Grain boundary diffusion of ¹¹³Sn in Al polycrystals was measured in the type-B kinetic regime. The grain boundary diffusion product P=sD _gb (s=segregation factor, =grain boundary width, D _gb=grain boundary diffusivity) was found to be strongly affected by the impurity content of aluminium. For Al polycrystals of 99.9992% nominal purity we obtained P _5N(T)=1.08×10^–8exp [–(96.9±7.5) kJ mol^–1/RT] m³ s^–1 and for less pure Al polycrystals of 99.99% nominal purity P _4N(T)=3.0×10^–10 exp [–(90.1±4.2) kJ mol^–1/RT] m³ s^–1 was determined. The grain boundary diffusion product in the purer material is more than one order of magnitude higher than in the less pure material. Very likely this is an effect of co-segregation of non-diffusant impurities into the grain boundaries.     

Ion aging effects on the dissociative-attachment instability in CO2 lasers

Onset of the dissociative-attachment instability requires that the rate coefficient for electron detachment (k _d) from negative ions be below a critical value. The predominant negative and positive ions in a CO₂N₂He gas-discharge plasma are known to change with time. As secondary by-products form and the predominant negative-ion species changes from CO ₃ ^– to NO ₂ ^– , a decrease ink _d occurs destabilizing the discharge. Since NO ₂ ^– and NO ₃ ^– are largely unreactive with respect to associative detachment,k _d depends in a sensitive fashion on the concentration of certain minority negative ions (O^–, O ₂ ^– ) and neutrals (CO, O, N). The sufficient conditions for the dissociative-attachment instability are much less sensitive to changes in the electron-ion and ion-ion recombination rate coefficients resulting from the ion aging process.     

TheCP N−1 1/N-action by inverse scattering transformation in angular momentum

The effective action which generates 1/N expansion of theCP _N–1 model in two dimensions is studied here by inverse-problem methods. The action contains a functional determinant, in which auxiliary scalar and vector fields are assumed to have a spherical symmetry. This leads to the introduction, as an associated linear problem, of a radial Schrödinger equation with two potentialsv and , and a potential-dependent centrifugal term {(–r)²/r ²–1/4r ²}. The full inverse scattering formalism is developed here for this diffusion problem. It is formulated in terms of two-component Jost solutions, and leads to a matricial Gel'fand-Levitan-Marchenko equation. The scattering data associated to the potentials by this IST are then used to obtain a closed local form for the whole effective action. This is indeed possible for theCP _N–1 model, owing to the classical integrability. Moreover it is found that no spherically symmetric instanton exists in this case. However the absence of supplementary informations on the 1/N series, due to the non-integrability at quantum level, does not allow safe quantitative conclusions on the general behaviour of the 1/N series at large orders.Laboratoire associé au CNRS UA 280     

Short Representations of SU(2,2/N) and Harmonic Superspace Analyticity

We consider the harmonic superspaces associated with SU(2,2/N) superconformal algebras. For arbitrary N, we show that massless representations, other than the chiral ones, correspond to [N/2] elementary ultrashort analytic superfields whose first component is a scalar in the k antisymmetric irrep of SU(N) (k=1...[N/2]) with top spin J _top=(N/2–k/2,0). For N=2n, we analyze UIR's obtained by tensoring the self-conjugate ultrashort multiplet J _top=(n/2,0) and show that N–1 different basic products give rise to all possible UIR's with residual shortening.     

Electron-electron bremsstrahlung in a non-equilibrium plasma

Electron-electron bremsstrahlung in a weakly ionized uniform non-stationary plasma is investigated. The respective problem is solved analytically for two initial electron-distributions: maxwellian with the temperatureT ₀, and the delta distribution. In the case of initial maxwellian distribution the radiation intensity is proportional to ^3/2, where=T+(T ₀–T) exp (–s),s=2mv ₁ t/M,v ₁ is the momentum transfer frequency, and the other symbols are standard. In the case of initial delta distribution the radiation intensity is proportional to [1 -exp (–s)]^3/2. The proportionality factors are known, and are expressed in terms of mathematical and physical constants.     

A solution spectrum of the nonlinear Schrödinger equation. II

It was shown in a previous communication that the nonlinear Schrödinger equation exhibits a spectrum of eigenfunctions of the form = _k,A _k (coshkx) ^–k and = _k B _k (coshkx) ^–k–1sinhkx, and the corresponding eigenvalues of the energy are related to a band structure with a characteristic energy gap as a significant feature. In the present paper, it is shown that a further spectrum exists exhibiting the general structure = _k=0 A _k(cosh kx)^–k–1/2and = _k=0 B_k(cosh kx)^–k–3/2sinhkx and yielding also a band structure. An extension of the solution spectrum to a nonlinear Klein-Gordon equation and a nonlinear Dirac equation does not imply essential difficulties, and the corresponding characteristic band structure has to be related to a mass spectrum.     

Inverse muon decay in a steady external field

A standard Weinberg-Salam model has been used to calculate the cross section of +e »v _e+ in steady crossed fields (EH=E ²–H ²=0). The asymptotic behavior of the cross section has been examined as a function of the kinematic and dynamic (field) invariant parameters.M. V. Lomonosov Moscow State University. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 106–111, December, 1992.     

Long-Time tails in a random diffusion model

Letw = {w(x)xZ^d} be a positive random field with i.i.d. distribution. Given its realization, letX _t be the position at timet of a particle starting at the origin and performing a simple random walk with jump rate w^–1(X_t). The processX={X _t:t0} combined withw on a common probability space is an example of random walk in random environment. We consider the quantities _t =(d/dt) E (X _t ² –M ^–1 t and _t(w) = (d/dt)E_w(X _t ² – M^– 1t). Here E_w. is expectation overX at fixedw and E = E_w (dw) is the expectation over bothX andw. We prove the following long-time tail results: (1) lim_t t^d/2_t= V²M^d/2–3(d/2)^d/2 and (2) lim_t t^d/4 _st(w)= Z_s weakly in path space, with {Z_s:s>0} the Gaussian process with EZ_s=0 and EZ_rZ_s= V²M^d/2–4(d)^d/2 (r + s)^–d/2. HereM and V² are the mean and variance of w(0) under . The main surprise is that fixingw changes the power of the long-time tail fromd/2 tod/4. Since , with ₀ the stationary measure for the environment process, our result (1) exhibits a long-time tail in an equilibrium autocorrelation function.     

Determination of the unsaturated losses and of the saturation intensity in the KrCl excimer laser

The unsaturated losses , and the saturation intensityI _s, were measured in an uv-preionized KrCl laser for optimized He and Ne based laser gas mixtures. The measurements were made as a function of the specific power loading and of the total pressure of the laser mixtures. Higher values for andI _s were found for the Ne-based laser mixture than for the He-based mixture. At 45 kV charging voltage and at 355 kPa of total pressure we measured =0.053 cm^–1 andI _s =9.4MW/cm² for the Ne based mixture, and =0.035 cm^–1 andI _s =5.1MW/cm² for the He based mixture.