Raman effect of light on argon atoms

Scalar scattering of light on the 3p and 3s subshells of the argon atom (Stokes scattering) and anti-Stokes scattering on the excited 4p and 4s states of argon are examined in the Hartree-Fock approximation. The calculation is made in a velocity form and in a length form. It is shown that the value in the r form is 1.5–2 times greater than in the form.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 36–42, January, 1977.     

Moments of ferromagnetic resonance absorption lines of a polycrystalline ferrite

The moments of ferromagnetic resonance absorption lines of a polycrystalline ferrite are computed in a spin-wave approximation and the independent grains approximation. The possibility of determining the limits of applicability of the above-mentioned approximations from experiment is predicted from a comparison of the formulas obtained for the moments.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 117–121, July, 1972.     

Analytic Properties of the Structure Function for the One-Dimensional One-Component Log–Gas

The structure function S(k; ) for the one-dimensional one-component log–gas is the Fourier transform of the charge–charge, or equivalently the density–density, correlation function. We show that for |k|j in the power series expansion of f(k; ) about k=0 is of the form of a polynomial in /2 of degree j divided by (/2)^j. The bulk of the paper is concerned with calculating these polynomials explicitly up to and including those of degree 9. It is remarked that the small k expansion of S(k; ) for the two-dimensional one-component plasma shares some properties in common with those of the one-dimensional one-component log–gas, but these break down at order k⁸.     

Vertex Operators of the q-Virasoro Algebra; Defining Relations,Adjoint Actions and Four Point Functions

Primary fields of the q-deformed Virasoro algebra are constructed. Commutation relations among the primary fields are studied. Adjoint actions of the deformed Virasoro current on the primary fields are represented by the shift operator f(x) = f(x). Four point functions of the primary fields enjoy the connection formula associated with the Boltzmann weights of the fusion Andrews–Baxter–Forrester model.     

Particles and scaling for lattice fields and Ising models

The conjectured inequality ⁽⁶⁾0 leads to the existence of _d ⁴ fields and the scaling (continuum) limit ford-dimensional Ising models. Assuming ⁽⁶⁾0 and Lorentz covariance of this construction, we show that ford6 these _d ⁴ fields are free fields unless the field strength renormalizationZ ^–1 diverges. Let be the bare charge and the lattice spacing. Under the same assumptions (⁽⁶⁾0, Lorentz covariance andd6) we show that if ^4–d is bounded as 0, thenZ ^–1 is bounded and the limit field is free.Supported in part by the National Science Foundation under Grant MPS 74-13252Supported in part by the National Science Foundation under Grant MPS 75-21212     

Analytic study of power spectra of the tent maps near band-splitting transitions

Successive band-splitting transitions occur in the one-dimensional map x_i+1=g(x_i),i=0, 1, 2,... withg(x)=x, (0 x 1/2) –x +, (1/2 <x 1) as the parameter is changed from 2 to 1. The transition point fromN (=2ⁿ) bands to 2Nbands is given by=(2)^1/N (n=0, 1,2,...). The time-correlation function _i=x_ix₀/(x₀)²,x_i x_i–x_i is studied in terms of the eigenvalues and eigenfunctions of the Frobenius-Perron operator of the map. It is shown that, near the transition point=2, _i–[(10–42)/17] _i,0-[(102-8)/51]_i,1 + [(7 + 42)/17](–1)ⁱe^–yi, where2(–2) is the damping constant and vanishes at=2, representing the critical slowing-down. This critical phenomenon is in strong contrast to the topologically invariant quantities, such as the Lyapunov exponent, which do not exhibit any anomaly at=2. The asymptotic expression for _i has been obtained by deriving an analytic form of _i for a sequence of which accumulates to 2 from the above. Near the transition point=(2)^1/N, the damping constant of _i fori N is given by _N=2(^N-2)/N. Numerical calculation is also carried out for arbitrary a and is shown to be consistent with the analytic results.     

On the Eigenstates of the Elliptic Calogero–Moser Model

It is known that the trigonometric Calogero–Sutherland model is obtained by the trigonometric limit (–1) of the elliptic Calogero–Moser model, where (1, ) is a basic period of the elliptic function. We show that for all square-integrable eigenstates and eigenvalues of the Hamiltonian of the Calogero–Sutherland model, if exp(2–1) is small enough then there exist square-integrable eigenstates and eigenvalues of the Hamiltonian of the elliptic Calogero–Moser model which converge to the ones of the Calogero–Sutherland model for the 2-particle and the coupling constant l is positive integer cases and the 3-particle and l=1 case. In other words, we justify the regular perturbation with respect to the parameter exp(2–1). With some assumptions, we show analogous results for N-particle and l is positive integer cases.     

Continuum and discretum—Unified field theory and elementary constants

Unitary field theories and SUPER-GUT theories work with an universal continuum, the structured spacetime of R. Descartes, B. Spinoza, B. Riemann, and A. Einstein, or a (Machian ^(1–3) ) structured vacuum according the quantum theory of unitary fields (Dirac, ^(4,5) and Heisenberg ^(6–8) ). The atomistic aspect of the substantial world is represented by the fundamental constants which are invariant against all transformations and which depend on nothings (Planck ^(9–11) ). A satisfactory unitary theory has to involve these constants like the mathematical numbers. Today, Planck's conception of the three elementary constants , c, and G may be the key to general relativistic quantum field theory like unitary theory. However, the elementary constants are a question of measurement-theory, also.According to Popper's theory ^(12–16) of induction, such unitary theories are universal explaining theories. The fundamental constants involve the complementarity between the universal statements in unitary theory and the basic statements in the language of classical observables.     

Heavy quark cascade mechanism of tetramuon production by neutrinos in a scale-breaking model

A few neutrino-induced tetramuon events have recently been reported by two experimental groups with a production rate of 10^–6 for( ^{– – + +})/ ( ^–). However, the rate for such events is not yet determined theoretically. In the present paper, we report on a detailed calculation of the rate in the framework of a heavy quark cascade mechanism, using the QCD-improved parton distribution functions parametrized by Buras and Gaemers, which have successfully fitted various experimental data. Our calculation for( ^{– – + +})/ () accords well with the CDHS and FHPRW rate. The computed rate is also in accord with that obtained via the radiative charm model calculation, whereby the normal charm dimuon production is accompanied by a radiative ^{+ –} pair.     

The surfboard Schrödinger equations

We study the large time behavior of solutions of time dependent Schrödinger equationsiu/t=–(1/2)u+t V(x/t)u with bounded potentialV(x). We show that (1) if>–1, all solutions are asymptotically free ast, (2) if–1 a solution becomes asymptotically free if and only if it has the momentum support outside of suppV for large time, (3) if –1 <0 all solutions are still asymptotically modified free ast and that (4) if 0 <2, for each local minimumx ₀ ofV(x), there exist solutions which are asymptotically Gaussians centered atx=tx ₀ and spreading slowly ast.     

Radiation of relativistic electrons in a magnetic undulator

Expressions are obtained for the spectral-angular characteristics of the radiation in two limiting cases: 1 and 1 ( is the angle of deflection of the electron in the field, and is the energy of the electron in units of mc²). It is shown that in the latter case the maximum of the radiation occurs at higher harmonics.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 88–91, October, 1973.In conclusion the authors thank Professor A. A. Sokolov for useful discussions.     

Ising Field Theory in a Magnetic Field: Analytic Properties of the Free Energy

We study the analytic properties of the scaling function associated with the 2D Ising model free energy in the critical domain TT _c , H0. The analysis is based on numerical data obtained through the Truncated Free Fermion Space Approach. We determine the discontinuities across the Yang–Lee and Langer branch cuts. We confirm the standard analyticity assumptions and propose extended analyticity; roughly speaking, the latter states that the Yang–Lee branching point is the nearest singularity under Langer's branch cut. We support the extended analyticity by evaluating numerically the associated extended dispersion relation.     

Strict inequalities for some critical exponents in two-dimensional percolation

For 2D percolation we slightly improve a result of Chayes and Chayes to the effect that the critical exponent for the percolation probability isstrictly less than 1. The same argument is applied to prove that ifL():={(x, y):x=r cos, y=r sin for some r0, or} and():=limpp _c [log(p–p _c )]^–1 log P_cr {itO is connected to by an occupied path inL()}, then() is strictly decreasing in on [0, 2]. Similarly, lim_n [–logn]^–1 logP _cr {itO is connected by an occupied path inL()() to the exterior of [–n, n]×[–n, n] is strictly decreasing in on [0, 2].     

Long-time tails in lattice Lorentz gases

We consider a Lorentz gas on a square lattice with a fraction c of scattering sites. The collision laws are deterministic (fixed mirror model) or stochastic (with transmission, reflection, and deflection probabilities ,, and respectively). If all mirrors are parallel, the mirror model is exactly solvable. For the general case a self-consistent ring kinetic equation is used to calculate the longtime tails of the velocity correlation function (0) (t) and the tensor correlation Q(0)Q(t) withQ= _{x y} . Both functions showt ^–2 tails, as opposed to the continuous Lorentz gas, where the tails are respectivelyt ^–2 andt ^–3. Inclusion of the self-consistent ring collisions increases the low-density coefficient of the tail in (0)(t) by 30–100% as compared to the simple ring collisions, depending on the model parameters.     

Four-parametric regular black hole solution

We present a regular class of exact black hole solutions of the Einstein equations coupled with a nonlinear electrodynamics source. For weak fields the nonlinear electrodynamics becomes the Maxwell theory, and asymptotically the solutions behave as the Reissner–Nordström one. The class is endowed with four parameters, which can be thought of as the mass m, charge q, and a sort of dipole and quadrupole moments and , respectively. For 3, 4, and |q|2s _c m the corresponding solutions are regular charged black holes. For = 3, they also satisfy the weak energy condition. For = = 0 we recover the Reissner–Nordström singular solution and for = 3, = 4 the family includes a previous regular black hole reported by the authors.     

Feasibility of an experiment to determine the branching ratio for the emission of a heavy neutrino after muon capture in3He

The triton energy of the muon capture reaction ³He t+v, where ³ He is the ground state of muonic³He, has been measured in order to investigate a possible heavy v admixture into the flavour with high sensitivity. ³ He has been formed via the pd fusion reaction by stopping ^– in an ionization chamber (IC) filled with an H/D gas mixture of 3% D concentration at a pressure of 161 bar. In a first short experiment 650 triton events were observed yielding an upper limit for the -heavy v mixing strength of 2.3×10^–3 atE _0v=60 MeV.     

The contrast gain in a guest-host nematic display due to a periodic boundary condition

The mean square tilt angle of a nematic slab with finite anchoring energy and periodic boundary conditions has been theoretically investigated, as a function of the slab geometry and of the reduced extrapolation length. If the anchoring strength is free-surfacelike, the contrast is affected by a loss 10% at room temperature if the ratio between the anchoring pitch and the cell thickness is 0.5.Glossary anchoring pitch - h cell thickness - /h - ( = x/, = y/h) reduced coordinates - (, ) local tilt angle - elastic constant - w_a anchoring energy anisotropy - b=/w _a de Gennes-Kleman extrapolation length - B=b/h reduced extrapolation length - T _NI nematic-isotropic transition temperature - :=(T/T _NI ) – 1 reduced temperature - easy axis direction - _MAX - _± ² mean square tilt angle along the boundary - () absorbance coefficients of the p-dye - r /: dichroic ratio - c contrast - G contrast gain - S order parameter     

Mössbauer evidence of reentrant spin-glass phase in the Fe0.45Mn0.25Al0.30 disordered alloy

Zero and longitudinal field SR have been used to study the evolution of spin correlations and magnetic order resulting from 10at% substitution of Zr for Nb in the weak itinerant antiferromagnet NbFe₂. Rapidly fluctuating atomic fields (=0.02s^–1) are found to persist almost unchanged to low temperatures. These coexist with a narrow distribution of static fields (=0.2s^–1) which evolves from a gaussian to lorentzian form between 90K and the Curie temperature of 43K. It is suggested that these effects may be a consequence of topologically frustrated exchange between Fe sites in the C14 structure.     

Noncommutative Unification of General Relativity and Quantum Mechanics

We propose a mathematical structure, based on anoncommutative geometry, which combines essentialaspects of general relativity with those of quantummechanics, and leads to correct limitingcases of both these physical theories. Thenoncommutative geometry of the fundamental level isnonlocal with no space and no time in the usual sense,which emerge only in the transition process to thecommutative case. It is shown that because of the originalnonlocality, quantum gravitational observables should belooked for among correlations of distant phenomenarather than among local effects. We compute the Einstein–Podolsky–Rosen effect; itcan be regarded as a remnant or a shadowof the noncommutative regime of the fundamental level.A toy model is computed predicting the value of thecosmological constant (in the quantum sector) which vanishes whengoing to the standard spacetime physics.     

Fractional noise

Fractional noiseN(t),t 0, is a stochastic process for every , and is defined as the fractional derivative or fractional integral of white noise. For = 1 we recover Brownian motion and for = 1/2 we findf ^–1-noise. For 1/2 1, a superposition of fractional noise is related to the fractional diffusion equation.