Instability in degenerate two-photon running wave laser

The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k>1+r(k=/,r=/; is the cavity loss of the field and , are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr<k<(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.     

A dynamical system with integer information dimension and fractal correlation exponent

In this paper we construct a family {T }, 0<<1/2, of exact endomorphisms of [0, 1] such that the invariant measurem ofT is equivalent to Lebesgue measure but has fractal correlation exponent =2. This shows that an almost complete dichotomy can exist between the information dimension and the correlation exponent in observable dynamical systems.Research supported by the Natural Sciences and Engineering Research Council of Canada     

The van der Waals limit for classical systems

For a -dimensional system of particles with the two-body potentialq(r)+ ^v K(r) and density , it is proved under fairly weak conditions onq andK that the canonical pressure (, ) and chemical potential (, ) tend to definite limits when 0. The limiting functions are absolutely continuous and are given in terms of the derivative of the limiting free energy density which was found in Part I.     

QCD sum rule analysis of the coupling constant g ωσγ

We employ QCD sum rules to calculate the coupling constant g by studying the three point -correlation function. Our result complements the analysis of this coupling constant utilizing the experimental value of the ⁰⁰ decay rate studied within the framework of chiral perturbation theory including vector meson and meson intermediate states.     

The nature of the C-defects in nickel and their rôle in the interpretation of radiation damage in metals

In previous Perturbed-Angular-Correlation (PAC) studies of the - emission of ¹¹¹In probe nuclei in cold-worked or particle-irradiated nickel, it has been found that thermal annealing in the temperature regime of recovery stage III leads to the formation of so-called C-defects (Cubic defects). This is indicated by the occurrence of a new frequency of about 80 Mrad/s, in addition to the frequency (200 Mrad/s) that is due to ¹¹¹In on substitutional sites. Obviously, the C-defects are complexes consisting of ¹¹¹In and the intrinsic point-defect species that migrates freely in recovery stage III. Therefore, they have played an important rôle in the long-standing controversy on whether the recovery-stage-III defects are vacancies (one-interstitial model) or self-interstitials (two-interstitial model). The present paper reports on a novel experimental effort to reveal the nature of the C-defects by combining PAC studies on nickel samples differently pretreated in a systematic way, investigations of the Extended X-ray Absorption Fine Structure (EXAFS) on In-doped nickel, and measurements of the decay rate of ¹¹¹In nuclei in the Electron-Capture-Induced Decay (ECID). On the basis of the results of these experiments it is concluded that the defects trapped by substitutional ¹¹¹In atoms (In_s) in recovery stage III are self-interstitials (I), as expected according to the two-interstitial model. Moreover, there is evidence that the C-defects are In interstitials on tetrahedral sites (In_i) that form exclusively in the vicinity of the specimen surface from In_s – I pairs via the reaction In_s+I In_i.     

The Anisotropic Free Energy of the Solid-Liquid Phase Boundary in Al

We have performed large-scale molecular dynamics simulations of solid-liquid interfaces in aluminum, in order to calculate their interfacial stiffness and free energy. The anisotropy of these properties, though small, is key for determining the steady-state solutions for solidification in three dimensions. We find that the interfacial free energy, (), can be well represented by the form () = ₀(1 + cos 4, where measures the angle relative to the [100] interface, rotating about a [001] direction. We find values of ₀ = 120 ± 6 mJ/m² and = 1.3 ± 0.4%, in agreement with previous estimates and current experimental results.     

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

Form of the NH3 spectral lines in the impact approximation and analytical expressions for the relaxation parameters

The half-width and cross-relaxation parameter are calculated for a series of rotational transitions on the basis of a rigorous theory taking account of the correlational broadening of the doublet components. The absorption of the doublet lines of the transition J = 4 5 for the system NH₃-N₂ and the transition J = 5 6 for NH₃-NH₃ is analyzed. For the vibrational ground state, analytical expressions are given for the parameters and .Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 6, pp. 3–7, June, 1984.     

Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Pauli-Dirac matrix generators of Clifford Algebras

This article presents a Pauli-Dirac matrix approach to Clifford Algebras. It is shown that the algebra C₂ is generated by two Pauli matrices i₂ and i₃; C₃ is generated by the three Pauli matrices ₁, ₂, ₃; C₄ is generated by four Dirac matrices ₀, ₁, ₂, ₃ and C₅ is generated by five Dirac matrices i₀, i₁, i₂, i₃, i₅. The higher dimensional anticommuting matrices which generate arbitrarily high order Clifford algebras are given in closed form. The results obtained with this Clifford algebra approach are compared with the vector product method which was described in a recent article [Found. Phys. 10, 531–553 (1980) by Poole, Farach and Aharonov] and with the Dirac, Rashevskii and Ramakrishnan methods of matrix generation.Supported by the National Science Foundation under Grant ISP-80-11451.     

Kinetic theory of granular shear flow: Constitutive relations for the hard-disk model

A kinetic theory for the constitutive Theological relations of rapid granular shear flow of hard circular disks, characterized by a coefficient of restitutione and a surface roughness coefficient, is formulated. From a set of general constitutive equations for single-particle dynamical variables, the approximate expressions for the limit of small and large dimensionless dissipative parameterR _t are obtained. HereR _t is defined as the ratio /, where is the fluctuation of translational velocity from the mean flow velocity, is the diameter of a disk, and is the shear rate. At smallR _t the theoretical predictions can be compared with exact computer simulation results of granular dynamics that are also reported. The agreement between theory and simulation is better than expected; the present theory is accurate up to high packing density in this region ofR _t .     

Combining Multifractal Additive and Multiplicative Chaos

The purpose of this article is the study of the new class of multifractal measures, which combines additive and multiplicative chaos, defined bywhere is any positive Borel measure on [0,1] and b is an integer 2. The singularities analysis of the measures _, involves new results on the mass distribution of when describes large classes of multifractal measures. These results generalize ubiquity theorems associated with the Lebesgue measure.Under suitable assumptions on , the multifractal spectrum of _, is linear on [0,h_, ] for some critical value h_, . Then is strictly concave on the right of h_, , and on this part it is deduced from the multifractal spectrum of by an affine transformation. This untypical shape is the result of the combination between Dirac masses and atomless multifractal measures. These measures satisfy multifractal formalisms. They open interesting perspectives in modeling discontinuous phenomena.     

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.     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

Elimination of variables in simple laser equations

The usual way of obtaining rate equations (RE) and a single equation for the field amplitude (EFA) from the semiclassical laser equations (Lorenz-Haken model) is reexamined by undertaking a systematic elimination procedure developed in synergetics. The RE and EFA are justified in the case 1 (, ) and case 2 (, ), respectively. We show that, because the eliminated variable happens to contain a considerable contribution from an unstable mode, the usual elimination technique in the case 3 (, ) leads to an inconsistency. As important by-products we obtain the RE and EFA for arbitrary cavity relaxation constant (). Some remarks are given on the direct elimination technique in the non-diagonal representation in the study of instabilities.     

Radiative decays of the Z boson

We calculate the Stokes parameters of the photons produced in the decays of neutral vector bosons Z, Z 1+¯1+ and Z q+¯q+, wherel=e, , or , and q is a quark. In the decays of unpolarized Z bosons (with the production of unpolarized leptons or quarks) the nonzero Stokes parameters for ₂ (circularly polarized photons) and ₃ (linearly polarized photons). The magnitude of ₃ does not depend on the parameters of the netural weak current of the leptons and the quarks (if their mass is neglected). The anomalous magnetic moment of the Z boson is studied.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 38–43, February, 1986.     

The critical point indices of ferroelectric and ferromagnetic phase transitions

Magnetic transitions are described by the critical indices0,1/3,4/3 while some ferroelectric transitions appear to give0,R~1/2,1. It is pointed out that these two sets of values for the critical indices are allowed by the scaling laws and stability conditions near the phase transitions.The authors thank Prof. R. S. Krishnan for his encouragement and Mr. B. Viswanathan for some discussions. The financial assistance from DAE and CSIR is also acknowledged.     

Amplitude-distortion factors for the inelastic scattering of an electron at a neon atom in an electric field

Inelastic electron scattering at a neon atom in the presence of an external electric field is considered. The distortion factors of the cross section _M (F) are calculated for a series of 4d and 5d levels. It is shown that the distortion factor in strong fields is a nonlinear and nonmonotonic function of the field. The distortion factors and transition probabilitiesA , are compared. The correlation between the behavior ofA , and _M (F) is explained by the dependence of the mean dipole moment of the Stark state on the field strength.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 97–110, January, 1996.     

The Critical Attractive Random Polymer in Dimension One

A polymer chain with attractive and repulsive forces between the building blocks is modeled by attaching a weight e ^– for every self-intersection and e ^/(2d) for every self-contact to the probability of an n-step simple random walk on ^d , where , >0 are parameters. It is known that for d=1 and > the chain collapses down to finitely many sites, while for d=1 and < it spreads out ballistically. Here we study for d=1 the critical case = corresponding to the collapse transition and show that the end-to-end distance runs on the scale _n = (log n)^–1/4. We describe the asymptotic shape of the accordingly scaled local times in terms of an explicit variational formula and prove that the scaled polymer chain occupies a region of size _n times a constant. Moreover, we derive the asymptotics of the partition function.     

Gamma-ray spectroscopy in 110Sn and 111Sn

Excited states in ¹¹⁰Sn and ¹¹¹Sn nuclei have been investigated using in-beam -ray spectroscopic methods. An ¹⁶O beam with an energy of 60-80MeV was used to bombard a ⁹⁸Mo target. On the basis of the relative excitation functions, -ray angular distributions, - and -time distributions, -ray multiplicity and total energy data, the level schemes of ¹¹⁰Sn and ¹¹¹Sn have been studied and extended up to E_exc 11.5MeV, I = 24, and E_exc 11.1MeV and I = (51/2), respectively. An extension of the intruder, g.s. and negative-parity bands, as well as 5 new band-like structures are proposed in ¹¹⁰Sn. The nature of newly introduced collective band 8 as well as 10⁺ states fed in the decay of the collective band is discussed. In the ¹¹¹Sn nucleus an intruder band based on the 23/2^- state has been reinvestigated and the extension of the g.s. band and second negative-parity band is given. Evidence for neutron-core coupling in ¹¹¹Sn is found. The structure and systematics of excited states in light Sn isotopes is discussed.