Calculation and optimization of parameters of radiating distributed feedback structures

A simple method is suggested for calculation of reflection, radiation and transmission coefficients for the distributed feedback structure in the second diffraction order. The method is based on a slight difference between coefficients of reflectionR and radiationI of the surface wave for = (where is the light wavelength corresponding to a precise resonance for the grating length I) and those for =_l (where _l is the light wavelength corresponding to the resonance for the finite grating length). The simplicity of the method makes it possible to use it for optimization of the distributed feedback structure by a number of parameters. The technique can be used in the case of thin-film and diffused waveguides for both TE and TM modes.     

Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

Rational forms for twistings of enveloping algebras of simple Lie algebras

We give rational forms for twistings of classical enveloping algebras. We also remark a link with the generalized formalism of Gurevich, Manin, and Cartier.     

Cλ-Extended Oscillator Algebras and Some of Their Deformations and Applications to Quantum Mechanics

C-extended oscillator algebras generalizing the Calogero—Vasiliev algebra,where C is the cyclic group of order , are studied both from mathematical andapplied viewpoints. Casimir operators of the algebras are obtained and used toprovide a complete classification of their unitary irreducible representations underthe assumption that the number operator spectrum is nondegenerate. Deformedalgebras admitting Casimir operators analogous to those of their undeformedcounterparts are looked for, yielding three new algebraic structures. One of themincludes the Brzezi´nski et al. deformation of the Calogero—Vasiliev algebra as aspecial case. In its bosonic Fock-space representation, the realization ofC-extended oscillator algebras as generalized deformed oscillator ones is shown toprovide a bosonization of several variants of supersymmetric quantum mechanics:parasupersymmetric quantum mechanics of order p = – 1 for any , as wellas pseudosupersymmetric and orthosupersymmetric quantum mechanics of ordertwo for = 3.     

Effective stimulated emission and excited-state absorption cross-section spectra of para-phenylene-ethynylene polymers

The effective stimulated emission cross-section spectra, em,eff(), the stimulated emission cross-section spectra, em(), and the excited-state absorption cross-section spectra, ex()=em()–em,eff(), of the conjugated polymers poly(2,5-dioctadecyloxy-paraphenylene-ethynylene-co-2,5-thienyl) (OPT) and poly(2,5-dioctadecyloxy-paraphenylene-ethynylene-co-2,5-pyridinyl) (OPP) in tetrahydrofuran are determined in the fluorescence region. em,eff() determined by a fluorescence amplification technique is found to be small compared to em() indicating that ex() is nearly as large as em(). The laser excitation to the wide inhomogeneously broadened S1-absorption band leads to the formation of spectrally structured inhomogeneously broadened lattice relaxed exciton conformations extending on average over two monomer units which are thought to be responsible for upper-to-lower-state stimulated emission and lower-to-upper-state (excited-state) absorption.     

Theory of fluctuations in limit-cycles of second-order bifurcation type

The fluctuations in limit cycles of second-order bifurcation (transition from a stable to an unstable focus) are investigated near the bifurcation point _c, being an external control parameter. Two different methods are applied: a time- and space-dependent Fokker-Planck equation obtained from an ^1/2-expansion of the master equation ( being the volume) and a time- and space-dependent Langevin equation. Both methods give the same results. It is shown that the dependence of the radial correlation on ² = | – _c| and the time-behaviour of the phase correlation (ensemble dephasing) are determined by the dimensionality of space.     

Differential equations in the spectral parameter,Darboux transformations and a hierarchy of master symmetries for KdV

We study a certain family of Schrödinger operators whose eigenfunctions (, ) satisfy a differential equation in the spectral parameter of the formB(, )=(x). We show that the flows of a hierarchy of master symmetries for KdV are tangent to the manifolds that compose the strata of this class ofbispectral potentials. This extends and complements a result of Duistermaat and Grünbaum concerning a similar property for the Adler and Moser potentials and the flows of the KdV hierarchy.     

The central limit theorem for the spectrum of the random one-dimensional Schrödinger operator

Let H_L = –d²/dt²+q(t,) be an one-dimensional random Schrödinger operator in ²(–L, L) with the classical boundary conditions. The random potential q(t,) has a form q(t, )=F(x_t), where x_t is a Brownian motion on the Euclidean v-dimensional torus, FS^v R¹ is a smooth function with the nondegenerated critical points, min_s ^v F = 0. Let are the eigenvalues of H_L) be a spectral distribution function in the volume [– L,L] and N() = lim_L(1/2L)N_L() be a corresponding limit distribution function.Theorem 1. If L then the normalized difference N _L ^* ()=[N_L() -2L·N()]2L tends (in the sense of Levi-Prokhorov) to the limit Gaussian process N^*(); N^*()0, 0, and N^*() has nondegenerated finitedimensional distributions on the spectrum (i.e., > 0). Theorem 2. The limit process N^*() is a continuous process with the locally independent increments.     

Soliton mass and surface tension in the (λ|Ø|4)2 quantum field model

The spectrum of the mass operator on the soliton sectors of the anisotropic (|ø|⁴)₂—and the (ø⁴)₂—quantum field models in the two phase region is analyzed. It is proven that, for small enough >0, the mass gapm _s() on the soliton sector is positive, andm _s()=0(^–1). This involves estimatingm _s() from below by a quantity () analogous to the surface tension in the statistical mechanics of two dimensional, classical spin systems and then estimating () by methods of Euclidean field theory. In principle, our methods apply to any two dimensional quantum field model with a spontaneously broken, internal symmetry group.A Sloan Foundation Fellow; Research supported in part by the U.S. National Science Foundation under Grant No. MPS 75-11864.Supported in part by the National Science Foundation under Grant No. PHY 76-17191     

Theoretical investigation of noncollinear phase-matched parametric four-photon amplification of ultrashort light pulses in isotropic media

The amplification of light signals (angular frequency _S in some isotropic media (D₂O, fused silica, and Schott type SF10 glasses) by noncollinear phase-matched parametric four-photon interaction ₁+_2S+₁ is studied theoretically. Computer simulations are carried out for fundamental and second-harmonic pump pulses of a mode-locked Nd: glass laser. Degenerate interaction (wavelength ₁=₂=1054nm or 527 nm) and nondegenerate interaction (₁=1054nm, ₂=527 nm are considered. Characteristic phase-matching parameters and gain parameters versus wavelength are determined. Limitations by spectral bandwidth, optical absorption, optical damage, self-phase modulation, self-focusing and stimulated Raman scattering are analysed.     

Scattering states and bound states in λ℘(φ)2

By analyzing the Bethe-Salpeter equation for even ()₂ models we show that for weak coupling the mass spectrum is discrete and of finite multiplicity below 2m. Moreover on even states of energy less than 4(m–) we show that theS matrix is unitary. Herem is the physical mass and =()0 as 0. Our results rely essentially only on a simple assumption about the analyticity of the Bethe-Salpeter kernel which has been verified for weak coupling. For the interaction ⁴, (/m _o ² 1) we show that there are no even bound states of energy less than 4(m–).Work supported in part by NSF, Grant MPS 74-13252     

Absence of absolutely continuous spectrum of Floquet operators

The spectrum of the Floquet operator associated with time-periodic perturbations of discrete Hamiltonians is considered. If the gap between successive eigenvalues _j of the unperturbed Hamiltonian grows as _j - _j-1 j and the multiplicity of _j grows asj with >0 asj tends to infinity, then the corresponding Floquet operator possesses no absolutely continuous spectrum provided the perturbation is smooth enough.     

The asymmetric contact process on a finite set

The contact process onZ has one phase transition; let _c be the critical value at which the transition occurs. Let _N be the extinction time of the contact process on {0,...,N}. Durrett and Liu (1988), Durrett and Schonmann (1988), and Durrett, Schonmann, and Tanaka (1989) have respectively proved that the subcritical, supercritical, and critical phases can be characterized using a large finite system (instead ofZ) in the following way. There are constants ₁() and ₂() such that if < _c , lim _{N N} /logN = 1/₁(); if > _c , lim _N log _N /N = ₂(); if = _c , lim _{N N} /N= and lim _{N N} /N ⁴=0 in probability. In this paper we consider the asymmetric contact process onZ when it has two distinct critical values _c1< _c2. The arguments of Durrett and Liu and of Durrett and Schonmann hold for < _c1 and > _c2. We show that for [ _c1< _c2), lim _{N N} /N=-1/, (where _i is an edge speed) and for = _c2, lim _N log _N /logN=2 in probability.     

Fractal drums and then-dimensional modified Weyl-Berry conjecture

In this paper, we study the spectrum of the Dirichlet Laplacian in a bounded (or, more generally, of finite volume) open set R ⁿ (n1) with fractal boundary of interior Minkowski dimension (n–1,n]. By means of the technique of tessellation of domains, we give the exact second term of the asymptotic expansion of the counting functionN() (i.e. the number of positive eigenvalues less than ) as +, which is of the form ^/2 times a negative, bounded and left-continuous function of . This explains the reason why the modified Weyl-Berry conjecture does not hold generally forn2. In addition, we also obtain explicit upper and lower bounds on the second term ofN().     

Search of the chemical change of the119mSn (T1/2=293 days) radioactive decay rate

The differences in decay rates of the nuclear isomer^119mSn (T_1/2=293 days; the strongly converted M4 transition) have been measured for different chemical compounds. The experimental results show that the^119mSn nuclei in the telluride SnTe decay faster then in the metal -Sn and in the dioxide SnO₂ [the relative change / of the decay probability is +(3.6±1.4)·10^–4]. No measurable difference between the decay rates of^119mSn in -Sn and SnO₂ has been observed [(/=–(0.1±1.2)·10^–4], irrespective of the great difference in electronic structure of the tin atoms. The results cannot be explained by considering the internal conversion of the valence electrons only. It is necessary to assume that the chemical changes of the decay rate are strongly influenced by the chemical changes of the probabilities of the internal conversion of electrons of the inner shells of the atom. This conclusion is confirmed by theoretical calculations. They show that for the deep inner subshells the relative changes _nlj/_nlj of the internal conversion coefficients _nlj are much greater than the relative changes _nlj/_nlj of the electron densities near the nucleus _nlj.     

Geometry and combinatorics of Julia sets of real quadratic maps

For real a correspondence is made between the Julia setB forz(z–)², in the hyperbolic case, and the set of-chains±(±(±..., with the aid of Cremer's theorem. It is shown how a number of features ofB can be understood in terms of-chains. The structure ofB is determined by certain equivalence classes of-chains, fixed by orders of visitation of certain real cycles; and the bifurcation history of a given cycle can be conveniently computed via the combinatorics of-chains. The functional equations obeyed by attractive cycles are investigated, and their relation to-chains is given. The first cascade of period-doubling bifurcations is described from the point of view of the associated Julia sets and-chains. Certain Julia sets associated with the Feigenbaum function and some theorems of Lanford are discussed.Supported by NSF grant No. MCS-8104862.Supported by NSF grant No. MCS-8203325.     

The ground state energy of Sdhrödinger operators

We studye()=inf spec(-+V) and examine whene()<0 for all 0. We prove thatc ²e()–d ² for suitableV and all small ||.Research partially funded under NSF grant number DMS-9101716.     

The inelastic reactions πp→λ(⌆) K with allowance for the contribution of branch cuts

The method of complex angular moments is used to analyze the experimental data on the inelastic reactions p ()K, taking into account branch cuts in the j-plane in the eikonal approximation. An optical model for the backward scattering is considered. Agreement with experiment is obtained in the region of small angles for the reactions (⁰)K⁰. In the case of ^–P K⁰(^–K⁺) processes, agreement is obtained with the experimental results for large (180) scattering angles.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 26–30, August, 1972.     

МЕТОД ДЛЯ ВЫЧИСЛЕНИЯ КОЛЕБАНИЙ НАРУШЕННО Й АТОМНОЙ ЦЕПОЧКИ

- . - , .     

A natural scalar field in the einstein gravitational theory

In a Riemannian space-time, the difference between the third-order tensor potentialH of the Riemann tensor (presented in a precedent paper) and the Lanczos generating function of the Weyl tensor is here shown to be characterized by a vectorV , obtained by contractionH . The significant role of such a vector, in the context of general relativity, is then discussed. Particular attention is paid to the scalar potential which characterizes the irrotational part ofV : such a scalar field satisfies a space-time wave equation of the Poisson type. Weak fields are also considered: in the particular case of a static metric, the scalar is found to be proportional to the classic Newtonian potential.This work was done in the sphere of activity of the C.N.R. Groups for mathematical research.