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.     

Infinite hierarchy of exponents in a two-component random resistor network

We have studied the voltage distribution for a two-component random mixture of conductances _a and _b. A scaling theory is developed for the moments of the distribution, which predicts, for small values ofh=_a/_b, an infinite number of crossover exponents, one for each moment, for Euclidean dimensiond >2, and only one crossover exponent ford=2. Monte Carlo results on the square lattice confirm this prediction.     

Nonlinear Kac model: Spatially homogeneous solutions and the Tjon effect

We study Kac's nonlinear model of the Boltzmann equation when the cross section() does not satisfy the special symmetry condition()=(-). We determine a differential system for the Laguerre moments of the odd and even velocity parts of the solutions. We consider the spatially homogeneous model in 1+1 dimensions (velocityv and timet) when the even velocity part of the solution is provided by the Bobylev-Krook-Wu closed solutions and study the associated odd velocity part. We find that the solutions depend on the microscopic models of(). For one class of(), which has sums of exponential terms for the Laguerre moments, we establish the relations allowing the construction of the time-dependent solutions associated with any initial distribution. We find sufficient conditions on() and on the even part such that the Laguerre series of the odd part converges. We establish a criterion for a well-defined linear combination of the moments cross section, and we check its validity for different numerical examples. We find that if the relaxation time for the even part is smaller than the corresponding one for the odd part and if the initial distribution has a narrow peak, then the Tjon effect exists for the complete B.K.W. solution (even+odd parts).     

Macroscopic short-time electrodynamics for conductors

In the macroscopic electrodynamics (MED) of good conductors (metals) based on Ohm's law j=E, the momentum relaxation time =m/ne² of the electrons limits the application to electromagnetic (EM) processes with characteristic timest. An interesting physical difficulty occurs in MED since the EM field damping time _R=/ of metals is very small compared with the minimum macroscopic time scale, _R. Consequently, the damping and propagation of EM waves and pulses in good conductors cannot be correctly described within the frame of conventional MED. New hyperbolic EM wave equations with relaxation and memory are proposed, which no longer exhibit the _R deficiency. The latter is caused by Ohm's law, which breaks down for short-time processes, due to neglect of electron inertia. The advantages of the proposed and the disadvantages of the conventional EM wave equations for good conductors are discussed in applications.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Asymptotics of decay of correlations for lattice spin fields at high temperatures. I. The Ising model

We find the asymptotic decrease of correlations < _{A +y} , _B >,yZ ^v +1, |y|, in the Ising model at high temperatures. For the case when monomials _A and _B both are odd, using the saddle-point method, we find the asymptotics of the correlations for any dimension . For even monomials _A , _B we formulate a general hypothesis about the form of the asymptotics and confirm it in two cases: (1) =1 and the vectory has an arbitrary direction, (2)y is directed along a fixed axis and arbitrary . Here we use besides the saddle-point method, some arguments from scattering theory.     

Resistance to dislocation motion in copper-based solid solutions with a statistically disordered atomic distribution

The stress _F due to friction forces in copper-based solid solutions was determined. Under the conditions of the procedure used to measure _F, on the basis of the half-wave hysteresis with polycrystalline samples, the value of d: _F = _F0 + K_Fd^–(1/2) where _F0 is the resistance to dislocation motion in an alloy having an infinite grain size, and K_F is a constant. It is shown that _F0 is governed by the interaction of moving dislocations with impurity atoms in the case of a statistically disordered atomic distribution. A study was made of the effects of various factors on _F and of the nature of the changes in _F0 caused by alloying.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No.3, pp. 18–23, March, 1971.     

The asymmetric contact process at its second critical value

The asymmetric contact process onZ has two distinct critical values ₁ > ₂ (at least with sufficient asymmetry). One can consider the process on {0,...,N} and analyze the time (which we call _N ) till complete vacany starting from complete occupation. Its behavior has already been resolved for all regions of except for =₂. For this value, Schinazi proved that lim _N log _N /logN=2 in probability and conjectured that _N /N ² converges in distribution. It is that result that we prove in this paper. We rely heavily on the Brownian motion behavior of the edge particle, which comes from Galves and Presutti and Kuczek.     

On the Brownian motion of a massive sphere suspended in a hard-sphere fluid. II. Molecular dynamics estimates of the friction coefficient

The friction coefficient exerted by a hard-sphere fluid on an infinitely massive Brownian sphere is calculated for several size ratios , where and are the diameters of the Brownian and fluid spheres, respectively. The exact microscopic expression derived in part I of this work from kinetic theory is transformed and shown to be proportional to the time integral of the autocorrelation function of the momentum transferred from the fluid to the Brownian sphere during instantaneous collisions. Three different methods are described to extract the friction coefficient from molecular dynamics simulations carried out onfinite systems. The three independent methods lead to estimates of which agree within statisticalerrors (typically 5%). The results are compared to the predictions of Enskog theory and of the hydrodynamic Stokes law. The former breaks down as the size ratio and/or the packing fraction of the fluid increase. Somewhat surprisingly, Stokes' law is found to hold withstick boundary conditions, in the range 1/4.5 explored in the present simulations, with a hydrodynamic diameterd=. The analysis of the moleuclar dynamics data on the basis of Stokes' law withslip boundary conditions is less conclusive, although the right trend is found as / increases.     

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.     

Surface tension from finite-volume vacuum tunneling in the 3D Ising model

We measure the surface tension in the broken phase of the 3D Ising model at a temperatureT=0.955T _c with two different methods which are taken from quantum field theory in finite volumes. Both methods rely on finite-size effects close to the phase transition. The first one measures from the size dependence of the vacuum tunneling energy, which is determined by the decay of a correlation, giving=0.030. The second one extracts from the size dependence of the rate of flip events and its corresponding correlation time. It leads to=0.027. Both values agree reasonably with other calculations.     

Iteration wave function for describing the (e, 2e) spectrum of the helium atom

The wave function of the ground state of the helium atom is derived by the variational-iteration technique with the Hylleraas-Eckart momentum representation of the wave function as a first approximation. This function is used to calculate the ratios of the differential cross sections (n=2)/(n=1) and (2p)/(2s) for helium ionized by an electron impact. The calculation is conducted in the plane-wave impulse approximation for symmetric noncoplanar kinematics of the (e, 2e) process. The results are compared with previous calculations in which variational wave functions of the configurational interaction type were used. Good agreement with the existing experimental data for (n=2)/(n=1) is obtained. The results are generalized to helium ions.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp. 45–50, December, 1986.     

Note: An Unusual Route to General Relativity Equation in Presence of Dust in Irrotational Motion

We show that the general relativity theory equation, in presence of pressureless matter (dust) in irrotational motion, can be recovered from a scalar-tensor like variational approach. In this approach, the kinetic energy, , of a dynamical scalar field , couples directly to gravity. The lagrangian, exempt of explicit matter term, is varied in the framework of the first order formalism, and a conformal transformation, restoring riemannian geometry, is made. In this approach, it turns out that a non-empty spacetime is necessarily four-dimensional.     

Charged surfaces and the analyticity properties of the string tension in lattice gauge theories

A method to prove the fact that the string tension in strongly coupled lattice gauge theories is of the form =–log +, where is an analytic function of the inverse coupling =1/g², is presented. Its relation to random surface methods, in particular to the work of Debrushin and Holický, Kotecký, and Zahradník, is discussed.This paper is based on a talk presented at the conference on Statistical Mechanics of Phase Transitions—Mathematical and Physical Aspects, Trebon, September 1–6, 1986.     

Dynamical bifurcation with noise

It was shown by A. Neishtadt that dynamical bifurcation, in which the control parameter is varied with a small but finite speed , is characterized by adelay in bifurcation, here denoted _j and depending on . Here we study dynamical bifurcation, in the framework and with the language of Landau theory of phase transitions, in the presence of a Gaussian noise of strength . By numerical experiments at fixed = ₀, we study the dependence of _j on a for order parameters of dimension 3; an exact scaling relation satisfied by the equations permits us to obtain for this the behavior for general . We find that in the smallnoise regime _j() a(^–b ), while in the strong-noise regime _j() – ce(^–d); we also measure the parameters in these formulas.     

Propagation of electromagnetic waves in a random medium and nonzero rest mass of the photon

The propagation of electromagnetic waves is studied in a Maxwell vacuum with 0. The photon loses energy during its propagation through this vacuum. This dissipation of energy is related to the fluctuation of the refractive index of the underlying vacuum. There exists a bounded and unique solution in the limit 0 in the asymptotic region. The geometric structure of the background space-time is Finslerian in nature.     

Mates toE=mc 2 and to the Heisenberg uncertainty relations

E=mc ² is found to be a special case ofE= ^±1cⁿ, where is any one of four susceptibilities, namely electric, magnetic, gravitational, and elastic. Letl be length,t time,t time dilation, andl a measure of Fitzgerald-Lorentz contraction. A particle is stated to be the manifestation of a collection of susceptibilities which arise when(l)/1=(t)/t. Then(E)/E=5 (t)/2t=±()/. Corresponding to susceptibility, special energy particles are postulated which exhibitSU(3) symmetry, Related to the susceptibilities are five new Heisenberg uncertainty relations. Three new conservation laws for particles are proposed.     

Mixing properties,differentiability of the free energy and the central limit theorem for a pure phase in the Ising model at low temperature

For the Ising model with nearest neighbour interaction it is shown that the spin correlations _{A B} - _{A B} decrease exponentially asd(A, B) in a pure phase when the temperature is well belowT _c. This is used to prove that the free energyF(,h) is infinitely differentiable in and has one sided derivatives inh of all orders forh=0. The bounds are also used to prove that the central limit theorem holds for several variables such as e.g. the total energy and the total magnetization of the system, the limit distribution being gaussian with variances determined by the second derivatives ofF(,h).     

Interfacial properties in solid-stabilized emulsions

We prepared concentrated monodisperse oil-in-water emulsions stabilized by solid particles. The osmotic resistance, , of the emulsions was measured for different oil volume fractions above the random close packing ( ). The dimensionless osmotic resistance, /(/R) ( being the interfacial tension and R being the undeformed drop radius), was always substantially higher than the corresponding values obtained for surfactant-stabilized emulsions. It can be concluded that droplet deformation in solid-stabilized emulsions is not controlled by the capillary pressure, /R, of the non-deformed droplets but rather by 0/R, 0 being a parameter characterizing the rigidity of the droplets surfaces. The data can be interpreted considering that the interfacial layers are elastic at small deformations and exhibit plasticity at intermediate deformations. 0 corresponds to the surface yield stress, i.e. the transition between elastic and plastic regimes. We discuss the origin of the surface behavior considering the strong lateral interactions that exist between the adsorbed solid particles. We propose an independent measurement of 0 based on the critical bulk stress that produces droplet fragmentation in dilute emulsions submitted to shear. Finally, the bulk shear elastic modulus was measured as a function of and confirms many of the features revealed by the osmotic resistance.