Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Magnetic circular dichroism of the first spin-forbidden transition in 2[Cr(en)3Cl3] . KCl . 6H2O

The longitudinal Zeeman effect of the ² E ←⁴ A ₂ transition of the Cr⁺³ ion in single crystals of 2[Cr(en)₃Cl₃] . KCl . 6H₂O has been measured using circularly polarized light as a function of magnetic field strength between 0 and 160 kgauss at ～80 K. The g factor for the ground state was determined to be g _‖(⁴ A ₂) = 2·01±0·05, in agreement with the E.S.R.-determined value. The ratio between the excited state g values and that of the ground state was determined; using the value g _‖(⁴ A ₂) = 1·99, the g factors g _‖(2) = 2·61±0·04 and g _‖() = 1·47±0·04 were obtained.     

The magnetic moment of the 10+ isomer in140Ce andE1 transitions inN=82 isotones caused by outer subshell configurations

Using the reaction¹³⁸Ba(α,2n)¹⁴⁰Ce the magnetic moment of the 10 ₁ ⁺ isomer atE _x =3714.7 keV in theN=82 nucleus¹⁴⁰Ce has been determined by means of the TDPAD method toμ=+10.3(4)μ _N . Measuredg-factors in¹⁴⁰Ce are compared to calculations within the shell model with configuration mixing. For the 10 ₁ ⁺ isomer in¹⁴⁰Ce the four proton configuration π(1g ₇ ^2/2 ,2d ₅ ^2/2 ) has been found to be dominant. From theg-factor measurement strong contributions of multiparticle excitations to thegp2d _3/2,π3s ₁ ² or π1h ₁₁ ² shells and admixtures of neutron excitations to the wave function of the 10 ₁ ⁺ state could be excluded. The strongE1γ-branch of the deexcitation of the 10 ₁ ⁺ isomer in¹⁴⁰Ce can be explained by means of small admixtures of configurations which contain the outer subshell excitationsπ2f _7/2 andπ1h _9/2. On this basisE1 transitions experimentally observed in theN=82 nuclei¹⁴⁰Ce,¹⁴¹Pr and¹⁴⁵Eu may be understood.     

Magneto-optical study of shallow donors in transmutation-doped GaAs

Lineshapes and peak positions of 1s→2p^?1, donor transitions in epitaxial GaAs samples of relatively low compensation have been studied as functions of magnetic field by use of photoconductivity measurements. Some of these samples were produced by transmutation doping using thermal neutrons—a method which is useful for the controlled introduction of donor impurities in GaAs. Two new effects, tentatively attributed to van der Waals interactions between neutral donor atoms, are observed: (1) although both Se and Ge donors are introduced by thermal neutron transmutation, the Se line is much broader than the Ge line, and (2) deviations from isolated-donor behavior occur in the magnetic field dependence of the chemical shift of the shallowest donor present. The separation of lines from two deeper donors, Ge and Si, verified the simple phenomenological theory of the magnetic field dependence of central cell corrections of isolated donors up to at least 10T.     

Consistency of field equations in “Self-Creation” cosmologies

It is pointed out that the field equations in one of Barber's two self-creation cosmologies are not only in disagreement with experiment, but are actually inconsistent, in general. The construction of consistent general relativistic field equations involving field variables, such as, without invoking Lagrangian techniques, requires careful checking that sufficient functional freedom has been provided so as to produce a consistent set of equations.     

Parity anomaly in a \mathcal{P}\mathcal{T}-symmetric quartic Hamiltonian

In this paper, two independent methods are used to show that the non-Hermitian -symmetric wrong-sign quartic Hamiltonian H = (1/2m)p ² − gx ⁴ is exactly equivalent to the conventional Hermitian Hamiltonian . First, this equivalence is demonstrated by using elementary differential-equation techniques and second, it is demonstrated by using functional-integration methods. As the linear term in the Hermitian Hamiltonian is proportional to ℏ, this term is anomalous; that is, the linear term in the potential has no classical analog. The anomaly is a consequence of the broken parity symmetry of the original non-Hermitian -symmetric Hamiltonian. The anomaly term in remains unchanged if an x ² term is introduced into H. When such a quadratic term is present in H, this Hamiltonian possesses bound states. The corresponding bound states in are a direct physical measure of the anomaly. If there were no anomaly term, there would be no bound states.     

Emergent <Emphasis Type=Italic>SO</Emphasis>(3) Symmetry of the Frictionless Shear Jamming Transition

We study the shear jamming of athermal frictionless soft spheres, and find that in the thermodynamic limit, a shear-jammed state exists with different elastic properties from the isotropically-jammed state. For example, shear-jammed states can have a non-zero residual shear stress in the thermodynamic limit that arises from long-range stress-stress correlations. As a result, the ratio of the shear and bulk moduli, which in isotropically-jammed systems vanishes as the jamming transition is approached from above, instead approaches a constant. Despite these striking differences, we argue that in a deeper sense, the shear jamming and isotropic jamming transitions actually have the same symmetry, and that the differences can be fully understood by rotating the six-dimensional basis of the elastic modulus tensor.     

Quantum size effects in the attractive hubbard model

We investigate superconducting pair correlations in the attractive Hubbard model on a finite square lattice. Our aim is to understand the pronounced size dependence which they display in the weak and intermediate coupling regimes. These size effects originate from the electronic shell structure of finite systems and severely complicate a reliable extrapolation of numerical simulation data from small systems to the thermodynamic limit. To analyze the size effects in detail, we use the BCS approximation, as well as a particle number conserving modification of it and compare the results with those of quantum Monte Carlo simulations. As an application, we explore the possibility of reducing the shell effects in simulation data by changing the shape of the system and the imposed boundary conditions and by making use of the size dependence of corresponding BCS data.     

Electrochemical characterization of core@shell CoFe2O4/Au composite

Quantum dots (QDs) have received considerable attention due to their unique optical and electrical properties. Although substantial research has focused on the potential applications and toxicological impacts of QDs, far less effort has been directed toward understanding their fate and transport in the environment. In this work, the effect of four coatings, polyethylene glycol functionalized polymer (PEGP), carboxyl derivatized polymer (COOHP), linoleic acid (LA), and polyacrylic acid-octylamine (PAA-OA), on the transport and retention of QDs in porous media were evaluated under environmentally relevant conditions. Aqueous QD suspensions (ca. 10 nM) were introduced into water-saturated columns packed with 40–50 mesh Ottawa sand at a pore-water velocity of 7.6 m/day. At an ionic strength (IS) of 3 mM and pH of 7, PEGP-coated QDs were completely retained within the column, while more than 60 % of COOHP-coated QDs were transported through a column run under identical conditions. When PAA-OA and LA were used as coatings, effluent QD recoveries increased to more than 65 and 89 % of the injected mass, respectively. Additionally, a decrease in pH from 9.5 to 5.0, or an increase of IS from 0 to 30 mM reduced the eluted mass of PAA-OA-coated QDs by more than 2 and 15 times, respectively. The relative mobility of coated QDs (LA > PAA-OA > COOHP > PEGP) was consistent with total interaction energy profiles between QDs and sand surfaces calculated based on Derjaguin–Landau–Verwey–Overbeek (DLVO) theory. At an IS of 3 mM (NaCl) and pH 7, a linear correlation was obtained between the fraction of eluted QDs and the magnitude of the primary interaction energy barrier. These findings demonstrate the strong dependence of QD transport on coating type and indicate that interaction energies based on DLVO theory can be used to predict the relative mobility of QDs in porous media.     

An integrative approach to 2D-macromodels of growth, price and inventory dynamics

This paper investigates two variants of a Keynesian model of monetary growth with sluggish price and quantity adjustments. The first model integrates the real growth dynamics of Rose's employment cycle, an inflationary dynamics of the Cagan type and Metzler's inventory dynamics. This model is based on intrinsic nonlinearities solely and it implies for the private sector six laws of motion, two for each of the subdynamics stated above. It is shown that the integrated model does not at all preserve the insights obtained from the three prototype subdynamics. Since this model can give rise to global instabilities even for moderate adjustment speeds of prices and quantities, a variant of this model is then introduced which exhibits one fundamental ‘nonintrinsic’ nonlinearity in its wage adjustment mechanism. This nonlinearity makes the considered 6D-dynamics at the same time extremely ‘viable’ and complex, in particular for a high adjustment speed of nominal wages.