Moments of two-time spin-pair correlation functions for a one-dimensional anisotropic Heisenberg model at infinite temperature

The first ten moments of the infinite-temperature space and frequency dependent two-spin correlation functions, $\text{?}{}^{\mathrm{x}}{}_{\mathrm{r}}\text{(ω)}$ and $\text{?}{}^{\mathrm{z}}{}_{\mathrm{r}}\text{(ω)}$ are obtained for the one-dimensional anisotropic Heisenberg model for r = 0 and r = 1. These are compared with those previously known.     

On the harmonic oscillator and free fields in the Araki approach

It is shown that in the Hamiltonian formalism the function $\text{(}\text{1}\text{π}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}\text{e}{}^{\mathrm{?x}}{}^2$ uniquely determines the Hamiltonian of the harmonic oscillator. Using the method of Araki [1] we have constructed uniquely the Hamiltonians for the representations of the CCR, which are obtained from the Fock one through operations on test functions.     

Transport in two dimensions. I the self-diffusion coefficient

The Mori formalism is used to study generalized transport coefficients in two dimensions. All finite multilinear products of the single particle density and momentum density comprise the set of the variables in the calculation of the self-diffusion coefficient. A self-consistent equation, which is a non-linear integral equation, is obtained for the leading asymptotic behavior of the generalized self-diffusion coefficient. An asymptotic solution is presented which for small wavevector (k) and frequency (s) behaves like $\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(s + k}{}^2\text{D)}{}^{\mathrm{?1}}$, where D has the dimensions of a diffusion coefficient. The mean square and mean fourth displacements of a tagged particle are also calculated. The long time behavior of the momentum correlation function exhibits a tail of the form $\text{[t}\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{(t)]}{}^{\mathrm{?1}}$ whose coefficient is dependent of the intermolecular potential.     

Gauge theory and bags

The surface dependent phase factor $\text{P}\text{(}\text{exp}\text{∫}\text{F}{}_{\mathrm{\mu \nu }}{}^1\text{d}\text{σ}{}^{\mathrm{\mu \nu }}$) is introduced and its variational derivatives are investigated. Under certain assumptions it is shown to satisfy a differential equation which coincides with the membrane equation.     

Theory of the quantized Hall effect (III)

In the previous paper, we have demonstrated the need for a phase transition as a function of θ in the non-linear σ-model describing the quantized Hall effect. In this work, we present arguments for the occurrence of exactly such a transition. We make use of a dilute gas instanton approximation as well as present a more rigorous duality argument to show that the usual scaling of the conductivity to zero at large distances is altered whenever $\text{σ}{}_{\mathrm{xy}}{}^{\mathrm{(0)}}\text{≈}\text{1}\text{2}\text{ne}{}^2\text{/h}$, n integer. This then completes our theory of the quantized Hall effect.     

The theory of the instability of a planar interface in a process of the phrase transformation

The theory of the instability of a planar interface during an isothermal phase transformation is developed. It is shown that for large times only perturbations with large wave length are essential. The amplitude of the deviation from a planar interface grows with time as an exponent, the argument of which is proportional to $\text{t}{}^{\mathrm{<mtext>1</mtext><mtext>4</mtext>}}$ instead of the usual simple exponential law.     

Transport in two dimensions. II the thermal conductivity coefficient

The study of generalized transport coefficients in two dimensions is continued. In this article, the thermal conductivity coefficient is examined. The Mori formalism is used and the set of variables consists of all finite multilinear products of two collective conserved variables, the energy density and the momentum density. The tensorial symmetry of Euler and dissipative matrix elements is taken into account explicitly. Two simultaneous non-linear integral equations are obtained, the asymptotic solution for which behave in the same manner as the self-diffusion coefficient studied in an earlier paper. However, the coefficient is dependent upon the intermolecular potential. The heat current auto-correlation function decays asymptotically as $\text{[t}\text{In}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{t]}{}^{\mathrm{?1}}$. The asymptotic form for the shear viscosity coefficient is examined briefly and found to be independent of the intermolecular potential. A better approximation for the coefficient of the asymptotic form of the self-diffusion coefficient is presented.     

Measurement of coherent pion-photoproduction on the 3He/3H isodoublet

Neutral and charged pion-photo production on ${}^3\text{H}$ and ${}^3\text{He}$ nuclei have been observed in the Δ(1232) resonance region. Resonance averaged cross-sections are presented as functions of momentum transfer.     

On the ratio Σ0/Λ in electroproduction off protons

Recent experimental results on electroproduction off protons show that the ratio σ(ep → eK⁺Σ⁰)/σ(ep → eK⁺Λ) decreases strongly with increasing Q². A simple argument is given in the framework of the quark parton model which could provide a qualitative understanding of this fact. The decrease of the Σ⁰/Λ ratio is related to the decrease of the ratio $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}\text{/F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}$ as Q² increases, where $\text{F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>p</mtext>}}\text{and F}{}_1{}^{\mathrm{<mtext>\gamma </mtext><mtext>n</mtext>}}$ are the usual structure functions for deep inelastic electron-nucleon scattering.     

Resonant motion of a spherical pendulum

The weakly nonlinear, resonant response of a damped, spherical pendulum (length l, damping ratio δ, natural frequency ω₀) to the planar displacement εl cos ωt (ε ? 1) of its point of suspension is examined in a four-dimensional phase space in which the coordinates are slowly varying amplitudes of a sinusoidal motion. The loci of equilibrium points and the corresponding bifurcation points in this space are determined. The control parameters are $\text{α= 2δ/ε}{}^{\mathrm{<mtext>2</mtext><mtext>3</mtext>}}$ and . If α < 0.441 there is a finite interval of v within which no stable equilibrium points exist. As v decreases through the upper bound (a Hopf-bifurcation point) of this interval the motion in the phase space becomes periodic and then, following a period-doubling cascade, chaotic. There may be alternating sub-intervals of chaotic and periodic motion. The chaotic trajectories in the phase space appear to lie on fractal attractors.     

Correlations between two identified charged hadrons at the CERN ISR

We have measured the value of the correlation R(h₁, h₂) between two identified charged hadrons $\text{(}\text{h}\text{= π}{}^{\mathrm{\pm }}\text{,}\text{K}{}^{\mathrm{\pm }}\text{,}\text{p or}\text{p}\text{?}\text{)}$ produced in pp collisions at the CERN ISR. One hardon was produced in the forward direction and the other at a large angle. Quantum number dependent effects have been observed.     

The moment map and collective motion

Given a Hamiltonian action of a Lie group G on a symplectic manifold M there is an induced map Φ: $\text{M → g}{}^1$ where $\text{g}{}^1$ is the dual space to the Lie algebra, g, of G. The map Φ is called the moment map. Any function P on $\text{g}{}^1$ then gives rise to a function F = P ° Φ on M which is a “collective Hamiltonian” associated to the group action G. We show how the rigid rotor, liquid drop, and other collective models of the nucleus fit into this framework. We describe the steps involved in integrating collective equations of motion and indicate some principles involved in the choice of collective Hamiltonians, i.e., the functions P. We discuss these constructions in some detail for the case that G is a semidirect product.     

Activation energy of field emission flicker noise power due to adsorbed potassium on tungsten

The temperature dependence of the field emission flicker noise spectral density functions has been investigated for potassium adsorbed on tungsten (112) planes by a probe hole technique. By integration of the spectral density functions $\text{W(?) = B}{}_{\mathrm{i}}\text{?}{}^{\mathrm{?ge}}\text{i}$ the noise power $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ for different frequency intervals Δ? is obtained. From the exponential temperature dependence of $\text{(δn}{}^2{}_{\mathrm{\Delta ?}}$ noise power “activation energies” q_Δ? are determined. Plots of these energies versus coverage show a similar “oscillating” behaviour as recently found for $\text{W(?}{}_{\mathrm{j}}\text{)}$ or which indicates phase transitions of the adsorbed potassium submonolayers. The noise activation energies are discussed in terms of existing models and a comparison is made between the experimental q values and surface diffusion energies E_d as determined by conventional methods.     

Vibration-rotation-inversion Hamiltonian of formaldehyde

An expression for the Hamiltonian of a vibrating-rotating-inverting formaldehyde molecule is derived. In this derivation, we have used one curvilinear coordinate corresponding to the angle between the CO bond and the bisector of the angle H?H, and five rectilinear coordinates (linearized valence coordinates). Making use of the zeroth-order Hamiltonian, we have fitted to least-squares (i) the three observed $\text{Δ}\text{G(v}{}_4\text{+}\text{1}\text{2}\text{)}$ values for inversion of H₂CO and (ii) five of D₂CO, both belonging to the $\text{A}\text{?}{}^1\text{A}{}_2$ excited electronic states, in two separate calculations. For this, we have employed two model potential functions: one consisting of a sum of quadratic and Gaussian and the other a sum of quadratic and Lorentzian terms. In each case, the refined parameters, when transferred to the isotopic molecules (D₂CO and HDCO in the one case; H₂CO and HDCO in the other), could not account for their observed $\text{Δ}\text{G(v}{}_4\text{+}\text{1}\text{2}\text{)}$ values to the expected degree. We attribute the discrepancies to the inadequacy of the model chosen for the formaldehyde molecule which takes into account only one large amplitude bending motion and which neglects vibration-inversion interactions.We have also obtained a number of quadratic squared sum relations among the Coriolis coupling constants $\text{ζ}{}_{\mathrm{kl}}{}^{\mathrm{\alpha }}$ and the inertial constants $\text{a}{}_{\mathrm{k}}{}^{\mathrm{\alpha \beta }}$. These are applicable to any molecule undergoing a large amplitude bending motion provided the reference configuration is chosen as described in the text.     

Singular perturbation potentials

This is a perturbative analysis of the eigenvalues and eigenfunctions of Schrödinger operators of the form ?Δ + A + λV, defined on the Hilbert space L²(Rⁿ), where $\text{Δ = Σ}{}_{\mathrm{i=1}}{}^{\mathrm{n}}\text{?}{}^2\text{?X}{}_{\mathrm{i}}{}^2$, A is a potential function and V is a positive perturbative potential function which diverges at some finite point, conventionally the origin. λ is a small real or complex parameter. The emphasis is on one-dimensional or separable problems, and in particular the typical example is the “spiked harmonic oscillator” Hamiltonian, $\text{?d}{}^2\text{dx}{}^2\text{+ x}{}^2\text{+}\text{l(l + 1)}\text{x}{}^2\text{+ λ|x|}{}^{\mathrm{?\alpha }}$, where α is a positive constant. When this kind of perturbation is very singular, the first-order Rayleigh-Schrödinger perturbative correction, (u₀, Vu₀), where u₀ is the unperturbed eigenfunction, diverges. This analysis constructs explicitly calculable terms in a modified perturbation series to a finite order, by using linear operator theory in concert with approximation methods for differential equations. Along the way a connection between a W-K-B type approximation and Bessel functions is exploited.     

Large cells in nonlinear marangoni convection

The classical problem of surface-tension-driven convection in a liquid film is considered. If the film is nearly thermally insulated, the longitudinal dimension of the convective cells is significantly greater (near the critical Marangoni number) than the film thickness. As a result one can separate horizontal and vertical space variables and so lower the dimensionality of the problem. For example, in the two-dimensional problem the dynamics of the formation and stabilization of cells is described by the following one-dimensional equation for the average temperature perturbation of the film:

$\text{?F}\text{?τ}\text{+}\text{1 ?}{}^4\text{F}\text{15 ?π}{}^4\text{+}\text{?}\text{?ξ}\text{(1?}\text{48}\text{35}\text{(}\text{?F}\text{?ξ}\text{)}{}^2\text{+}\text{13?}{}^2\text{F}\text{10?ξ}{}^2\text{)}\text{?F}\text{?ξ}\text{+βF=0}$

     

Accurate measurements of E2 lifetimes using the coincidence recoil-distance method

Mean lives of four E2 transitions in the (2s, 1d) shell have been measured using the recoil-distance method (RDM), γ-rays de-exciting the level of interest were detected in coincidence with particles detected in an annular detector at a backward angle thereby reducing the background and producing a beam of recoiling nuclei of well-defined energy and recoil direction. Lifetimes measured were: ${}^{22}\text{Ne}\text{, 1.275}\text{MeV level}\text{(2}{}^{\mathrm{+}}\text{→ 0}{}^{\mathrm{+}}\text{), 5.16±0.13}\text{ps}\text{;}{}^{26}\text{Mg}\text{, 3.588}\text{MeV level}\text{(0}{}^{\mathrm{+}}\text{→ 2}{}^{\mathrm{+}}\text{), 9.29±0.23}\text{ps}\text{;}{}^{30}\text{Si}\text{, 3.788}\text{MeV level}\text{(0}{}^{\mathrm{+}}\text{→ 2}{}^{\mathrm{+}}\text{), 12.00±0.70}\text{ps}\text{;}{}^{38}\text{Ar}\text{, 3.377}\text{MeV level}\text{(0}{}^{\mathrm{+}}\text{→ 2}{}^{\mathrm{+}}\text{), 34.5±1.5}\text{ps}$. The present measurements are compared to those of previous investigators. For the ²²Ne level, averaged results from four different measurement techniques are compared and found to be in good agreement. The experimental results are compared to shell-model calculations.     

Brownian motion in a critical fluid; A critical long time tail

The frictioncoefficient of a Brownian particle in a critical fluid was evaluated, taking into account the finite correlation length of density fluctuations. A $\text{t}{}^{\mathrm{<mtext>?3</mtext><mtext>2</mtext>}}$ tail of the Brownian particle velocity autocorrelation function exists close to the critical point whose amplitude is 10²–10³ times the amplitude of the usual long time tail found far from the critical point.     

A further contribution to the theory of the transient hot-wire technique for thermal conductivity measurements

We study the density of states of a one-dimensional tightbinding electron model with random hopping elements. The Hamiltonian is $\text{H = -∑}{}_{\mathrm{i}}\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}\text{(a}{}^{\mathrm{+}}{}_{\mathrm{i}}\text{a}{}_{\mathrm{i+1}}\text{+a}{}^{\mathrm{+}}{}_{\mathrm{i+1}}\text{a}{}_{\mathrm{i}}\text{)}$, where the $\text{J}{}_{\mathrm{<mtext>i+</mtext><mtext>1</mtext><mtext>2</mtext>}}$'s are independent identically distributed random variables. It is proved that the single particle density of states D(E) diverges near E = 0 as $\text{1}\text{|(E}\text{log}{}^3\text{|E|)|}$.