On asymptotic behaviour of four spin correlation functions in a linear chain of spins

Second and fourth moments of the four spin frequency correlation functions S^Z_i(t) S^Z_i+1 (t) S^Z_j+1 〉_k,ω and 〈S^x_i(t) S^z_i+1 (t) S^x_jS^z_j+1 〉_kω have been calculated in the high temperature limit for an arbitrary spin with an isotropic Heisenberg Hamiltonian.     

Dynamic structure function of liquid 3He

The dynamic structure function S(Q, ω) of liquid ³He is evaluated in the impulse approximation, based on a theoretically calculated momentum distribution n(k). The gap of n(k) at the Fermi surface gives rise to discontinuities in the slope of S(Q = const., ω) which may be detectable in neutron- or γ-ray scattering experiments.     

Effects of finite size and shape on scattering and thermodynamic quantities at 2D Ising critical points

Using recent results by Cardy based on the conformal invariance of critical correlation functions we calculate universal results for scattering functions S(k), susceptibilities, correlation lengths and specific heat correction terms for finite Ising systems in two dimensions with circular and rectangular shapes and free boundary conditions. Our results specify the effect of shape on these quantities at the critical point. In particular, the half-width and lineshape of the scattering function is found to be strongly influenced by geometry. For a circle, S(k) follows the infinite system behavior 1/k^2−η, η = 0.25 only for very large k. For a substantial range of intermediate k values it is well represented by 1/k^2−η_app, with an “apparent” exponent η_app. We also discuss the probable influence of end, edge and domain wall effects on the correlation lengths, susceptibilities and specific heat correction terms. The application of our results to experimental systems and other theoretical models is considered.     

Study of two-phonon excitations in superfluid 4He

We explain the second branch of excitations in superfluid ⁴He observed by Cowley and Woods, by accounting for two-phonon contributions to the dynamic structure function, S(k, ω). Our theory gives a good fit with the experimental data in the high energy region for several values of momentum transfer. It is observed that the contribution to S(k, ω) due to two-phonon excitations is of the order of k² as against its k⁴ dependence reported in earlier theories.     

The structure factor and the transport properties of dense fluids having molecules with square well potential,a possible generalization

An analytical expression of the static structure factor S(k) has been presented, treating the square well potential as a perturbation on the hard sphere system incorporating the correct equation of state given by Carnahan and Starling (CS). Reasonable values of potential parameters are obtained from a fit with the experimental peak of S(k). The present calculation of transport coefficients for liquid sodium at 373 K, is found to be in closer agreement with the experimental data. The role of back scattering correction is also discussed.     

Fluctuations with a 1/f α spectrum in nonequilibrium phase transitions in a spatially distributed system

Statistics of fluctuations in a spatially distributed system describing the interaction of nonequilibrium phase transitions is studied. It is shown that for a certain value of the intensity of external white noise acting on phase transitions, the time and spatial spectra of fluctuations exhibit power dependences S(f) ～ f ^?α and S(k) ～ k ^?γ. The dependence of exponents α and γ on the diffusion coefficient determining the spatial interaction of fluctuations is determined. Extremal low-frequency fluctuations are singled out and the distribution functions of their duration (P(τ) ～ τ^?β) and size (P(s) ～ s^?ν)) are constructed. It is found that exponent α in the time spectral dependence and exponent β in the duration of fluctuations are connected via the relation α + β = 2. Exponents γ and ν in the spatial spectral dependence and in the size distribution function are connected via an analogous relation (γ + ν = 2).     

Renormalization of the Higgs model: Minimizers,propagators and the stability of mean field theory

We study the effective actionsS ^(k) obtained byk iterations of a renormalization transformation of the U(1) Higgs model ind=2 or 3 spacetime dimensions. We identify a quadratic approximationS _Q ^(k) toS ^(k) which we call mean field theory, and which will serve as the starting point for a convergent expansion of the Green's functions, uniformly in the lattice spacing. Here we show how the approximationsS _Q ^(k) arise and how to handle gauge fixing, necessary for the analysis of the continuum limit. We also establish stability bounds onS _Q ^(k) , uniformly ink. This is an essential step toward proving the existence of a gap in the mass spectrum and exponential decay of gauge invariant correlations.Dedicated to the memory of Kurt SymanzikSupported in part by the National Science Foundation under Grant PHY 82-03669     

Role of metastable atoms and molecules of helium in excitation transfer to hydrogen atoms

The afterglow of a discharge in helium with a small admixture of hydrogen is studied spectroscopically (p=40 Torr, [e]≤10¹¹ cm^?3). The time-resolved measurements of intensities of the first four lines of the Balmer series are performed. The concentrations of metastable helium atoms and molecules are evaluated from the relative intensity of the absorption lines. The ratios of excitation transfer rates from atoms He(2 ³ S ₁) k ₁(n) and molecules of helium He₂(a 2sσ ³Σ _u ⁺ ) k ₂(n) to atomic hydrogen H*(n) are measured to be k ₁(n=3)/k ₂(n=3)=0.04±0.02 and k ₁(n=4)/k ₂(n=4)=0.01±0.02. The ratios of excitation rate constants k ₂(n) corresponding to different states H(n) are measured to be k ₁(n=4)/k ₂(n=3)=0.023±0.01; k ₁(n=5)/k ₂(n=3)≤0.013; and k ₁(n=6)/k ₂(n=3)≤0.007.     

Factorizable Z(N) models

The factorizable S-matrix with Z(N) symmetry is constructed. It is speculated that the field theory belonging to this S-matrix matrix is related to the scaling limit of Z(N) generalizations of the Ising model.     

Comments on the presence of a peak in the static structure factor of an electron liquid

Emphasis is laid on the fact that the peak in the static structure factor S(k) observed in a recent experiment at k≈2k_F for conduction electrons in beryllium agrees well with the one predicted by us theoretically some time back. The error in the calculation of the pair correlation function g(r) using the experimental data on S(k) is pointed out. The position of the peak obtained in our g(r) clearly indicates that the effect of electron correlation is to condense into a Wigner lattice at a distance equal to the average interparticle separation rather than making a Mott type transition to an atomic-like state.     

Doublet coulomb-nuclear scattering length and other parameters of the effective-range function for proton-deuteron scattering from an analysis of present-day data

Parameters of the effective-range function K(k ²) having a pole are found from the results that were obtained by calculating the S-wave phase shifts for doublet proton-deuteron scattering and the binding energies of three-nucleon nuclei on the basis of Faddeev equations and within the N/D method and which are known from the literature. The convergence of the expansion of K(k ²) in powers of the momentum is studied. The energy of the proton-deuteron resonance corresponding to the virtual triton state is calculated.     

Effective-range function for doublet nd scattering from an analysis of modern data

The parameters of the generalized effective-range function K(k ²) having a pole are found by using the results that were obtained by calculating the S-wave phase shift δ(E) for doublet nd scattering and the triton binding energy on the basis of Faddeev equations and within the N/D method and which were presented in the literature. The convergence of the expansion of K(k ²) in powers of momentum is studied. The binding energy of the virtual triton and the residues of the partial-wave scattering amplitudes at the poles corresponding to the bound and virtual states are calculated. Correlations between the binding energies of the bound and virtual states of the triton, on one hand, and the doublet scattering length for nd interaction, on the other hand, are considered. The function K(k ²) is also calculated within a two-body model featuring various potentials.     

Biquadratic exchange interaction between Ru5+ ions in (Ru2O9) clusters

The energy levels of a Ru₂O₉ cluster have been calculated, including a higher order spin interaction. The Ru⁵⁺-Ru⁵⁺ coupling is described by the Hamiltonian ?= -2JS₁· S₂ ?j(S₁·S₂)². The temperature dependence of the magnetic susceptibility is used to determine the values of the bilinear J and biquadratic j exchange integrals: J/k = -161K and j/k = 6.6K. The second term in the Hamiltonian corresponds to a fourth order perturbation involving low spin states.     

Adiabatic theorem in axiomatic quantum field theory

It is shown that Møller matricesS _± and scattering matrixS in axiomatic field theory can be expressed through their adiabatic analogs. In particular, it is proved under certain conditions that \(S_ - = \mathop {s\lim }\limits_{\alpha \to 0} S_\alpha (0,\infty )W_\alpha \) whereW _α is a trivial phase factor [i.e. a unitary operator of the form exp i / α ∝r(k)a ⁺ (k)a(k)dk]. Corresponding results in Hamiltonian approach are discussed.     

Hyperfine structure of the <Emphasis Type="Italic">S</Emphasis> levels of the muonic helium ion

Corrections of the α⁵ and α⁶ orders to the energy spectrum of the hyperfine splitting of the 1S and 2S levels of the muonic helium ion are calculated with the inclusion of the electron vacuum polarization effects, nuclear-structure corrections, and recoil effects. The values ΔE ^hfs(1S) = ?1334.56 meV and ΔE ^hfs(2S) = ?166.62 meV obtained for hyperfine splitting values can be considered as reliable estimates for comparison with experimental data. The hyperfine structure interval Δ₁₂ = 8ΔE ^hfs(2S) ? ΔE ^hfs(1S) = 1.64 meV can be used to verify QED predictions.     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Kinetic Limit of N-Body Description of Wave–Particle Self-Consistent Interaction

A system of N particles $\xi ^N = x_1 ,\upsilon_1,...,x_N ,\upsilon _N )$ interacting self-consistently with one wave Z = A exp(iφ) is considered. Given initial data (Z ^(N)(0), ξ ^N (0)), it evolves according to Hamiltonian dynamics to (Z ^(N)(t), ξ ^N (t)). In the limit N → ∞, this generates a Vlasov-like kinetic equation for the distribution function f(x, v, t), abbreviated as f(t), coupled to the envelope equation for Z: initial data (Z ^(∞)(0), f(0)) evolve to (Z ^(∞)(t), f(t)). The solution (Z, f) exists and is unique for any initial data with finite energy. Moreover, for any time T>0, given a sequence of initial data with N particles distributed so that the particle distribution f ^N(0) → f(0) weakly and with Z ^(N)(0) → Z(0) as N → ∞, the states generated by the Hamiltonian dynamics at all times 0 ≤ t ≤ T are such that (Z ^(N)(t), f ^N(t)) converges weakly to (Z ^(∞)(t), f(t)).     

Nuclear-medium modification of the ρ0(1S) and ρ′(2S) mesons in coherent photo-and electroproduction: Coupled-channel analysis

We study medium modifications of the dilepton e ⁺ e ^? and μ⁺μ^? mass spectra in coherent photo-and electroproduction of ρ⁰(1S)-and ρ′(2S)-meson resonances on nuclear targets. The analysis is performed within the coupled ρ⁰(1S), ρ′(2S), ... channel formalism, where nuclear modifications derive from off-diagonal rescatterings. We find that the effect of off-diagonal rescatterings on the shape of the dilepton-mass spectrum in the ρ⁰(1S)-meson mass region is only marginal, but it is very important in the ρ′(2S) mass region. The main off-diagonal contribution in the ρ′(2S) mass region comes from the sequential mechanism γ* → ρ⁰(1S) → ρ′(2S), which dominates ρ′(2S) production for heavy nuclei. Our results also show that, in the ρ′(2S) mass region, there is a considerable interference of the Breit-Wigner tail of the amplitude for the decay ρ⁰(1S) to e ⁺ e ^? and μ⁺μ^? with the amplitude for the decay of ρ′(2S) to e ⁺ e ^? and μ⁺μ^?.     

A Markovian Growth Dynamics on Rooted Binary Trees Evolving According to the Gompertz Curve

Inspired by biological dynamics, we consider a growth Markov process taking values on the space of rooted binary trees, similar to the Aldous-Shields (Probab. Theory Relat. Fields 79(4):509?C542, 1988) model. Fix n??1 and ??>0. We start at time 0 with the tree composed of a root only. At any time, each node with no descendants, independently from the other nodes, produces two successors at rate ??(n?k)/n, where k is the distance from the node to the root. Denote by Z _n (t) the number of nodes with no descendants at time t and let T _n =?? ^?1 nln(n/ln4)+(ln2)/(2??). We prove that 2^?n Z _n (T _n +n??), ?????, converges to the Gompertz curve exp(?(ln2)?e ^??|? ). We also prove a central limit theorem for the martingale associated to Z _n (t).