Perturbation of the Laplacian supported by null sets,with applications to polymer measures and quantum fields

We discuss hamiltonians in L²(R^d, dx) of the form H = ?Δ + V, with V a potential supported by a zero measure set C. In particular if C is a path of a brownian motion b such that V(x) = ∫₀¹λ(x, ω)δ(x-b(s, ω)) ds, we show that H exists as a nontrivial, self-adjoint, lower bounded perturbation of ?Δ when d ?5. We must choose λ to be an infinitesimal, negative function for d = 4,5, but for d ? 3 any bounded real-valued function λ will do. The connection with Edward's model of polymers as well as with quantum fields of the ?_d⁴-type is also discussed. The proofs use methods of nonstandard analysis.     

Effects of cross-correlation between the real and imaginary parts of the quantum noise in a two-mode saturation laser system

A two-mode saturation laser model with cross-correlation between the real and imaginary parts of the quantum noise is considered. The laser intensity Langevin equation and corresponding Fokker-Planck equation are derived by the phase-locking method. The effects of the cross-correlation strength λ between the real and imaginary parts of quantum noise and the cavity decay constant K on the steady-state intensity distribution Q(I₁,I₂), the mean light intensity 〈I〉, the normalization autocorrelation λ₁₁(0) and cross correlation λ₁₂(0) are studied by numerical calculation. The results show that as λ increases the Qs(I₁,I₂) show two extrema, and λ almost does not affect the 〈I〉, λ₁₁(0) and λ₁₂(0) when the laser system is operated far above threshold. Nevertheless, when the laser system is operated at and below threshold, λ makes the curves of Qs(I₁,I₂) have the higher peak and drop faster. Furthermore, it enhances the deviation of λ₁₁(0) and λ₁₂(0) and lessens the mean light intensity 〈I〉 when the laser system is operated at and below threshold.     

Spectroscopic properties of SbH

Relativistic configuration interaction calculations which include spin-orbit interaction are carried out for nine low-lying ω-ω states and four λ-s states. Spectroscopic properties of six bound ω-ω states are reported. These calculations not only enable assignment of the experimentally observed X₁, X₂, A₁, A₂, and B states but also predict the properties of other electronic states (0⁺(II), 0⁺(IV), 2, 2(II), 1(II), 0⁻) which are yet to be observed. The dissociation energy of SbH is predicted to be 2.7 ± 0.2 eV.     

Effects of QCD multi-jet contributions in electron-positron annihilation

By means of a recently proposed Monte Carlo procedure for computing QCD multi-jet finals states in the leading-logarithm approximation, we calculate the effects of multi-emission on the hadronic final state in electron-positron annihilation. In particular, we present quantitative predictions for the growth with energy of the average multiplicity, which increases faster than log W, and for the average transverse momentum, for which ee find 〈p_T²〉 ∝ α_s(W²) W, in contrast with the ∝ α_s(W²) W² behaviour expected in lowest perturbative order calculations.     

Measurement of π−p → π0n at large momentum transfer

New results on a high statistics measurement of pion-nucleon charge exchange scattering at 40 GeV/c, extending in momentum transfer up to ?t = 1.8 (GeV/c)², are reported and compared with an optical impact parameter model, together with previous data for the reaction π^?p → ηn at the same energy. The imaginary part of the pole trajectory b₀(s) is determined from the slope of the tangent to the maxima of $\text{(?t)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}\text{d}\text{σ}\text{d}\text{t}$. The linear increase of Im b₀(s) with log s, which has been observed at low energies, continues up to 40 GeV/c.     

Multiplicity distributions in the generalized Feynman gas model

Multiplicity distributions Ψ_n^(k) in the generalized Feynman gas model of order k (defined by saying that all integrated correlation functions f_n except f₁,…,f_k are zero) are derived and expressed in terms of Poisson distributions with different ”average multiplicities”, which are related to the integrated correlation functions. The relations between Ψ_n^(k) and Ψ_n^(j) for arbitrary positive integers k,j are found. An intuitive picture to gain a better feeling for these relations is developed.On the basis of our formulae we show that the experimentally observed multiplicity distributions (between 50 GeV/c and 303 GeV/c incoming momentum) can be well reproduced by those of a Feynman gas model of order two. Other applications of our formulae are suggested.     

Aspects of supersymmetric quantum mechanics

We review the properties of supersymmetric quantum mechanics for a class of models proposed by Witten. Using both Hamiltonian and path integral formulations, we give general conditions for which supersymmetry is broken (unbroken) by quantum fluctuations. The spectrum of states is discussed, and a virial theorem is derived for the energy. We also show that the euclidean path integral for supersymmetric quantum mechanics is equivalent to a classical stochastic process when the supersymmetry is unbroken (E₀ = 0). By solving a Fokker-Planck equation for the classical probability distribution, we find P_c(y) is identical to |Ψ₀(y)|² in the quantum theory.     

Three-fold photoelectron counting statistics for gaussian light

The three-fold generating function Q(λ₁, λ₂, λ₃) for photocount statistics is evaluated directly from the gap integral equation in the short counting time regime. The triple joint probabilities and the triple photoelectron correlation function are obtained via Q(λ₁, λ₂, λ₃) in terms of the field correlation function of the incident quasimonochromatic radiation. Three-fold moments are also evaluated via another approach which permits an extension to arbitrary counting times.     

Inclusive cross sections in the central region and the supercritical pomeron

Using the double-Regge formalism and a supercritical pomeron with α_P(0)=1+Δ, we analyse the energy dependence of inclusive cross sections for negatively charged particles (c⁻) and K_s⁰ at CM rapidity y=0 in the CERN PS-Sp̄pS collider energy range. The values of Δ(c⁻)=0.170±0.008 and Δ(K_s⁰)=0.167±0.024 are found to be very close to each other and compatible with estimates of Δ derived from the total cross sections.     

Hybrid of chitin and humic acid as high performance sorbent for Ni(II)

Hybrid of humic acid (HA) and chitin has been synthesized and the hybrid material (chitin-HA) was then applied as sorbent to adsorb Ni(II). The HA was extracted from peat soil of Gambut District, South Kalimantan, Indonesia, according to the procedure recommended by IHSS (International Humic Substances Society). The chitin was isolated from crab shell waste of sea food restaurants through deproteination using NaOH 3.5% (w/v) and followed by removal of inorganic impurities using HCl 1 M. The synthesis of chitin-HA was performed by reacting gelatinous chitin solution in HCl 0.5 M and HA solution in NaOH 0.5 M. Parameters investigated in this work consists of effect of medium acidity on the sorption, sorption rate (k_s) and desorption rate (k_d) constants, Langmuir (monolayer) and Freundlich (multilayer) sorption capacities, and energy (E) of sorption. The k_s and k_d were determined according to a kinetic model of first order sorption reaching equilibrium, monolayer sorption capacity (b) and energy (E) were determined according to the Langmuir isotherm model, and multilayer sorption capacity (B) was determined based on the Freundlich isotherm model.Sorption of Ni(II) on both chitin and chitin-HA was maximum at pH 8.0. The kinetic expression resulted from the proposed kinetic model has been shown to be more applicable than the commonly known Lagergren equation obtained from the pseudo-first order sorption model. The application of the proposed model revealed that the presence of HA increased the k_s from 0.018 min⁻¹ for chitin to 0.031 min⁻¹ for chitin-HA. As for k_s, the value of b was also bigger in the presence of HA, i.e. 7.42 × 10⁻⁵ mol/g for chitin and 9.93 × 10⁻⁵ mol/g for the chitin-HA. Unlike k_s and b, the value of E slightly decreased from 23.23 to 21.51 kJ/mol for the absence and presence of HA, respectively. It can also be deduced that the presence of HA on chitin contributed more to the additional layer of Ni(II) sorbed on sorbent. Without HA, B for chitin was only 6.17 times higher than b, while with the presence of HA, the enhancement of the sorption capacity from the multilayer (B) to the monolayer (b) was 19.40. The increase of k_s, b, B, and the decrease of E would be very benefit in the real application of chitin-HA for the recovery of Ni(II) from aqueous samples.     

Interaction effects on atomic laboratory trapped Bose-Einstein condensates

We discuss the effect of inter-atoms interactions on the condensation temperature T _c of an atomic laboratory trapped Bose-Einstein condensate. We show that, in the mean-field Hartree-Fock and semiclassical approximations, interactions produce a shift Δ T _c /T _c ⁰ ≈ b ₁(a/λ _{T c} ) + b ₂(a/λ _{T c} )² + ψ[a / λ _{T c} ] with a the s-wave scattering length, λ _T the thermal wavelength and ψ[a / λ _{T c} ] a non-analytic function such that ψ[0] = ψ′[0] = ψ′′[0] = 0 and |ψ′′′[0]| = ∞. Therefore, with no more assumptions than Hartree-Fock and semiclassical approximations, interaction effecs are perturbative to second order in a / λ _{T c} and the expected non-perturbativity of physical quantities at critical temperature appears only to third order. We compare this finding with different results by other authors, which are based on more than the Hartree-Fock and semiclassical approximations. Moreover, we obtain an analytical estimation for b ₂ ? 18.8 which improves a previous numerical result. We also discuss how the discrepancy between b ₂ and the empirical value of b ₂ = 46 ± 5 may be explained with no need to resort to beyond-mean field effects.     

Large deviations and Lifshitz singularity of the integrated density of states of random Hamiltonians

We consider the integrated density of states (IDS) ρ_∞(λ) of random Hamiltonian H_ω=?Δ+V_ω, V_ω being a random field on ? ^d which satisfies a mixing condition. We prove that the probability of large fluctuations of the finite volume IDS |Λ|^?1ρ(λ, H_Λ(ω)), Λ ? ? ^d , around the thermodynamic limit ρ_∞(λ) is bounded from above by exp {?k|Λ|},k>0. In this case ρ_∞(λ) can be recovered from a variational principle. Furthermore we show the existence of a Lifshitztype of singularity of ρ_∞(λ) as λ → 0⁺ in the case where V_ω is non-negative. More precisely we prove the following bound: ρ_∞(λ)≦exp(?kλ^?d/2) as λ → 0⁺ k>0. This last result is then discussed in some examples.     

An ESCA investigation of some thiocyanato complexes

A series of simple thiocyanato complex ions have been investigated as their tetraphenylphosphonium and potassium salts. The binding energies of N, C and S were determined as well as those of the metals. From the first-mentioned data effective charge-values were estimated for the atoms of the ligands. For this purpose linear relations E_b = kq + E_b0 were used that had been previously established within a scheme having C_1s (phenyl) as the internal standard.From the data thus obtained the effective charge on the metal atoms was estimated. For elements where we have sufficient data the same type of linear relation seems to he followed. Tentatively valid examples are E_b(Ni) = 6.74q_Ni + 848.3 eV and E_b(Pd) = 4.45q_Pd + 333.9 eV.In this interpretation the atoms of the metals are considered to be positively charged and surrounded by the negative charge of the electrons occupying the s band.It is further suggested for complexes with pronounced π backbonding (Pt(SCN)₄^2?, Pd(SCN)₄^2? and Hg(SCN)₄^2?) that the C 1s binding energy measured for the carbon atom of the SCN^? ligand is composed of the ionisation energy from the 1s level and an additional term corresponding to the intraligand π → π* transition.     

Inclusive neutral kaon and lambda production in 69 GeV pp interactions

From a study of 180 neutral vees in the hydrogen bubble chamber Mirabell, we have obtained respectively, for the cross sections of the inclusive reactions pp → K⁰X and pp → λX, 8.4 ± 1.1 and 3.6 ± 0.5 mb. Data presented for the neutral kaons and λ in terms of the invariant cross sections F(x, p_⊥, s) show, when compared with lower and higher energy results, that scaling is approximately valid at our energy for K^o and λ production.     

Lower bounds on the slope parameter

A rigorous lower bound on the slope parameter γ(s, t) = d ln A(s, t)/dt is derived for 0 < t < t₀ where A(s, t) is the absorptive part of the elastic scattering amplitude and t₀ is related to the right extreme of the Lehmann-Martin ellipse. When A(s, t) has high-energy behavior like s^α(t)ln^η(t)s…, this lower bound on α(s, t) is used to obtain lower bounds on α′(t) for 0 < t < t₀, which saturate for ‘parabolic trajectories’. We also obtain a lower bound on γ(s, t) for t < 0 which can be used to find the nearforward region in which γ(s, t) cannot vanish.     

Higher order QCD corrections to an exclusive two-photon process

We calculate the next-to-leading order QCD corrections in the $\text{MS}$ scheme to the coefficient functions in an operator product expansion of the amplitude T(q², p²) for the process $\text{γ}{}^1\text{(q) + γ}{}^1\text{(p) →}\text{helicity-zero}$, flavour non-singlet meson in which ?q² is large and ?p² ? 0. For an asymptotic wave function the complete O(α_s) correction for a pseudoscalar meson is about 16% for p² = 0 and α_s = 0.3; most of this correction can be removed by using a modified evolution equation for the wave function, leaving a correction of about 7%. For large p² the complete O(α_s) correction for a pseudoscalar meson is about 10%. We discuss how our results can be combined with similar calculations for the pion form factor F_π(Q²) to give a prediction: F_π(Q²) = Aα_s(Q²)T_π²(q², 0)(1 + Bα_s) that is independent of the as yet unknown two-loop anomalous dimension matrix.     

Isometric immersions of pseudo-Riemannian space forms

In this paper we study local isometric immersions f:M_sⁿ(K)→N_s+q²ⁿ⁻¹(c) of a time-like n-submanifold M_sⁿ(K) with constant sectional curvature K and index s into a pseudo-Riemannian space form N_s+q²ⁿ⁻¹(c) with constant sectional curvature c and index s+q, where q≥0, 1≤s≤n−1 and K≠c. We first prove the existence of Chebyshev coordinates of a time-like submanifold M_sⁿ(K) in certain conditions. Afterwards, we generalize the classical Bäcklund theorem for space-like (or time-like) submanifolds in N_n−1²ⁿ⁻¹(c) and N₁²ⁿ⁻¹(c). Finally as an application, in the Chebyshev coordinates, we use the Bäcklund theorem to give a Bäcklund transformation and a permutability formula between the generalized sine-Laplace equation and the generalized sinh-Laplace equation.     

Diffusion Effects on the Breakdown of a Linear Amplifier Model Driven by the Square of a Gaussian Field

We investigate solutions to the equation ? _t ?? $\mathcal{D}$ Δ?=λS ²?, where S(x, t) is a Gaussian stochastic field with covariance C(x?x′, t, t′), and x∈ $\mathbb{R}$ ^d . It is shown that the coupling λ _cN (t) at which the N-th moment <? ^N (x, t)> diverges at time t, is always less or equal for $\mathcal{D}$ >0 than for $\mathcal{D}$ =0. Equality holds under some reasonable assumptions on C and, in this case, λ _cN (t)=Nλ _c (t) where λ _c (t) is the value of λ at which <exp[λ ∫ ^t ₀ S ²(0, s) ds]> diverges. The $\mathcal{D}$ =0 case is solved for a class of S. The dependence of λ _cN (t) on d is analyzed. Similar behavior is conjectured when diffusion is replaced by diffraction, $\mathcal{D}$ →i $\mathcal{D}$ , the case of interest for backscattering instabilities in laser-plasma interaction.     

Phase transition in Ising, XY and Heisenberg magnetic films

The phase transition and magnetic properties of a ferromagnet spin-S, a disordered diluted thin and semi-infinite film with a face-centered cubic lattice are investigated using the high-temperature series expansions technique extrapolated with Padé approximants method for Heisenberg, XY and Ising models. The reduced critical temperature of the system τ_c is studied as function of the thickness of the thin film and the exchange interactions in the bulk, and within the surfaces J_b, J_s and J_⊥, respectively. It is found that τ_c increases with the exchange interactions of surface. The magnetic phase diagrams (τ_c versus the dilution x) and the percolation threshold are obtained. The shifts of the critical temperatures T_c(l) from the bulk value (T_c(∞)/T_c(l) − 1) can be described by a power law l^−λ, where λ = 1/υ is the inverse of the correlation length exponent.     

Cross sections for scattering of deuterium mesic atoms on deuterium nuclei

Cross sections have been calculated for elastic scattering of deuterium mesic atoms in ortho and para states on deuterium nuclei in the 0–50 eV energy range; cross sections for spin-flip have also been calculated. The calculations have been performed in the adiabatic representation where the initial problem of slow collisions in a three-body system is reduced to the multichannel scattering problem. The temperature dependence of the ortho-para transition rate λ_hf(T) for dμ atoms is obtained for a deuterium target. The calculated rate 37.2×10⁶ s^-1 (at 30 K) is in good agreement with the recent experimental value, λ_exp(30 K) = (37.0±0.74)×10⁶ s^-1 (Vienna-SIN group, 1983).