The vacuum and lightcone quantization of interaction Hamiltonians

Let denote the conformally invariant neutral free scalar field on ×S ⁿ. The naive lightcone Hamiltonian for a ^p interaction is given by c^p, where C denotes a lightcone in ×S ⁿ, and the Wick power is relative to the free vacuum. We show that this sesquilinear form annihilates the free vacuum if n3 is odd, p>2, and p(n–1)0 mod 4.     

Optical and electron spin resonance spectra ofZ 2(Eu) centers in alkali halide crystals

The ESR spectra ofZ ₂(Eu)-centers in KBr and KCl are presented and correlated to the optical absorption and the electron spin resonance of the Europium vacancy complex. The fine structure of theZ ₂ spectra can be described by a Spin-Hamiltonian with an axialb ₂ ⁰ -parameter only. At room temperature it amounts to 1,761 10^–4 cm^–1 for KBr, 1,854 10^–4 cm^–1 for KCl and 1,453 10^–4 cm^–1 for RbCl. Accordingly theZ ₂(Eu)-center must posses a strict axial 100-symmetry in these crystals.     

Observation of variable range hopping at “natural” phonon frequencies

Hill's analysis of hopping conductivity data has been applied to ion-bombarded amorphous-silicon samples. The apparent hopping conductivity parameters derived from a standardT ^–0.25 plot undergo changes by several orders of magnitude when plotted with the exact scaling of the abscissa. A typical example is characterized by a temperature dependence ofdc conductivity according to= ₀ exp (—(T ₀/T) ^m ), withm=0.45,T ₀ =6.410⁴K and ₀=6.610^{1 –1} cm^–1. From ₀ a phonon frequency of about 3–1510¹² s^–1 is derived.     

Experimental investigation of the lattice parameter and length change near the melting point of gallium in search for premelting effects

The lattice parameter of nearly perfect gallium crystals was measured by x-ray diffraction on (440), (308) and (046) planes between 10°C and 10^–4°C close to the melting point. The thermal expansion coefficients in the three main crystallographic directions are 1.33, 3.19 and 1.62 10^–5 1/°C without anomalies. The length change was measured between 10°C and about 5 mK below the melting point in (100), (010), and (001) direction. The thermal expansion coefficients in these directions are 1.12, 3.38, and 1.85 10^–5 1/°C without anomalies. The change of the vacancy concentration between 283 K and the melting point can be estimated to 4 10^–5, the vacancy formation energy to about 0.23 eV. Premelting effects could not be detected.     

The effect of low-temperature electron irradiation on the transition temperature of YBa2Cu3O7−δ superconductors

Measurements of the complex susceptibility =–i of electron-irradiated YBa₂Cu₃O_7– show a strong influence of the electron irradiation dose, ·t on the transition temperatureT _c . For irradiation doses of ·t=2.2·10¹⁹ e^–/cm² we find a damage rate of T _c /(·t)=–1.6·10^–19 K/(e^–/cm²). It is assumed that the decrease ofT _c is mainly a bulk effect due to the production of atomic defects like vacancies and interstitials in the Cu–O–Cu chains and in the basal planes of the unit cells.     

Luminescence of AgCl excited by u.v. laser light

The spectral distribution and decay of the blue-green luminescence of AgCl has been measured at very low temperatures, using u.v. laser excitation. A structure was observed in the emission band at 77°K. The decay consists of three processes: a) a very fast process which follows the laser pulse (10^–8 sec), b) a fast exponential process which is also observed with low intensity u.v. excitation,(10^–4–10^–5 sec) and, finally, c) a slow exponential process (seconds).     

Spin-1/2 Maxwell Fields

Requiring covariance of Maxwell's equations without a priori imposing charge invariance allows for both spin-1 and spin-1/2 transformations of the complete Maxwell field and current. The spin-1/2 case yields new transformation rules, with new invariants, for all traditional Maxwell field and source quantities. The accompanying spin-1/2 representations of the Lorentz group employ the Minkowski metric, and consequently the primary spin-1/2 Maxwell invariants are also spin-1 invariants; for example, ²–A ², E ²–B ²+2i EB–(₀ +A)². The associated Maxwell Lagrangian density is also the same for both spin-1 and spin-1/2 fields. However, in the spin-1/2 case, standard field and source quantities are complex and both charge and gauge invariance are lost. Requiring the potentials to satisfy the Klein–Gordon equation equates the Maxwell and field-potential equations with two Dirac equations of the Klein–Gordon mass, and thus one complex Klein–Gordon Maxwell field describes either two real vector fields or two Dirac fields, all of the same mass.     

Exact Solution of the Infinite-Range-Hopping Bose–Hubbard Model

The thermodynamic behavior of the Bose–Hubbard model is solved for any temperature and any chemical potential. It is found that there is a range of critical coupling strengths _c1 < _c2 < _c3 < in this model. For coupling strengths between _c,k and _c,k+1, Bose–Einstein condensation is suppressed at densities near the integer values = 1,...,k with an energy gap. This is known as a Mott insulator phase and was previously shown only for zero temperature. In the context of ultra-cold atoms, this phenomenon was experimentally observed in 2002(1) but, in the Bose–Hubbard model, it manifests itself also in the pressure-volume diagram at high pressures. It is suggested that this phenomenon persists for finite-range hopping and might also be experimentally observable.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

Tunable UV radiation at short wavelengths (188–240 nm) generated by sum-frequency mixing in lithium borate

Sum-frequency mixing (₃=₁+₂) of UV laser radiation (₁=266 nm and 213 nm) and tunable coherent infrared light (₂=1.2–2.6 m) in lithium borate (LBO) generates radiation at short wavelengths (₃=188–242 nm). The UV radiation at ₁ is produced by the fourth and fifth harmonic of a pulsed Nd-YAG laser. The infrared light is generated with an optical parametric oscillator of beta barium borate. The phase-matching angle is measured as function of ₃ and compared with calculated values. For UV laser radiation at shorter wavelengths (173 nm₁213 nm) the calculations predict an extension of the tuning range of the sum-frequency generated at ₃ to wavelengths as short as the LBO transmission cutoff at 160 nm.     

Energy spectrum and angular distribution of muons from the decay of heavy leptons produced in colliding electron-positron beams

On the basis of an arbitrary (V, A) structure of the neutral weak ¯ee and LL currents (L=^–, M⁰) a study is made of the processes of production in colliding electron-positron beams of pairs of heavy leptons with subsequent decays in accordance with the schemes e⁺e^––(µ^–v_µv) + ⁺( anything) and e⁺e^–M⁰(µ^–e⁺v_e) + M⁰( anything). The energy spectrum and asymmetry of the distribution of the produced muons are investigated.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 66–70, February, 1981.     

A Rigorous Derivation of a Linear Kinetic Equation of Fokker–Planck Type in the Limit of Grazing Collisions

We rigorously derive a linear kinetic equation of Fokker–Planck type for a 2-D Lorentz gas in which the obstacles are randomly distributed. Each obstacle of the Lorentz gas generates a potential V( ), where V is a smooth radially symmetric function with compact support, and >0. The density of obstacles diverges as ^– , where >0. We prove that when 0< <1/8 and =2+1, the probability density of a test particle converges as 0 to a solution of our kinetic equation.     

Role of Activator and Vacancy Centers in the Decay of the Gamma Scintillators of CsI–Na Crystals

The influence of the concentration of an activator (C _NaI) and of plastic deformation on a change in the contribution of a slow component to the decay of the -scintillations of CsI–Na crystals was investigated, as well as the influence of C _NaI on a change in the shape of the luminescence excitation spectrum in the region of absorption of activator centers (AC) and of vacancy-related centers (VRC) and also on a change in the intercenter time of deexcitation of the centers indicated. It is shown that AC and VRC participate in the photoluminescence and -scintillations of CsI–Na crystals. In the -scintillations, AC are responsible for the component ₁ = 370 nsec, whereas the components ₁ = 460 nsec and ₂ 2 sec are associated with VRC. The reduction of ₁ from 770 to 560 nsec with an increase in C _NaI from 2·10^–3 to 3·10^–2 mole% and from 570 to 470 nsec after plastic deformation of the crystals ( = 5%) along the 111 axis is caused by a decrease in the number of VRC. The mechanisms underlying the -scintillations of the CaI–Na crystals containing AC and VRC and also the decrease in the number of VRC are discussed.     

Nelson's symmetry and the infinite volume behavior of the vacuum inP(φ)2

LetH _l be the Hamiltonian in aP()₂ theory with sharp space cutoff in the interval (–l/2,l/2). LetE _l =inf(H _l ), (l)=–E _l /l, and let _l be the vacuum forH _l . discuss properties of (l) and _l . In particular, asl, there are finite constants <0 and such that (l), ((l)–)l, and hence (l)=+/l+o(l ^–1). Moreover exp(–c ₁ l) _{l 1}exp(–c ₂ l) forc ₁,c ₂ positive constants, where _{l 1} is theL ¹(Q, d₀) norm of ₁ with respect to the Fock vacuum measure. We also present a new proof of recent estimates of Glimm and Jaffe on local perturbations ofH _l in the infinite volume limit.Research sponsored by AFOSR under Contract No. F44620-71-C-0108.On leave from Istituto di Fisica Teorica, Universitá di Napoli and Istituto Nazionale di Fisica Nucleare, Sezione di Napoli.A. Sloan Foundation Fellow.     

Slowing down of retrieval in the hopfield model

The variation of the convergence time, as a function of the storage capacity is studied numerically for systems ranging in size fromN=1000 toN=16,000 neurons. is found to increase likeexp[–A(_c–)] as one nears the critical storage capacity _c =0.142=0.002.     

Synthesis and Reactivity of Mg(II)–Fe(II)–Fe(III) Hydroxycarbonates

Green rust-like compounds (GRs) were discovered as natural minerals in various hydromorphic soils, where anoxic conditions allow their stability. They may control some redox processes in aquifers and participate to the transformation of various pollutants. Since Mg(II) cations are present in the fields where GRs were discovered, a partial substitution of Mg(II) to Fe(II) leading to intermediate compounds between GRs and usual Mg(II)–Fe(III) hydroxysalts is suspected. Mg(II)–Fe(II)–Fe(II) hydroxycarbonates can be obtained as intermediate oxidation products of (Mg, Fe)(OH)₂ in carbonate-containing aqueous media obeying to [Fe^II _4(1–x)Mg^II _4x Fe^III ₂(OH)₁₂]²⁺ [CO₃ ^2– nH₂O]^–2. TMS spectra at 12 K are similar to those of GRs, i.e., two quadrupole doublets, one due to Fe(II) with a large isomer shift =1.29 mms^–1 (with respect to -iron at room temperature) and quadrupole splitting E _Q=2.76 mms^–1, the other one due to Fe(III) with smaller hyperfine parameters =0.49 mms^–1 and E _Q=0.44 mms^–1. Fe(II) ions oxidise rapidly into Fe(III) with dissolved O₂. The reactivity is similar to that of Fe(II)–Fe(III) hydroxysalts GR, and thus the potential of Mg(II)–Fe(II)–Fe(III) compounds for reducing pollutants.     

The electric fieldgradient of the transition element impurities57Fe,99Ru,197Au in scandium and193Ir in beryllium

The electric fieldgradient of the transition element impurities⁵⁷Fe,⁹⁹Ru,¹⁹⁷Au in Sc and¹⁹³Ir in Be has been determined by Mössbauer measurements. The following values were obtained: (+)4.06(9)10¹⁷ V/cm² for⁵⁷Fe in Sc, ±19.2(4.1)10¹⁷ V/cm² for⁹⁹Ru in Sc, ±11.6(4)10¹⁷ V/cm² for¹⁹⁷Au in Sc, and ±6.4(1.5)10¹⁷ V/cm² for¹⁹³Ir in Be. The results for⁵⁷Fe,⁹⁹Ru and¹⁹⁷Au in Sc are incompatible with the universal correlation between the electronic and the ionic fieldgradient observed in numerous other metals. The data suggest, that a strong contribution to the electric fieldgradient arises from electrons localized at the impurity, if the host is a transition metal and the impurity belongs to the second half of a transition series.     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

Attenuation of powerful ruby laser pulses in the atmosphere by resonant absorption of water vapor

The attenuation of a ruby laser pulse at the wavelength = 6943.8å is calculated under conditions of spectroscopic saturation for a parallel beam and a diverging beam with divergence angle = 10^–5 rad. It is shown that deviation from the Bouguer law may reach 45% at a path length = 2 km for an initial power level of I₀ = 0.5I_s for the parallel beam, and 20% for I₀ = 0.25I_s for the divergent beam (I_s, saturation power).Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 7–12, February, 1978.     

The Experimental Evaluation of Decay Rate Variations of 57Co by the Δλ/λ Method

The measurement of the relative changes / of the radioactive decay by the electron capture process is a direct experimental way to determine the relative changes of the electron charge density on the nucleus. Here we present the results of the experiment with ⁵⁷Co, where the differences of the decay rate were determined for different chemical states of ⁵⁷Co. We analyzed the experimental time dependences of the activity of ⁵⁷Co by means of the direct approximation method and the specialized optimization tool – a genetic algorithm. Using these methods improved the accuracy of the final / values between ⁵⁷Co and ⁵⁷Co(Pd), ⁵⁷CoCl₂,⁵⁷CoS, ⁵⁷CoSO₄7H₂O, which are in good agreement with theoretical considerations reflecting the electron charge rearrangement and screening effects.