Stochastic Schrödinger operators and Jacobi matrices on the strip

We discuss stochastic Schrödinger operators and Jacobi matrices with wave functions, taking values in ^l so there are 2l Lyaponov exponents ₁..._l0 _l+1..._2l =–₁. Our results include the fact that if ₁=0 on a set positive measure, thenV is deterministic and one that says that {E|exactly 2j 's are zero} is the essential support of the a.c. spectrum of multiplicity 2j.Research partially supported by USNSF under grant DMS-8416049     

Some critical exponent inequalities for percolation

For a large class of independent (site or bond, short- or long-range) percolation models, we show the following: (1) If the percolation densityP (p) is discontinuous atp _c , then the critical exponent (defined by the divergence of expected cluster size, nP _n (p) (P _c –P)^– asp p _c ) must satisfy 2. (2) or (defined analogously to, but asp p _c ) and [P _n (p _c ) (n ^–1–1/) asn ] must satisfy, 2(1 – 1/). These inequalities for improve the previously known bound 1(Aizenman and Newman), since 2 (Aizenman and Barsky). Additionally, result 1may be useful, in standardd-dimensional percolation, for proving rigorously (ind>2) that, as expected,P _x has no discontinuity atp _c .     

МЕТОД ОБРАБОТКИ ДВУХ МЕРНЫХ СПЕКТРОВ СОВП АДЕНИЙ И ЕГО ПРИМЕНЕНИЕ К АНА ЛИЗУ γ-γ-СОВПАДЕНИЙ НА Ge(Li)-ДЕТЕКТОРАХ ПРИ РА СПАДЕ155Tb

The method of data processing of two-dimensional coincidence spectra is described and its application for the --coincidence spectra analysis in¹⁵⁵Tb is shown. The existence of levels with energies 86·5; 105·3; 118·0; 235·2; 266·6; 268·6; 286·8; 326·0; 367·7; 427· 4; 451·3; 488·8 keV in¹⁵⁵Gd nucleus is proved on the basis of --coincidences measured in¹⁵⁵Tb decay with Ge(Li)-detectors. Two new transitions with energies of 192 and 163 keV were found.     

Gamma-X-ray coincidence Mössbauer emission spectroscopy on57Co/CoO

The time integral Mössbauer emission spectrum of a⁵⁷Co/Co_1–x O source (x 10^–5) at RT consists of two single Lorentzian lines of an Fe²⁺ (76%) charge state and an Fe³⁺ (24%) aliovalent charge state. The spectrum measured by -X-ray coincidence spectrpscopy shows the same fraction of the aliovalent charge state, contrary to the expectation derived from the competing acceptor model as successfully applied by Tejada and Parak [1], who could explain the dependence of the formation of aliovalent charge states after the nuclear transformation on the stoichiometric parameterx. The consequences of this unexpected behaviour for the competing acceptor model are discussed.     

Hyperfine anomalies and nuclear γ-factors of56Co,57Co and60Co isotopes studied by NMR/ON

The results of NMR/ON measurements on^56,57,60Co isotopes in iron are presented in the paper. To avoid the uncertainties caused by local demagnetizing field inhomogeneities the measurements on two cobalt isotopes in one sample have been carried out. The values of nuclear-factors ratios ⁵⁷/ ⁶⁰=1·805(20), ⁶⁰/ ⁵⁶ = 0·761(20), ⁵⁶/ ⁵⁷ = 0·726(20) and hyperfme anomalies^{56 60} = –0·036(10),^{60 57} = 0·017(10) and^{57 56} = 0·018(10) have been calculated from the experimental results.Dedicated to the 30th anniversary of the Joint Institute for Nuclear Research.     

The structure of28Si above 10 MeV excitation energy I: gamma-decay modes and radiative widths of levels

The systematics of-decay modes and radiative widths of highly excited states in²⁸Si has been extended by taking-ray spectra on 60 resonances of the²⁷Al(p,) reaction in the range 1097 keVE _p 4492 keV (12643 keVE _x 15915 keV) and on the²⁴Mg(,) resonances atE =3355, 3431, 4003 keV (E _x =12860, 12925, 13 415 keV). The-decay modes of levels in the sub-resonance region (E _x =10–12.5 MeV) were studied with both the²⁷ A1(p, ) reaction and the²⁷ A1(d, n) reaction at E_d=4,5,6 MeV. Information on radiative widths of levels was obtained by measuring the resonance strengthsS =(2I+1) _p / for 52 resonances of the²⁷Al(p, ) reaction with an emphasis on prospective T=1 states.     

A “hydrodynamic” theory of surface reaction rates

The Brownian motion of adsorbed particles is described in terms of the first four velocity moments of the distribution function (number density, momentum density, energy density and energy current density). The resulting hydrodynamic equations turn out to be sufficient for a simple derivation and extension of Kramers' results for chemical reaction rates in terms of the friction constant of an underlying Fokker-Planck equation. An interpolation formula is obtained for() containing Kramers' results for small and large as limiting cases. For temperaturesT small compared to the well depthV ₀ one finds a large regionT/V ₀/v ₀V ₀/T in which Eyring's absolute rate theory is approximately valid.On leave of absence from Physikdepartment der TUM, München-Garching     

Phase segregation dynamics in particle systems with long range interactions. I. Macroscopic limits

We present and discuss the derivation of a nonlinear nonlocal integrodifferential equation for the macroscopic time evolution of the conserved order parameter (r, t) of a binary alloy undergoing phase segregation. Our model is ad-dimensional lattice gas evolving via Kawasaki exchange with respect to the Gibbs measure for a Hamiltonian which includes both short-range (local) and long-range (nonlocal) interactions. The nonlocal part is given by a pair potential ^dJ(|x–y|), >0 x and y in ^d, in the limit 0. The macroscopic evolution is observed on the spatial scale ^–1 and time scale ^–2, i.e., the density (r, t) is the empirical average of the occupation numbers over a small macroscopic volume element centered atr=x. A rigorous derivation is presented in the case in which there is no local interaction. In a subsequent paper (Part II) we discuss the phase segregation phenomena in the model. In particular we argue that the phase boundary evolutions, arising as sharp interface limits of the family of equations derived in this paper, are the same as the ones obtained from the corresponding limits for the Cahn-Hilliard equation.     

High-spin isomer in 93Mo

The high-spin states of ⁹³Mo have been studied by a ⁸²Se( ¹⁶O, 5n) ⁹³Mo reaction at a beam energy of 100 MeV using techniques of in-beam -ray spectroscopy. Measurements of -t, --t coincidences, -ray angular distributions and -ray linear polarizations were performed. The high-spin isomer was found as a (39/2^-) state at about 9.7 MeV. The near-yrast states in ⁹³Mo were interpreted using the weak-coupling picture of a d_5/2 neutron to a neutron magic core nucleus ⁹²Mo.     

The exact phase diagram of the quantumXY spin glass model in a transverse field

The infinite rangeXY spin glass model in a transverse field is investigated by means of the Trotter-Suzuki approach. The exact phase diagram is obtained showing that a spin glass transition takes place for non-zero values of the transverse field up to a critical value _c =1.440.01. The present numerically exact calculations are in good agreement with our previous approximate results and they clear remaining discrepancies from previous work.     

Geodesics in Gödel-type space-times

We investigate the geodesic curves of the homogeneous Gödel-type space-times, which constitute a two-parameter (l and ) class of solutions presented to several theories of gravitation (general relativity, Einstein-Cartan and higher derivative). To this end, we first examine the qualitative properties of those curves by means of the introduction of an effective potential and then accomplish the analytical integration of the equations of motion. We show that some of the qualitative features of the free motion in GSdel's universe (l ²=2²) are preserved in all space-times, namely: (a) the projections of the geodesics onto the 2-surface (r, ) are simple closed curves (with some exceptions forl ²4²), and (b) the geodesies for which the ratio of azimuthal angular momentum to total energy,, is equal to zero always cross the originr=0. However, two new cases appear: (i) radially unbounded geodesies with assuming any (real) value, which may occur only for the causal space-times (l ²4²), and (ii) geodesies with bounded both below and above, which always occur for the circular family (l ²<0) of space-times.     

Spectroscopic study of potential magneto-optic storage layers

We present an experimental investigation of magneto-optic (MO) thin film materials of interest in optical storage. XPS valence band spectra of ultrahigh vacuum deposited rare earth — Fe₅₀Co₅₀ alloys are correlated to magneto-optic and reflectivity spectra measured ex-situ in the photon energy range 0.5 E _ph 5.5 eV. It is found that 4f ⁿ 4f ^n–15d ¹ optical transitions contribute to room temperature Kerr spectra in Pr-FeCo and Nd-FeCo, but only in the UV spectral region (300 nm). Eu is found to enter Eu-FeCo intermetallic alloys with a 4f ⁷ ground state at –2 eV binding energy. However, no substantial contribution to the Kerr effect from excitations of this electronic state has been observed n either at room temperaturen or at 100 K. We present a general argument that 4f excitations of RE ions in typical intermetallic alloys can never be expected to contribute more than some tenths of a degree to _k in contrast to the well known huge rotations in RE-chalcogenides.For Yb-FeCo we have observed in XPS a mixed valence behavior of Yb showing a discontinuous transition from divalent Yb²⁺ in the pure metal to mixed valent Yb^2.55+ in amorphous Yb-FeCo films. Nofd contributions to the room temperature MO spectra have been detected. Strong optical enhancement effects are presented for metallic bilayer and multilayer structures of the type MO-layer/reflector. The total thickness of an optimized structure corresponds to about two times the penetration depth of light. Enhancement occurs predominantly at photon energies below the plasma frequency of the reflector material and is caused by low values of the optical constantsn andk of the reflector. In storage materials like Tb-FeCo the read-out performance can be improved by about a factor of 2 with a bilayer of 30 nm Tb-FeCo on Cu. Quantitative modelling of the optical and magneto-optic properties of these films is discussed.     

Interpretation of measurements of π0-meson photoproduction partial cross sections on a6Li nucleus with O+ level excitation

The anomalously large measured values of the cross section of the reaction +⁶Li ⁰ +⁶Li^* (3.56 MeV), which were obtained in two different laboratories, 260–450 MeV -rays, are discussed. It is shown that the disagreement between theory and experiment is due to the background reaction +⁷Li ⁰ + n +⁶Li^* (3.56 MeV), which became possible as a result of the poor isotropic purity of the target. This background reaction is discussed with respect to obtaining data on ⁰-meson photoproduction on neutrons.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, 92–96, November, 1991.     

On the 3+ level in Os186 populated in Re186 Β-decay

The coincidences of the 400–1100 keV gammas with the conversion electrons of the 137 keV transition were measured with the intermediate image spectrometer modified for - coincidences. The e_L 137- 770 keV coincidences were observed. Consequently, in addition to the known 768 keV transition, there is another one with closed energy. For this transition the relative intensity ratioI ⁶³² /I ⁷⁷³ =8±2 was determined. The corrected decay scheme of Re¹⁸⁶ is presented.     

Enhancement of activated decay of metastable states by resonant pumping

We consider the effect of a high-frequency pumping cost on the escape rate of a classical underdamped Brownian particle out of a deep potential well. The energy dependence of the oscillation frequency(E) is assumed to be weak on the scale of thermal energy,_E(0)T(0)T/V₀ (0)[_E(0) is the derivative of(E) atE= 0,V ₀ is the barrier height,V ₀ T]. The quadratic-in- contribution to the decay rate is calculated in two different regimes: (1) for the case of resonance of the pumping frequency with the nth harmonic of the internal motion at an energye, when = n(e); (2) for a rollout region of the basic resonance near the bottom of the potential well, when ¦-(0)¦ and is the damping coefficient. In the latter case the absorption spectrum and the enhancement of the decay rate are calculated as functions of two reduced parameters, the anharmonicity of the potential,v _E (0)T/, and the resonance mismatch, [ —(0)]/. It is shown that the effect of the pumping increases with diminishing ¦v¦ and at small v is proportional tov ^–1. In this regime, the dependence on is stepwise: the pumping contribution is large for v > 0 and small for v < 0. In the frame of our theory, the decay rate is invariant against the simultaneous alternation of the signs of andv. The spectrum of the energy absorption has the standard Lorentzian shape in the absence of anharmonicity,v=0, and with increasing of ¦v¦ shifts and widens retaining its bell-shape form.     

Behavior at small distances and low temperatures of the ion-ion distribution function of the two-dimensional Coulomb gas

We compute upper and lower bounds for the canonical ion-ion distribution functiong ₁₁ ^(N) (r) of the two-dimensional Coulomb gas for smallr and 1<<2, where is the plasma parameter. Both bounds are proportional tor ^2-/(-1), which proves thatg ₁₁ ^(N) (r) behaves asr ^2-, as conjectured by Hansen and Viot. We conjecture that, in the thermodynamic limit,g ₁₁(r) ~ 2(-1)^-1(r/a)^2-, wherea=(n)^–1/2 is the mean interionic distance. We also compute the canonical one-body distribution function with one pair (+,–) in a disk, for anyr and any.     

High spin states in77Se populated by the74Ge(α,n γ) reaction

⁷⁷Se has been investigated by the reaction⁷⁴Ge(,n) at 14 MeV. Gamma singles spectra, gamma angular distributions and gamma-gamma coincidences have been taken. A level scheme has been established, spins and parities have been assigned. States of a rotational band on the 1/2^– ground state, a rotational band on the 5/2^– 249.7 keV state and an anormal band have been identified. Nuclear Reaction ⁷⁴Ge(,n )E =14 MeV; measuredE ,I ,--Coin.,-ang. distr.⁷⁷Se deduced levels,J, . Enriched target, Ge (Li).     

Effects of high-temperature annealing on magnetic ordering in thin films of Bi2O3-CaO-Fe2O3

Magnetic properties of rf sputtered (0.5–x) Bi₂O₃-x CaO-0.5 Fe₂O₃ (x=0–0.5) have been studied through magnetization and ferromagnetic resonance (FMR) measurements. Films prepared in a mixed oxygen-argon atmosphere are amorphous and paramagnetic. Samples annealed in air at temperatures of 700–1000 K show a ferrimagnetic behavior even though X-ray diffraction data for the films do not indicate the precipitation of any crystalline ferrimagnetic compounds. The room-temperature saturation magnetization 4M and the uniaxial anisotropy field H _u , decrease with increasing x. The Curie temperature and the gyromagnetic ratio increase with increase in the concentration of CaO. Studies on the effects of sputtering atmospheres on magnetic parameters show that films sputtered in oxygen-rich atmospheres have a large 4M and H _u , and a relatively small and FMR line-width. Ordered amorphous clusters are suggested to give rise to the observed ferrimagnetic character in the annealed films.     

Central limit theorems for percolation models

Letp 1/2 be the open-bond probability in Broadbent and Hammersley's percolation model on the square lattice. LetW _x be the cluster of sites connected tox by open paths, and let(n) be any sequence of circuits with interiors . It is shown that for certain sequences of functions {f _n }, converges in distribution to the standard normal law when properly normalized. This result answers a problem posed by Kunz and Souillard, proving that the numberS _n of sites inside(n) which are connected by open paths to(n) is approximately normal for large circuits(n).