Degenerate four-wave-mixing spectroscopy in NaH

We performed DFWM spectroscopy on X ^–1+–A ¹⁺ transitions in NaH produced in an indirect photochemical reaction between Na(3p) and H₂ and detected v=1, 2 and 3 ground state vibrational levels of NaH molecules, whereas with resonance enhanced CARS, we observed v=0 levels only. This different sensitivity can be explained by considering the Franck-Condon-factors and the relevant damping coefficients for the corresponding transitions in the NaH molecule. Time resolved DFWM spectroscopy showed that NaH(v=1) molecules effectively live much longer than Na(3p) atoms which merely follow the laser excitation pulse.     

On the significance of Killing tensors

Killing vectors give the linear first integrals of the geodesic equations on Riemannian manifolds and spacetimes, while Killing tensors give the quadratic, cubic, and higher-order first integrals. Here it is shown that the Lie algebra of Killing vectors,, is extended by Killing tensors into a graded algebra,. This sheds some light on the comment by Xanthopoulos [1] on the apparent scarcity of irreducible Killing tensors. Examples are presented of the graded algebras when is abelian and when is nonabelian.     

О ЗАТУХАНИИ ФАЗОВЫХ К ОЛЕБАНИЙ В СИНХРОТРОНЕ СО СЛАБ ОЙ ФОКУСИРОВКОЙ

, , . , . , - , , [1], .

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On the damping of phase oscillations in a weak-focusing synchroton

An equation of the phase oscillations in a weak-focusing synchroton is derived for the case that an arbitrary high-frequency field of sinusoidal time dependence is distributed on the circumference of the accelerator. It is shown that the damping of phase oscillations is practically independent of the shape of the high-frequency field. From this we get the special case that any adjustments to the accelerator gaps, considered for example in [1], are useless.

     

ВЛИЯНИЕ СПЕКТРАЛЬНО ГО ПРОФИЛЯ ДУБЛЕТАKα 1 α 2 И ДИФРАКЦИОННОГО РАС ШИРЕНИЯ НА ИНТЕГРАЛЬ НУЮ ИНТЕНСИВНОСТЬ ДИФРА КЦИЙ ПРИ ВЫСОКИХ УГЛА Х БРЭГГА

, K _{1 2} LP . 75°85° K , . , <80°. ( , ) <83°. , 90° , , , . >83° , , .

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The influence of the spectral profile of theK₁₂ doublet and diffraction broadening on the integrated intensities of high angle diffractions

Relations are derived giving the influence of the spectral profile of theK _{1 2} doublet and the influence of diffraction broadening on the productLP of the Lorentz and polarization factor. The relations are used to calculate the numerical values of the corresponding corrections for the theoretical values of the integrated intensities of diffractions in the angular region 75°85° and for the most frequently usedK radiation of copper, cobalt and iron.It follows from the calculated values of the corrections that, due to the accuracy at present attainable in experimental measurements, the influence of the spectral profile in diffractions with an angle<80° can be neglected when calculating the theoretical values of the integrated intensities. The influence of diffraction broadening need not be taken into account in diffractions with an angle<83° even when the broadening is large (e. g. five-fold). As the angle approaches 90°, of eourse, the corrections for both above influences suddenly increase, particularly those for diffraction broadening, and their limitation becomes difficult and is not single-valued. For this reason the use of diffractions with angles>83° does not appear very suitable for solving problems based on exact measurement of the integrated intensities and their comparison with the corresponding theoretical values.

     

Operators with singular continuous spectrum: II. Rank one operators

For an operator,A, with cyclic vector , we studyA+P, whereP is the rank one projection onto multiples of . If [,] spec (A) andA has no a.c. spectrum, we prove thatA+P has purely singular continuous spectrum on (,) for a denseG of 's.Research partially supported by DGAPA-UNAM and CONACYT.This material is based upon work suported by the National Science Foundation under Grant No. DMS-9207071. The Government has certain rights in this material.This material is based upon work supported by the National Science Foundation under Grant No. DMS-9101715. The Government has certain rights in this material.     

Symmetries and half-sided modular inclusions of von Neumann algebras

LetN, be a von Neumann algebras on a Hilbert space , a common cyclic and separating vector. Assume to be cyclic and also separating forN . Denote by , _N , _N the modular operators to (, ), (N, ), resp (N , ). Assume now ^-it N ^it N for allt 0. (Such type of inclusions ((N U, ) , ) are called half-sided modular.) Then the modular groups ^it , _N ^ir , _N ^is ,t, r, s generate a unitary representation of the group S1(2, )/Z ₂ of positive energy.Another result is related to two half-sided modular inclusions (₁ , ) and (₂ , ). Under proper conditions the three modular groups ^it , ₁ ^ir , ₂ ^is ,t, r, s generate the three-dimensional subgroup of O(2, 1) of two commuting translations and the Lorentz transformation.Partly supported by the DFG, SFB 288 Differentialgeometrie und Quantenphysik.     

Wavevector scaling,surface critical behavior,and wetting in the 2-d, 3-state chiral clock model

The controversial 2-d, 3-state chiral Potts model is studied using transfer matrix finite size scaling. at =0, we find dq _N/dN ^–4/5, whereq is the wavevector, the chiral field, andN the strip width (N=4–10). The result is consistent with den Nijs's crossover exponent =1/6. With surface fields on the infinite free boundaries, exponents associated with bulk magnetizationy _H, surface magnetizationy _H, and surface susceptibility are computed vs. ; results are similar for or to the infinite direction. Preliminary results are given for the bulk specific heat critical amplitudes, to test the universality of amplitude ratios. The interface wetting line is located for 01/4 using simple transfer matrix calculations of surface tensions in the solid-on-solid approximation. Overhangs or bubbles seem relatively unimportant at all temperatures.     

The chiral determinant and the eta invariant

For { _y },y, a one parameter family of invertible Weyl operators of possibly non-zero index acting on spinors over an even dimensional compact manifoldX, we express the phase of the chiral determinant det _– in terms of the invariant of a Dirac operator acting on spinors over ×X.Supported in part by NSF Grant No. PHY-82-15249Supported in part by NSF Grant PHY 8605978 and the Robert A. Welch Foundation     

A contribution to the semi-focusing method with a flat polycrystalline sample

Condition are derived for the approximate focusing of diffraction lines in the chosen, relatively wide angular region, using the semi-focusing method with a flat sample, if a bent crystal monochromator is employed. The form of the absorption factor for a flat polycrystalline sample is derived for the case of uniform oscillation of the sample in the angular region ± around the axis of the camera.

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, . ± , .

     

Die halbleitende Vebbindung SiTe

Ohne Zusammenfassung

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SiTe

     

p-adic Heisenberg group and Maslov index

A system of coordinates on a set of selfdual lattices in a two-dimensionalp-adic symplectic space (V,) is suggested. A unitary irreducible representation of the Heisenberg group of the space (V,) depending on a lattice (an analogue of the Cartier representation) is constructed and its properties are investigated. By the use of such representations for three different lattices one defines the Maslov index =(₁,₂,₃) of a triple of lattices. Properties of the index are investigated and values of in coordinates for different triples of lattices are calculated.     

Implementation of comparative probability by normal states. Infinite dimensional case

Let be an infinite dimensional Hilbert space and () the set of all (orthogonal) projections on . A comparative probability on () is a linear preorder on () such thatOP1,1O and such that ifP┴R,Q┴R, thenPQP+RQ+R for allP, Q, R in (). We give a sufficient and necessary condition for to be implemented in a canonical way by a normal state onB(), the bounded linear operators on .     

A contribution to the theory of the triple crystal diffractometer

The first part of the paper gives a general equation for triple-crystal arrangement with perfect crystals on the assumption that the third crystal is rotated. It is shown that in the case of perfect crystals the shape of the reflection curve is practically independent of the vertical divergence. The case of mosaic crystals is also solved and the possibility of rotation by other than the third crystal is considered. A method is proposed for investigating the imperfection of a crystal which is different from methods used up to now. The paper is supplemented by some experimental results.

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, . , . , , . , . .

     

СМЕШАННАЯ КРАЕВАЯ ЗА ДАЧА ПЛОСКОЙ ТЕОРИИ УПРУГОСТИ ДЛЯ КОЛЬЦА

: , — . -. - , , , .     

Orthogonalization of channel spaces in the quark resonating group model

A recently developed coupled-channel resonating group method with orthogonalized function spaces is tested. As test example a six-quark three-channel resonating group model is used. The channels are theNN-, - andCC- (hidden colour) channels. In earlier calculations without orthogonalization of channel spaces the relative motion function of theNN-channel had a node in theS-wave at approximately 0.5 fm. In the new treatment, in which the - andCC-channels are only orthogonal corrections to theNN-channel, this node is no longer present. The newNN wave function is very similar to the one of the single-channel approximation. Thus, in the one- and three-channel approximation, we consistently find that the six-quark resonating group model does not support the notion of a short-distance node in theNN wave function.     

Mean-Field Critical Behavior for the Contact Process

The contact process is a model of spread of an infectious disease. Combining with the result of ref. 1, we prove that the critical exponents take on the mean-field values for sufficiently high dimensional nearest-neighbor models and for sufficiently spread-out models with d>4:()– _c as _c and ()( _c–)^–1 as _c, where () and () are the spread probability and the susceptibility of the infection respectively, and _c is the critical infection rate. Our results imply that the upper critical dimension for the contact process is at most 4.     

The number of bound states of singular oscillating potentials

For a spherically symmetric potential such that rVL ¹(a, ), a>0, and is such that, if we define W=– _r V(t) d(t), W belongs to L ¹ (0, ) and rW0 as r0, we show that the number of bound states in any partial-wave satisfies the bound n2 ₀ r W ² dr. It was shown in a previous paper [1] that this class of potentials is regular from the point of view of abstract scattering theory as well as from the time-independent theory and the Jost function approach. We show also that, for large values of the coupling constant, n(gV) has the asymptotic behaviour C _±g ₀ W(r) dr as g±.     

A generalized fluctuation-dissipation theorem for the one-dimensional diffusion process

The [, , ]-Langevin equation describes the time evolution of a real stationary process withT-positivity (reflection positivity) originating in the axiomatic quantum field theory. For this [, , ]-Langevin equation a generalized fluctuation-dissipation theorem is proved. We shall obtain, as its application, a generalized fluctuation-dissipation theorem for the one-dimensional non-linear diffusion process, which presents one solution of Ryogo Kubo's problem in physics.     

Long-range order in the XXZ model

The existence of long-range order is proved under certain conditions for the antiferromagnetic quantum spin system with anisotropic interactions (XXZ model) on the simple cubic or the square lattice. In three dimensions (the simple cubic lattice), finite long-range order exists at sufficiently low temperatures for any anisotropy(0) ifS1, and for 0<0.29 (XY-like) or>1.19 (Ising-like) ifS=1/2. In two dimensions (the square lattice), ground-state long-range order exists under the following conditions: for any anisotropy (0) ifS3/2; 0<0.032 (XY-like) or 0.67<<1.34 (almost isotropic) or>1.80 (Ising-like) ifS=1;>1.93 (Ising-like) ifS=1/2. We conjecture that the two-dimensional spin-1/2XY model (=0) has finite ground-state long-range order. Numerical evidence supporting this conjecture is given.     

Влияние переменного магнитного поля на остаточное состоя ние магнитно — Мягких материалов

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The influence of an alternating magnetic field on the remanent state of magnetically soft materials

A study is made of the influence of an alternating magnetic field of varying maximum amplitude on the remanent state, or rather, apparent remanent state of toroidal and open samples of metallic and non-metallic magnetically soft ferromagnetics. An interpretation of the corresponding dependences is given on the basis of Kondorski's conception of the composition of a polycrystalline jerromagnetic material.