Inductive limit automorphisms of the irrational rotation algebra

It is shown that the flip automorphismUU ^*,VV ^* of the irrational rotation algebra A is an inductive limit automorphism. Here, the algebra A is generated by unitariesU, V satisfyingVU=e²ⁱ UV, where is an irrational number. Recently, Elliott and Evans proved that A can be approximated by unital subalgebras isomorphic to a direct sum of two matrix algebras over , the algebra of continuous functions on the unit circle. This is the central result which they used to obtain their structure theorem on A; namely, that A is the inductive limit of an increasing sequence of subalgebras each isomorphic to a direct sum of two matrix algebras over . In their proof, they devised a subtle construction of two complementary towers of projections. In the present paper it is shown that the two towers can be chosen so that each summand of their approximating basic building blocks is invariant under the flip automorphism and, in particular, that the unit projection of the first summand is unitarily equivalent to the complement of the unit of the second by a unitary which is fixed under the flip. Also, an explicit computation of the flip on the approximating basic building blocks of A is given. Further, combining this result along with others, including a theorem of Su and a spectral argument of Bratteli, Evans, and Kishimoto, a two-tower proof is obtained of the fact established by Bratteli and Kishimoto that the fixed point subalgebra B (under the flip) is approximately finite dimensional. Also used here is the fact that B has the cancellation property and is gifted with four basic unbounded trace functionals. The question is raised whether other finite order automorphisms of A (arising from a matrix in SL(2,)) are inductive limit automorphisms - or evenalmost inductive limit automorphisms in the sense of Voiculescu.Research partly supported by NSERC grant OGP0169928     

Exact exponent for the number of persistent spins in the zero-temperature dynamics of the one-dimensional Potts model

For the zero-temperature Glauber dynamics of theq-state Potts model, the fractionr(q, t) of spins which never flip up to timet decays like a power lawr(q, t)t ^–(q) when the initial condition is random. By mapping the problem onto an exactly soluble one-species coagulation model (A+AA) or alternatively by transforming the problem into a free-fermion model, we obtain the exact expression of (q) for all values ofq. The exponent (q) is in general irrational, (3)=0.53795082..., (4)=0.63151575..., ..., with the exception ofq=2 andq=, for which (2)=3/8 and ()=1.     

Opto-thermal study of the melting transition of benzophenone

We report a series of opto-thermal transient emission radiometry (OTTER) measurements on benzophenone over the temperature range 20–80°C, which includes the melting transition at 48°C. At temperatures sufficiently close, but below the melting point, the form of the opto-thermal decay curves was found to change, when the laser pulse energy was sufficient to cause transient melting near the surface. Such measurements could be useful in the study of re-crystallation dynamics in pulsed laser annealing and similar surface treatments. In addition, the experiment gives a direct measure of ₀, the initial jump in surface temperature, and a comparison of solid and liquid thermal diffusivities. The values found in the present study are ₀, andD(solid)/D(liquid)=2.2±0.2.     

Some experimental data about the two contributions to magnetoresistance for n-type silicon crystal at 125 K

The transverse magnetoresistance (MR) was measured versus magnetic field strengthB at different rotational angles between the directions of bothB and currentI for n-type silicon crystal with charge carrier concentration of 1·8×10¹⁵cm^–3. The direction of the current through the two samples was chosen so that the angles between the current vector and [100] crystallographic axis were 50° and 70°, respectively. These measurements were done under weak electric and magnetic fields atT=125 K. It was found that the MR exhibits two types of anomalous effects, one of them at two opposite directions ofB at different, and the other at the same angles, when=50° and=70°. This shows that the anomalous behaviour of MR is not onlyB and dependent, but depends also on the current direction. Also the values ofB which are separated between the negative and positive parts of MR curves at the same depend on the magnitude of. These results may be attributed to the anomalous motion of charge carriers ink-space as a result of deviation of current direction from the symmetry axis.     

Isotropic spherical coordinates

The method of using regularization to analyze singularities is applied to the Schwarzschild metric in isotropic spherical coordinates (3). It is found that there arises a singularity at the gravitational radius which does not satisfy the conditions of physical realizability (T =T ,T ₀ ⁰ =T =0). Consequently, this metric cannot be considered as corresponding to pure vacuum.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 4, pp. 84–87, April, 1987.     

Measurement of the2H(d, γ)4He reaction at intermediate excitation energies

The²H(d, )⁴He differential cross section was measured at deuteron laboratory energies of 20, 24, and 28 MeV between _cm=45° and _cm=135°. AtE _d =28 MeV a complete angular distribution was determined and fitted with Legendre polynomials. The ratioR=d/d (_cm=90°)/d/d (_cm=135°) was measured for each deuteron energy.     

Possibility of a Lifshitz phase transition in Cd observed by a singularity in the muon Knight shift

During the past much effort has been devoted to a systematic study of the muon Knight shiftK in metallic environments and its implications on the local electronic structure of hydrogen in metals [1]. These measurements in simple metals were essentially all carried out in polycrystalline samples at room temperature. The present measurements in Cd in polycrystalline and single crystal samples cover a temperature range between 20 K and the melting point of this strongly anisotropic metal (hcp crystal structure,c/a ratio 1.89 — idealc/a ratio 1.63). These measurements add qualitatively new and interesting aspects and insights on the screening of a light hydrogen isotope in a metal as well as on certain properties of the host material itself. The outstanding features of the muon Knight shift in Cd are: (i) a strong intrinsic temperature dependence with an increase ofK of more than 100% between 20 K and the melting point (T=593 K), (ii) an anomaly at 110 K in the form of a singularity in the isotropic part ofK which is interpreted as a band structure effect, (iii) an anisotropic Knight shift contribution fitting the expressionK(T,)=K _iso(T)+K _ax(T) * (3 · cos² –1)/2, where both, the isotropic and the axial contribution ofK , are strongly temperature dependent.     

Charge spectra of dyonic quarks

Considering quarks as dyons, we analyze different possibilities for free fractional electric charges and monopoles to coexist. For nonvanishing vacuum angle, electric charges of dyons are not exactly fractional, but carry extra charges proportional to. The average extra charge vanishes for mesons, but not for baryons.     

Comparisons of vector analyzing-power data and calculations for neutron-deuteron elastic scattering from 10 to 14 MeV

High-accuracy analyzing-powerA _y() data forn-d elastic scattering at 12 MeV have been measured using the polarized-neutron facilities at the Triangle Universities Nuclear Laboratory (TUNL). The present data have been combined with our previousn-d measurements at 10, 12, and 14.1 MeV to form the highest-accuracyA _y() data set forn-d elastic scattering below 20 MeV. These data are compared to recent Faddeev-based neutron-deuteron (n-d) calculations which use the Paris and Bonn equivalent separable potentials PEST and BEST, as well as Doleschall's representation of theP- andD-wave nucleon-nucleon interactions. None of these models adequately describe the data in the angular region around the maximum ofA _y(). Possible reasons for the discrepancies are discussed. The sensitivity of the present Faddeev-based calculations to various angular momentum components of the nucleon-nucleon interaction are examined.     

Magnetic and electric hyperfine interactions in the system EuSm

Magnetic and electric hyperfine interactions in the system EuSm were investigated with the isomeric 11/2^– state in¹⁴⁵Eu by applying the time-differential perturbed angular distribution (TDPAD) method. The temperature dependence of paramagnetism was studied between 90 K and 1000 K by measuring the magnetic hyperfine interaction frequency _L=g_NN¹ (T)B_ext. The paramagnetic correction factor strictly follows the Curie-Weiss relation =1+C/(T-), withC=–50(2) K and =–29(5) K. This is compatible with a hyperfine field ofB _int(0)=–25(1) T, a valence of two for Eu in Sm, and antiferromagnetic order at low temperatures.The temperature dependence of the electric quandrupole coupling constant v_Q, investigated between 100 K and 400 K, can be reproduced by a linear temperature variation v_Q(T)=v_Q(0) (1-AT), with v_Q(0)=16.2(4) MHz andA=7.2(8)·10^–4 K^–1.The paramagnetic relaxation time _rel of the nuclear alignment is proportional to the temperature of the sample, with _rel T^–1=3.7(2) ·10^–9s K^–1.This leads to the Korringa relation _J T=const=5.1(5)·10^–11s K for the relaxation time of the 4f electronic spinJ. Assuming that the relaxation ofJ is mainly caused by exchange interaction between conduction electrons and localized 4f electrons at the Eu site, an exchange integral of |J _eff|=0.10(2) eV can be deduced.     

The sphaleron at finite mixing angle

The exact sphaleron solution in the bosonic sector of the electro-weak standard model is only known for weak mixing angle _w =0. To investigate the behaviour closer to the experimental value _W ^exp 30° we construct a non-contractible loop in configuration space that is sensitive to _W . Our numerical results for the energy and the magnetic dipole moment, combined with previous perturbative results, indicate that the dependence on _W is weak.     

Sensitivity ofn-p scattering observables to charge-independence breaking of the3 P N-N phase shifts

The sensitivity of neutron-proton scattering observables to the recently reported charge-independence breaking of the isospinT=1³ P nucleon-nucleon interaction has been calculated. It is shown that only the analyzing powerA _y () at extreme forward angles and at =90° c.m. and the spin-correlation coefficientA _zx () at 90° c.m. exhibit a measurable sensitivity. It is concluded that the determination ofA _y at 90° c.m. is currently the most accurate approach to verify independently charge-independence breaking in the³ P nucleon-nucleon phase shifts, considering the status of present experimental techniques.     

Isotope effects in the interaction of hydrogen and deuterium with a rhodium (110) surface

The adsorption of H₂ and D₂ on a Rh (110) surface at 100 K leads to a sequence of ordered phases, among others 1×2 phases at _H =0.5 and at _H =1.5 which likely involve a partial surface reconstruction consisting of a small perpendicular displacement of Rh surface atoms. The structure of the adsorbate phases is strongly correlated with the binding energy of the adsorbed phases. Three H (D) binding states (₁,₂ and) are populated at saturation as determined by thermal desorption spectroscopy (TDS). Whereas the peak temperature of the state is invariant with the hydrogen isotope, the D ₁ state appears at a 8 Klower and theD ₂ state at a 5 Khigher temperature than the respective H states. Generally the D phases exhibit a better long-range order than the H phases. The rate of adsorption is identical for the first three adsorbed phases but D₂ adsorbs appreciably faster in the 1×2–3H and the final l×1–2H phases.Zero point energy effects as well as a H coverage dependent local interaction model could account for the observed effects.     

Linewidth studies on the Kr+ 469.4 nm and 473.9 nm lines excited in a helium-krypton hollow cathode discharge

Collisional and Doppler linewidths (v _C and v _D ) of the 469.4 nm and 473.9 nm Kr ion lines were measured in a He-Kr hollow cathode discharge using Fabry-Perot technique. A linear dependence of v _C on He pressure was found for both lines. Significant differences were found between the temperature values deduced from the v _D -s of the two lines, and an unexpected temperature dependence of the broadening parameter for the Kr⁺ 469 nm line was also observed. The temperature difference between the two lines is explained by excitation of the upper level of the 469 nm line by second kind collisions between metastable He atoms and ground-state Kr ions, while the temperature dependence of the broadening parameter of the Kr⁺ 469 nm line is suggested to be due to the inverse process.     

Non-commutative spheres

LetA be the irrational rotation algebra, i.e. theC ^*-algebra generated by two unitariesU, V satisfyingVU=e ²ⁱ UV, with irrational, and consider the fixed point subalgebraB under the flip automorphismUU ^–1,VV ^–1. We prove thatB is an AF-algebra.Dedicated to Professor Huzihiro Araki on the occasion of his 60'th birthday     

<Emphasis Type="Italic">θ</Emphasis>-Deformations as Compact Quantum Metric Spaces

Let M be a compact spin manifold with a smooth action of the n-torus. Connes and Landi constructed -deformations M of M, parameterized by n×n real skew-symmetric matrices . The Ms together with the canonical Dirac operator (D,) on M are an isospectral deformation of M. The Dirac operator D defines a Lipschitz seminorm on C(M), which defines a metric on the state space of C(M). We show that when M is connected, this metric induces the weak-* topology. This means that M is a compact quantum metric space in the sense of Rieffel.     

Supertransferred hyperfine interaction in magnetic insulators (I)

Two additive contributions to the supertransferred hyperfine (STHF) interaction are suggested to be taken into account in its semi-quantitative analysis of the N-O-M chain: (i) that of bonding molecular orbitals, (ii) that of antibonding orbitals, by calculation of spin-polarization of s-electrons in the N-ion due to the superexchange interaction with d-electrons of the M-ion. Generalized forms of the operator and angular dependence of the STHF interaction were considered due to the use of irreducible tensor operators to the point O_h group. Analytical expressions for the value of the hyperfine fieldH _STHF at the nucleus of the N-ion induced by the magnetic M-ion (both in non-degenerateA ₁,A ₂ ground states and in degenerateE, T ₁,T ₂ states as well) are derived. The value ofH _STHF is dependent upon the type of the M-ion ground state and the geometry of the N-O-M bond. The value ofH _STHF induced by M-ions ofA ₁,A ₂,E states was shown to depend only on the bond angle , and that ofT ₁,T ₂ states on the combinations sin² cos 2, sin² sin 2. The importance of orbital anisotropy in the STHF interaction is emphasized. The orbital anisotropic contribution toH _STHF is drastically dependent on the ground state and its splitting in the crystalline field of low symmetry: the isotropic contribution is determined mainly by the occupation numbers of thet _2g ande _g subshells.     

Propagation of electromagnetic surface waves in a radially inhomogeneous optical waveguide

The propagation of electromagnetic surface waves along a radially inhomogeneous dielectric waveguide is investigated. The problem is formulated in terms of differential equations to be satisfied by the radially dependent parts of the electromagnetic field vectors. The dielectric waveguide is assumed to consist of a homogeneous cladding of infinite extent and a radially inhomogeneous core of higher permittivity. Numerical solutions of the differential equations in the core are obtained by two different methods, viz. by direct numerical integration and by substitution of an appropriate power series expansion. In the cladding the field is expressed in terms of modified Bessel functions. Imposing the boundary conditions at the interface of core and cladding, an equation for the unknown propagation coefficient is obtained. From this equation the propagation coefficients for the lower order modes are computed numerically. Numerical results are presented for some permittivity profiles of practical interest in single-mode transmission along optical fibres.Nomenclature a radius of the core - a _q vector coefficient in the power series expansion off() - A _i constants - A square matrix - b _q coefficient in the power series expansion of _r() - B square matrix - C square matrix - c _n unknown constant - d _n unknown constant - D() fundamental matrix - E,E _r,,z electric field vector and components - E,e _r,,z radially dependent parts ofe _r,,z - f solution vector - G _q square matrix - H,H _r,,z magnetic field vector and components - h _r,,z radially dependent parts ofE _r,,z - h reduced wavenumber - i radial mode number - j imaginary unit - k _0,m wave number - K _n modified Bessel function of the second kind and order n - n azimuthal mode number - t time - U normalized propagation constant - Z _m plane wave impedance of the cladding - r, , z cylindrical co-ordinates - p, q, s integers - propagation coefficient - increment - _0,m,r permittivity - normalized radiusr - ₀ wavelength in free space - ₀ permeability - angular frequency - d _r, differentiation with respect tor, Engineering and Professor H. J. Frankena of the Physics Department for their valuable discussions.     

Structure of the generalized momentum of a charged test particle and the inverse problem in the general theory of relativity

The work of Sedov [1] examined the navigational problem which involves finding the metric tensor g_i of space of general relativity from the results of physical measurements. The problem of the approximate determination of g_i from the mutual deflection of test particles in gravitational fields was studied in [2], The problem of finding g_i from the second integrals of the geodesic equations in gravitational fields was solved in [3]. The connection of the first integrals of the Hamilton-Jacobi equation of the test particles with the symmetry of StÄckel spaces was investigated by Shapovalov [4, 5].Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 60–64, July, 1981.     

Adsorption of oxygen and hydrogen on Pt(111) studied with second-harmonic generation

The adsorption of oxygen and hydrogen on a Pt(111) surface has been studied with phase-sensitive Second-Harmonic Generation (SHG) signal detection. The SHG-signal change measured with p-in, p-out polarization during the adsorption of oxygen and hydrogen was found to be different in amplitude and phase for the two adsorbates. At the wavelength used (1064 nm), only a localized interaction between adsorbate and substrate is seen, leading to a linear dependence of the susceptibility on the coverage. Sticking coefficients,s, and their coverage dependence were determined. For hydrogen, a linear decrease ins with coverage was found; the initial sticking coefficient beings ₀=0.06 at a temperature ofT=130 K. For oxygen,s whows a quadratic decrease with coverage, strongly dependent on temperature, withs ₀=0.05 atT=350 K.A method based on these results is proposed, which would allow the determination of adsorbate coverages of coadsorption systems with SHG using phase-sensitive signal detection.Presented at the 129th WE-Heraues-Seminar on Surface Studies by Nonliner Laser Spectroscopies, Kassel, Germany, May 30 to June 1, 1994