A spectral characterization of KMS states

Let be a state on aC*-dynamical system . For each of the following properties of : (1) is -K MS with respect to for some given , 0<+, (2) is either a KMS state or a ground state, necessary and sufficient conditions are given involving only the spectral subspaces of associated with . The results provide a new insight in the concept of passivity, introduced by W. Pusz and S. L. Woronowicz.Aangesteld navorser N.F.W.O., Belgium, on leave from Katholieke Universiteit Leuven. Research partially supported by N.A.T.O.     

The modular group and super-KMS functionals

Every normal, faithful, self-adjoint functional on a von Neumann algebraA canonically determines a one-parameter-weakly continuous *-automorphism group (the analog of the modular group) and a canonical ₂ grading onA, commuting with . We show that the functional satisfies the weak super-KMS property with respect to and Furthermore, we prove that and are the unique pair of a-weakly continuous one-parameter *-automorphism group and a grading of the algebra, commuting with each other, with respect to which is weakly super-KMS. The above results thus provide a complete extension of the theory of Tomita and Takesaki to the nonpositive case.Supported in part by the National Science Foundation under Grant DMS-8922002.     

Cubic nonlinear tensor of a ferromagnet

The nonlinear properties of a ferromagnet are studied. Many-time retarded Green's functions are used to obtain an expression for the cubic nonlinearity tensor with allowance for spatial dispersion of a uniaxial ferromagnet. The components due to the dipole-dipole interaction of the spins and also due to the anisotropy energy are found. A comparative analysis is made of the different components of the cubic nonlinearity tensor in both the nonresonance case and for various resonances, in particular when ₀, 3 2w₀, 2 ₀, 3 ₀ for the case in tripling of the frequency. Here, is the frequency of the incident wave and ₀ is the frequency of uniform precession. It is shown that in the non-resonance case the largest components are those that are nonvanishing when no allowance is made for spatial dispersion; in the resonance cases the largest components are those due to the dipole-dipole interaction of the ferromagnetism spins.Translated from Izvestiya VUZ. Fizika, No. 12, pp. 53–58, December, 1973.     

Normal mode configuration in an inorganic medium containing defects

The vibrational structure in an inorganic medium containing defects is analyzed as a function of the frequency of the applied field. Since the dispersion relations for the medium are nonlinear, the configuration of the normal modes depends differently upon and . It is shown that exponential damping of the optic branches is observed for <₀, and that the structure of these modes changes significantly over the range 0<<₀, so that only in the neighborhood of ₀ does it correspond to long wavelength vibrations with configurations of stress deviator waves.Institute for the Physics of Strength and Materials Science, Russian Academy of Sciences, Siberian Division. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 10, pp. 87–90, October, 1994.     

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 .     

Deposition of silver films by plasma-enhanced chemical vapour deposition

Plasma-enhanced chemical vapour deposition of silver films has been performed using perfluoro-1-methylpropenylsilver as a precursor. Under most conditions of rf power, substrate temperature and gas composition shiny films with resistivities of 2 cm and impurities of 1 % are obtained.     

Total dynamic structure factor of icosahedral and As-quenched and relaxed glassy Pd58.8Si20.6U20.6 measured at 296 K

The total dynamic structure factorsS(Q, ) of icosahedral, glassy Pd_58.8Si_20.6U_20.6, and the crystallized sample have been determined at room temperature using inelastic scattering of cold neutrons (IN6 of ILL). In contrast to the static structure factorS(Q), where the long range bond orientational order (BOO) leads to pronounced diffraction peaks with finite half width, the dynamic structure factor shows little or no influence of the long range BOO on the atomic dynamics of icosahedral PdSiU in the range of frequencies (0.525 meV) and momentum transfers Q(5Q30 nm^–1 for inelastic scattering) investigated here. The wavelength-dependence of the atomic dynamics of icosahedral PdSiU is very similar to that of the metallic glass and is different from that of the crystallized sample. As for glassy PdSiU no well defined vibrational collective excitations are found as peaks in the inelastic part ofS(Q, ) of the icosahedral sample,-quite in contrast to theoretical expectations and to the dispersions of pronounced excitations determined under identical experimental conditions fromS(Q, ) of the crystallized sample. On structural relaxation of the metallic glass Pd_58.8Si_20.6U_20.6 the largest amount of low energy modes is annealed out at lowest energy.Dedicated to Professor Harry Thomas on the occasion of his 60th birthday     

Temperature dependence of the afr frequencies of a uniaxial antiferromagnet

The method of two-time Green's functions is used to calculate the temperature dependences of the antiferromagnetic-resonance (AFR) frequencies for a uniaxial antiferromagnet in the field range below sublattice-reversal fields. The AFR frequency has a [K(T)/M(T)]^1/2 dependence on the anisotropy constant K(T). For the simplest case of single-ion anisotropy, the normalized AFR frequency is proportional to the relative sublattice magnetization: (T) /(0) (T).Translated from Izvestiya VUZ. Fizika, No. 12, pp. 39–44, December, 1969.     

Electromagnetic wave excitation in a dense plasma (ωPe>ωBe) by “tail” electrons

We consider the possibility of electromagnetic wave generation in a plasma with _Pe>_Be by tail electrons which scatter on anomalous Doppler resonance of potential waves with _2Be. These oscillations, organized into periodic waves, resonantly excite potential waves of harmonic frequencies ₁=s·_2Pe, s=2, 3, .., easily transformable to electromagnetic radiation. A coherent mechanism for solar radio flares is developed.Deceased.Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 118–122, July, 1994.     

Spectral superbroadening of self-focused picosecond laser pulses in D2O

Intense picosecond light pulses of a mode-locked Nd: glass laser at _L =1054 nm (fundamental wavelength) and _SH =527 nm (second harmonic wavelength) are passed through a sample of D₂O under self-focusing conditions. Spectrally structured superbroadened, spatially bell-shaped emission in the forward direction is obtained. Primary generation processes are pump-pulse-degenerate stimulated parametric four-photon interaction (₁ + _{1 3} + ₄) and stimulated Raman scattering (_{1 R} + ), which occur concurrently (₁= _L or _SH angular pump frequency, #x03C9; _R first Stokes frequency, #x03C9; signal frequency, #x03C9;₃ signal frequency, #x03C9;₄ idler frequency). The parametric four-photon interaction occurs under collinear non-phase-matched conditions and under longitudinally phase-matched, transversally non-phase-matched (erenkov-like) conditions. Subsequent interaction processes are pump-pulse-nondegenerate four-photon interaction of the type ₁ + _{R 3} + ₄, coherent antiStokes Raman scattering (CARS, ₁ + ₁ – _{4 3}), inverse Raman scattering ( _A + ₁ + ), and cascading light up-conversion of the type ₁ + _(i) – _{R (i+1)}.     

Some exact models for nonspherical collapse.I

Evolution of incoherent matter distributions with cylindrical, pseudoplanar, and toroidal symmetries is considered. The system is described in terms of the scale factora (R, T) and the anisotropy factor (R, T) of the (x², x³ surfaces. A number of exact solutions is obtained under the assumptions=(a), =(R), and=(T) and their physical properties are breifly discussed. In particular, the solution with=(T) is noncollapsing and describes a matter distribution with unchanging density.     

Reflection of millimeter-range electromagnetic radiation from slightly doped gallium arsenide

The reflection coefficient R and the phase angle of the reflected electromagnetic wave are calculated with an account of various scattering mechanisms (scattering by ionized impurity and by optical phonons) for wavelengths in the 2-mm range at room temperature. Simplified semiclassical equations for the complex reflection coefficient R* are shown to be valid. The equations are used to calculate R and for n-type GaAs as functions of the dimensionless frequencies y = /p and p. The experimental values of R and for n-type GaAs single crystals at 2.2 mm agree with the theoretical values, within the experimental error. The concentrations and mobilities determined from the experimental data agree well with the results of Hall measurements.Translated from Izvestiya VUZ. Fizika, No. 7, pp. 7–11, July, 1970.     

The Debye-Waller factor and the diffusion process for hydrogen in Nb,Ta, and V single crystals investigated by neutron spectroscopy

Quasielastic scattering of slow neutrons on hydrogen diffusing in the-phase of NbH_0.02, TaH_0.13 and VH_0.07 single crystals was investigated in a wide range of temperatures and scattering vectorsQ (0.5Q2.5 Å^–1). The incoherent scattering lawS _d (Q,) for four different diffusion models was consistently compared with the measured lineshapes. At elevated temperatures one had to introduce correlated jumps to describe the experimental data, whereas at room temperature a model with jumps between adjacent sites is sufficient. The integrated quasielastic intensityI(Q) obtained from the fit ofS _d (Q,) with the measured spectra follows an isotropic Debye-Waller factor with mean square amplitudes u ²=0.02–0.04 Ų for H in Ta (20°C–500°C), and u ²=0.03–0.04 Ų for H in Nb (20°C–300°C). For H in V,I(Q) obtained from the analysis of the quasielastic scattering deviates from a normal Debye-Waller factor behaviour. This effect is assumed to be due to the flight process between the interstitial sites. On the other hand, a normal Debye-Waller factor was obtained from theQ-dependence of the inelastic scattering of the band modes, with values of u ²=0.02–0.04 Ų (135°C–500°C). The observed values of u ² were compared with theoretical calculations.     

Muon catalyzed fusion: old and new aspects of energy production

Muon catalyzed fusion of deuterium and tritium (CF) yields the same energy gain per reaction as fusion with magnetic or inertial confinement (17.6 MeV). The crucial points of Cf are, however, very different, namely (a) the energy costW ₍₎ for production of one ^– and (b) the numbern of reactions a single muon can catalyze on the average. (b) is ultimately limited by theeffective sticking probability _f :n1/ _f. With standard methods one hasW ₍₎5 GeV, _f=0.5%. Hence a standard CF reactor can never reach a net energy gain. To solve this problem, ways discussed since about a decade are to increase the efficiency by both (i) energy multiplication using a fissionable blanket and (ii) breeding. A new way to increase the safety of fission devices mostly due to Yu. Petrov is outlined. On the other hand there is a hope to lowerW ₍₎ slightly and _f drastically, the latter by artificial reactivation. New theoretical results for beam cooling in an omegatron type driven integrated CF reactor, important forW ₍₎ and, in particular, _f, is presented.     

Proton spin-lattice relaxation times in ytterbium hydrides

The measurements of the proton (NMR) spinlattice relaxation times have been made in a series of ytterbium hydrides, YbH _x . Results are reported forx=1.80, 1.95, 2.00 and 2.62 and temperatures 4.2T297K. In the orthorhombic phase (1.80x2.00), the spin-lattice relaxation times are dominated by the hyperfine interaction of protons with conduction electrons and the spin diffusion mechanism. In the cubic phase (x=2.62), the relaxation times are five orders of magnitude shorter than in the orthorhombic one. This is interpreted in terms of the proton coupling with the Yb³⁺ ion spin fluctuations.     

Derivation and solution of a low-friction Fokker-Planck equation for a bound Brownian particle

The low-friction region of an anharmonically bound Brownian particle is examined using systematic elimination procedures. We obtain an asymptotic expression for the spectrum of the Fokker-Planck operator. Asymptotic means both small anharmonicities and small friction constants compared to the oscillatory frequency . We conclude that Kramers' low-friction equation is generally valid only for 0<0.01 and has to be modified for 0.01 by including phase-dependent terms. From these the nonlinear part of the force field in connection with a finite temperature is shown to shorten the correlation time of the equilibrium velocity autocorrelation function and to renormalize the frequency of the corresponding spectral density.     

Some exact models for nonspherical collapse. III

The gravitational nonradiative collapse of dust configurations in the presence of electromagnetic field is analyzed in terms of exact dynamical solutions for a wide range of spacetime symmetries: cylindrical, pseudoplanar, toroidal, and also spherical, planar, and pseudospherical [when the anisotropy factor of the (x ²,x ³) surfaces,(R, T), is replaced by a massless scalar field]. The condition that the collapse is nonradiative leaves three possibilities for the coordinate dependence of(R,T) (i)=(a),a (R, T) being the scale factor of the (x ²,x ³) surfaces, (ii)=(T), and (iii)=(R). Almost all (in the meaning indicated in the text) solutions for charged dust with=(a) and for dust in the external electromagnetic field with=(T) and=(R) have been obtained and discussed. A wideranging discussion concerning the topics of papers I–III is given. Special attention is paid to the question of horizon existence and formation and also the perspective of extension of the techniques developed onto the more realistic case of axial symmetry.     

Oxygen content of superconducting Ba2YCu3O6.5+x

Single-phase non-stoichiometric Ba₂YCu₃O_6.5+x with –0.248x0.300 can be obtained by annealing prereacted samples at 0.01–1 bar oxygen partial pressure. Samples withx=–0.248 are semiconducting, samples at 0.239x0.300 are metallic withT _c increasing from 92.2 to 94.0 K for annealing in 0.02–1 bar O₂.     

Flow of an elastico-viscous fluid past an oscillating plate

An exact solution for the flow of an elastico-viscous fluid (Walters' liquid B') due to an oscillating infinite plate has been derived. It has been observed that forgwt=0, ( — frequency,t — time) the flow near the plate may become unstable with increasing whereas fort>0, the velocity increases with increasing. The shearing stress decreases with increasing.I wish to thank the referee for his useful comments which led to the improvement of this paper.     

57Fe Mössbauer investigations in the series Fe4−2xRuxSix(1.0≦x≦1.7)

⁵⁷Fe Mössbauer and magnetization studies on a new series Fe_4–2xRu_xSi_x (1.0x1.7) are reported. The system is seen to transform from a collinear ferromagnet for x1.2 to a cluster spin glass for x>=1.54 In the intermediate region the magnetic behaviour of the system, as probed by the Mössbauer effect, is dominated by the presence of clusters and their dynamics. The alloys have large ordering temperatures ( 750 K) throughout the series except for x>1.54 where they drop sharply. The moment values, in contrast, fall sharply from 4.8_B at x=1 to 0.5_B at x=1.6C. The average value of the HF at⁵⁷Fe measured at 15 K does not change significantly throughout the series.