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.     

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.     

Periodic Motion of Atoms Near a Charged Wire

We study the classical motion of an atom in the vicinity of an infinite straight wire which carries an oscillating uniform charge. This system has been proposed as a mechanism for trapping cold neutral atoms. The parameters of the problem are the magnitude Q and frequency of oscillation of the charge, the mass M and polarizability of the atom, and the angular momentum L of the atom about the wire. For 0 and 2MQ ² greater than, but close to, L ², we prove that the atom's radial motion is periodic (with period 2/), and that the atom moves in a helical path around the wire. For 2MQ ² L ² we prove that the atom must either collide with the wire or else escape to infinity in the radial direction.     

Averaged electron Green function and CDW pinning in one-dimensional random potential

The averaged retarded electron Green functionG ⁺(,k) in 1d disordered metal is calculated using the Berezinsky diagram technique. Using the Gorkov's theory it is shown, that the substitution of inG ⁺ (,k) by the square of the external frequency atk=0 gives the dependence of Fröhlich conductivity _F(). This dependence describes the impurity pinning of CDW in 1d disordered metals. The good agreement of this dependence with experimental data Zeller et al. about _F() in quasi-1d conductor KCP is found     

Extensible Embeddings of Black-Hole Geometries

Removing a black hole conic singularity by means of Kruskal representation is equivalent to imposing extensibility on the Kasner–Fronsdal local isometric embedding of the corresponding black hole geometry. Allowing for globally non-trivial embeddings, living in Kaluza–Klein-like M ₅ × S ₁ (rather than in standard Minkowski M ₆ ) and parametrized by some wave number k, extensibility can be achieved for apparently forbidden frequencies in the range ₁ (k) ₂ (k). As k 0, _{1, 2} (0) _H (e.g., _H = 1/4M in the Schwarzschild case) such that the Hawking–Gibbons limit is fully recovered. The various Kruskal sheets are then viewed as slices of the Kaluza–Klein background. Euclidean k discreteness, dictated by imaginary time periodicity, is correlated with flux quantization of the underlying embedding gauge field.     

Two-photon resonance degenerate four-wave mixing in a three-level polar molecule (model calculations)

The third-order non-linear susceptibility, ⁽³⁾(; , , –), describing the phase conjugation by degenerate four-wave mixing (DFWM) is calculated for a three-level polar system under a two-photon resonance (TPR) condition. The part of the susceptibility expressed only by the transitional dipole moments and the part resulting from the permanent dipole moments are distinguished. The spectra of ⁽³⁾(; , , –), as well as the DFWM power-reflection and power-transmission spectra near to the TPR, are modelled for polar molecules. The effect of enhanced reflectivity of TPR-DFWM is obtained numerically.     

Instabilities of plasma with intense azimuthal streams and radially dependent density

The flute instabilities of a cold magnetoactive plasma with radially dependent density and strong azimuthal streams of particles (ions) are studied. The effect of non-zero perpendicular temperatureT of the ions on these oscillations is investigated. For systems withT 0, the continuation of drift-cyclotron instability in a strongly inhomogeneous plasma is found. Further, the stability of electron plasma oscillations (² _pe ² cos² ) is investigated.The authors are indebted to V. KopeckS, J. Teichmann and J. Vàclavik for discussions.     

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.     

Classical theory of the interaction between a spinor field and the gravitational field: First-order field equations

The classical theory of the interaction of a neutral spin-1/2 Dirac field and the gravitational field is studied. For the purely gravitational part of the Lagrangian, written in terms of a vierbein and the local connection coefficient _ab , (regarded as independent field variables), the usual first-order form is adopted. For the Dirac part, however, a different choice is made, in which the covariant derivative of is built with the aid of the vierbein instead of with _ab . This still yields a first-order formalism, but one in which _ab is related to the vierbein in the same way as it would be in the absence of. This ensures that the global connection remains symmetric in andv in the presence of. The way in which the vierbein field equation leads to a familiar Einstein equation with a symmetric and conserved stress tensor on its right side is also analyzed.     

830 nm emission in sodium vapor

We demonstrate that the intriguing 830 nm coherent emission, which is observed when sodium vapor is pumped with a high-power pulsed laser tuned near the 3S4D two-photon transition, is due to an axially phase-matched six-wave mixing process. This conclusion is based upon the observation of emission near 584 nm, which is coupled to the 830 nm emission in the six-wave mixing process: ₁+₂=2_L–_4D4P –_4P3D . In addition, we have observed coherent emission near 1.16 m, which is due to an analogous process involving cascade through the 4S (as opposed to the 3D) state. We calculate the wavelengths of all photons involved in these processes using the standard formulas of parametric wave-mixing theory, and show that they can be predicted to within experimental uncertainties. Finally we report observations of significant blue shifts of the 830 nm and 1.16 m emissions in a mixed sodium-potassium vapor. These shifts can be readily understood by considering the effect of the potassium on the frequency-dependent refractive index of the vapor. Due to these results, other recent interpretations of the 830 nm emission as stimulated excimer emission on the Na₂ 1³ _g ⁺ 1³ _u ⁺ band must now be rejected.     

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)}.     

Ultrasound in spin glasses

The change of the sound velocity v(,T) and the damping of sound waves (,T) in spin glasses are calculated in the frame-work of an Ising model with a random distribution of exchange interactions. The calculation is based on linearized equations of motion for the spins and on an improved mean field approximation which includes the Onsager reaction field. Near to the freezing temperatureT _f and at high temperatures v(,T) and (,T) turn out to be approximately proportional to the real and the imaginary parts of the dynamical susceptibility. For the special case of infinite range interactions atT=T _f one has v(, T_f) ( )^1/2 and (, T_f) (/)^1/2 where is the relaxation time of independent spins. However, already slightly aboveT _f the frequency dependence of both quantities becomes rather small for RKKY spin glasses. At high temperatures both, v(,T) and (,T) vary asT ^–1.SFB 125 Aachen-Jülich-Köln     

Positive resonances and the limiting amplitude principle

We define the positive resonance points of self-adjoint operators without using the analytical continuation of corresponding resolvents and show that the limiting amplitude principle for the abstract wave equation does not take place in general, if ² = , where is the disturbing frequency and is the resonance point. The asymptotics of corresponding solutions as t are obtained, which imply the growth of the oscillation amplitude as t , 0<<1, or as ln t, t .     

On Borchers' Theorem

We give a simplified proof of the following important theorem,which is due to Borchers. Let be a von Neumann algebra with cyclic and separating vector and let U(t), t R, be a group with positive generator, which leaves fixed and induces for positive arguments endomorphisms of . The modular group of (, ) acts then as dilatations on this group. Our proof can also be applied to half-sided modular inclusions.     

Ferromagnetic resonance in media with an inhomogeneous saturation magnetization

The method of transition probabilities is used to calculate the line width of ferromagnetic resonance in a medium with an inhomogeneous saturation magnetization. It is shown that in addition to linear (with respect to the Fourier components of the function describing inhomogeneities) terms, the perturbation Hamiltonian must include also quadratic terms. The frequency dependence of the contribution of the porosity to H is fundamentally different from the frequency dependence of the magnetic anisotropy contribution. This anisotropy contribution H_a() decreases on increase in the frequency and has a maximum at = (2/3)_M, whereas the porosity contribution H_p increases on increase in the frequency and vanishes at = (2/3)_M.deceasedTranslated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 12, pp.48–52, December, 1980.     

A Boltzmann map for quantum oscillators

We define a map on the space of quasifree states of the CCR or CAR of more than one harmonic oscillator which increases entropy except at fixed points ofx. The map is the composition of a doubly stochastic map T^* and the quasifree reductionQ. Under mixing conditions onT, iterates of take any initial state to the Gibbs state, provided that the oscillator frequencies are mutually rational. We give an example of a system with three degrees of freedom with energies ₁, ₂, and ₃ mutually irrational, but obeying a relation n₁₁+n₂₂=n₃₃,n _i . The iterated Boltzmann map converges from an initial statep to independent Gibbs states of the three oscillators at betas (inverse temperatures) ₁,₂, ₃ obeying the equation n₁₁₁+n₂₂₂=n₃₃₃. The equilibrium state can be rewritten as a grand canonical state. We show that for two, three, or four fermions we can get the usual rate equations as a special case.     

Some results on electronic two- and one photon raman scattering in CdS

Two photon Raman scattering (TPRS) via virtually excited biexcitons is observed in CdS over a rather large spectral region in a scattering configuration which favours stimulated emission. We observe either a pure longitudinal exciton or-for the first time—a bound exciton (I ₂) as final state particles. Furthermore, the anomaly in the relation between _exc and _R at _exc= E_blex is observed for the first time in a II–VI compound, indicating an energy of the ₁ biexciton level of 5.098 eV in agreement with two photon absorption measurements. With an applied magnetic fieldB, the corresponding shift of the exciton eigenenergies can be observed. For the longitudinal exciton, the diamagnetic shift is 0.35 meV atB=10T forBc in agreement with theoretical predictions. In this configuration also a stimulated one photon spin flip Raman scattering is observed, yielding the well known electronicg-value of 1.78.     

Neutron scattering from spatio-temporal patterns in thermal convection

We have investigated the thermal convection of a nematic liquid crystal in a two-dimensional, vertical slab container with long edgesa (horizontal) andb (vertical). Using a real-time and real-space neutron scattering technique, we find that the frequencies of oscillatory convection is given by a formula whose geometrical part is ² (h ² +k ²/b ²). For the Fourier indices (h,k) we find the selection rule(h+k)=2n withn=1,2 ... The variation of ² with the vertical temperature difference T, as T approaches the convection threshold T _c , is found to be surprisingly well fitted by the two-dimensional, critical Ising index .     

Excited-state absorption and third-order optical nonlinearities in symmetric π-electron organic molecules

Excited-State Absorption (ESA), Two-Photon Absorption (TPA) and the third-order polarizability (;,, – ) have been investigated for a model dichloride derivative of a symmetrically substituted benzylidene analine (SBAC), using a multielectron configuration-interaction procedure. The calculations indicate that SBAC exhibits ESA across the visible region of the spectrum, but that it is not as extensive as for molecules such as the phthalocyanines. The magnitude of the third-order polarizability is dominated by resonance enhancement from a very strongA _g B _u one-photon absorption. The calculated off-resonance value for (;,, – ) suggests that SBAC is a potential candidate for ultrafast switching applications.     

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.