Spatial representation of groups of automorphisms of von Neumann algebras with properly infinite commutant

Theorem. Let a topological groupG be represented (a→φ _a ) by *-automorphisms of a von Neumann algebraR acting on a separable Hilbert spaceH. Suppose that

1. G is locally compact and separable,
2. R′ is properly infinite,
3. for anyT∈R,x,y∈H the function

$$a \to \left\langle {\phi _a (T)x,y} \right\rangle _H $$ is measurable onG. Then there exists a strongly continuous unitary representation ofG onH,a→U _a , such that forT∈R,a∈G, $$\phi _\alpha (T) = U_a TU_a *.$$ .     

Dynamical enhanced electron emission and discharges at contaminated surfaces

Broad-area electrodes show electron emission already at electric field strengthsF≈10⁷ V/m. This enhanced field emission (EFE) occurs only for contaminated surfaces. EFE is accompanied by photon emission and gas desorption yielding finally discharges. EFE is caused by dust and contaminants initiating the following effects:

an electron is stochastically emitted in a trigger zone

the electron gains energyΔE?eΔxF ^*

which excites electronic states

which relax by the emission of electrons, photons, and atoms

where the positive charges left behind enhanceF ^*=βF (β?1) initiating so an electron avalanche, i.e., a high conductivity channel. Because of charge migration and neutralization, this avalanche has a life time. This pulsating EFE is accompanied by light emission and gas desorption yielding finally a gas cloud and a discharge.

The pulsating, self-sustained EFE has the same root as:

the enhanced secondary emission found first by Malter

the conductivity switching exhibited by thin (≈ 1 μm) layers of semiconductors or insulators

the normal cathode fall and

the firing-wave instability in neurodynamics.

     

Absence of singular continuous spectrum for certain self-adjoint operators

We give a sufficient condition for a self-adjoint operator to have the following properties in a neighborhood of a pointE of its spectrum:

1. its point spectrum is finite;
2. its singular continuous spectrum is empty;
3. its resolvent satisfies a class of a priori estimates.

     

Quasi-particles at finite temperatures

We study the consequences of the KMS-condition on the properties of quasi-particles, assuming their existence. We establish

1. If the correlation functions decay sufficiently, we can create them by quasi-free field operators.
2. The outgoing and incoming quasi-free fields coincide, there is no scattering.
3. There are may age-operatorsT conjugate toH. For special forms of the dispersion law ε(k) of the quasi-particles there is aT commuting with the number of quasi-particles and its time-monotonicity describes how the quasi-particles travel to infinity.

     

Magnetostriction measurement by means of strain modulated ferromagnetic resonance (SMFMR)

A novel method for measuring magnetostriction constants is presented. A strain, periodic in time, applied to the sample, causes a modulation of the ferromagnetic resonance line position. The height of the signal obtained after phase-sensitive detection is proportional to the strain modulation depth. The appropriate magnetostriction constant λ is obtained by comparing the height of the SMFMR signal with that of the FMR line, as recorded by means of magnetic field modulation. Features of the new technique are:

1. high sensitivity: λ_min? 10_?9 forM=100 Oe and linewidth ΔH _d=1 Oe;
2. λ's belonging to distinct precession modes are separately determined;
3. applicable to thin layers for which strain gauge techniques cannot be used;
4. wide temperature range: 1.2 K<T<300 K;
5. uniform stress.

An illustrative example (YIG layer on GGG substrate) is given.     

Magnetic field and doppler velocity correlation in quiescent solar prominences

Analyzing statistically the magnetic and Doppler velocity data for 85 quiescent prominences observed in 1983–1987 by Nikolsky's magnetograph, we came to the following preliminary conclusions:

The average longitudinal magnetic field of the prominence determines the dynamic velocity of the latter: the stronger magnetic fields correspond to the higher Doppler velocities.

A longitudinal magnetic field less than 25 G allows the material to move with arbitrary velocity within the limits of several kilometers per second. A magnetic field higher than 25 G suppresses such movements.

The horizontal length of the flux tube exceeds its vertical part by 1.5 orders of magnitude (the upper limit).

There is an angle of 10°between the horizontal component of the velocity vector in quiescent prominences and the long axis of the filament.

The maximum velocity in quiescent prominences is about 7 km/s.

     

Small-angle X-ray scattering on spinodal,nucleotic or coarsening processes in two-phase systems containing spherical,fibrillar or lamellar inhomogeneities

We study the effects of some of the most important and typical structural changes in two-phase systems on selected structural parameters obtained from small-angle x-ray scattering (SAXS) measurements. To limit the present study, it was assumed that the Phase, 1, embedded in the matrix

1. is monodispersed and homogeneous,
2. possesses one of the three most extreme shapes (spherical, fibrillar or lamellar) and
3. changes its behaviour

1. through type change (spinodal or nucleotic or coarsening), without changing the shape,
2. through a change of the shape only, or
3. through a) (type change) and b) (shape change) simultaneously.

To find the type of change for three basically different shapes of Phase 1 and to calculate its intensity (amount of the change) the following three SAXS parameters must be compared before and after the treatment of the system:

1. chord lengthl ₁ (and/or radius of gyrationR),
2. volume partw ₁ of the Phase 1, and
3. relative inner surfaceS _v of the system.

It is shown by this comparison that by the pure type change in the case of

1. spinodal change, all three SAXRS parameters are increasing or decreasing simultaneously and proportional to a power of the intensity of the change,
2. nucleotic change,l ₁ (and/orR) is unchanged, the other two (w ₁ andS _v ) are increasing or decreasing simultaneously and directly proportional to the intensity,
3. coarsening change,w ₁ is unchanged and anincreasing ofl ₁ is always accompanied by adecreasing ofS _v and vice versa.

In addition to this type change, the cases of mere changes of the shape (“shape change”) and finally of simultaneous type and/or shape change are studied. For the case of pure shape change the alteration of the dimensions (chord lengthl ₁ and/or radius of gyrationR) must be followed. The limitations of the analyses of the simultaneous type and/or shape change are discussed in detail.     

Bestimmung der wahren Halbwertsbreite derMζ-Linien der Elemente 38 Sr bis 47 Ag

1. The intensity distribution of theMζ-lines (40<λ<110Å) was measured using a 2m concave grating spectrometer.
2. The instrumental profile of the spectrometer could be determined by solving a modified folding equation by the method of successive approximations. For the spectrometer used we found that the instrumental response was a Gaußian, and that its width is independant of wavelength.
3. A graphical method is applied by which the natural width of theMζ-lines can be determined if the instrumenta profile is a Gaußian. Widths for Sr, Ru, Rh and Ag are presented for the first time.

     

Bounds on the number of eigenvalues of the Schrödinger operator

Inequalities on eigenvalues of the Schrödinger operator are re-examined in the case of spherically symmetric potentials. In particular, we obtain:

1. A connection between the moments of order (n ? 1)/2 of the eigenvalues of a one-dimensional problem and the total number of bound statesN _n, inn space dimensions;
2. optimal bounds on the total number of bound states below a given energy in one dimension;
3. alower bound onN ₂;
4. a self-contained proof of the inequality for α ≧ 0,n ≧ 3, leading to the optimalC ₀₄,C ₃;
5. solutions of non-linear variation equations which lead, forn ≧ 7, to counter examples to the conjecture thatC _0n is given either by the one-bound state case or by the classic limit; at the same time a conjecture on the nodal structure of the wave functions is disproved.

     

On the existence of crossing symmetric and unitary scattering amplitudes with Regge poles

We give a complete proof of the existence of scattering amplitudesA(s,t,u) with the following properties

1. the amplitudes are total symmetric ins,t, andu.
2. they satisfy elastic unitarity for 4≦s≦16, and
3. they develop resonances forl≧2 on a bounded Regge trajectory which dominates the asymptotics for large energies.

     

Strong cluster properties for classical systems with finite range interaction

In a previous paper, “strong” decrease properties of the truncated correlation functions, taking into account the separation of all particles with respect to each other, have been presented and discussed. In this paper, we prove these properties for finite range interactions in various situations, in particular

1. at low activity for lattice and continuous systems,
2. at arbitrary activity and high temperature for lattice systems,
3. at ReH≠0, β arbitrary and atH=0 for appropriate temperatures in the case of ferromagnets.

We also give some general results, in particular an equivalence, on the links between analyticity and strong cluster properties of the truncated correlation functions.     

Unbounded derivations ofC*-algebras II

It is demonstrated that a closed symmetric derivation δ of aC?-algebra \(\mathfrak{A}\) generates a strongly continuous one-parameter group of automorphisms of aC?-algebra \(\mathfrak{A}\) if and only if, it satisfies one of the following three conditions

1. (αδ+1)(D(δ))= \(\mathfrak{A}\) , α∈?\{0}.
2. δ possesses a dense set of analytic elements.
3. δ possesses a dense set of geometric elements.

Together with one of the following two conditions

1. ∥(αδ+1)(A)∥≧∥A∥, α∈IR,A∈D(δ).
2. If α∈IR andA∈D(δ) then (αδ+1)(A)≧0 impliesA≧0.

Other characterizations are given in terms of invariant states and the invariance ofD(δ) under the square root operation of positive elements.     

Testing general relativity: Progress,problems, and prospects

Recent results from radar and radio gravity experiments are:

1. Retardation of radar signals: 1.02 +?0.05 (planetary radar), 1.00 +? 0.04 (spacecraft);
2. Deflection of radio waves: 0.99 +? 0.12 (short baseline interferometry), +0.15 1.04 (short baseline interferometry), ?0.10. 0.90 +? 0.05 (short baseline interferometry);
3. Relativistic perihelion advance of Mercury: 0.99 +? 0.03 (planetary radar), 1.00 +? 0.01 (radar plus optical);
4. Time variation of the gravitational constant: (G/G) < 4 ×10^?10/yr (planetary radar). The first three results are expressed as fractions of the corresponding effects predicted by general relativity. In terms of the Eddington-Robertson parameters, the first two are approximately equal to (1+γ)/2 and the third to (2 + 2γ-β)/3. The third result depends on the assumption that the solar gravitational quadrupole moment vanishes; its effects cannot be separated usefully from those of general relativity with the present data set. The uncertainties are as given by the individual experimenters; in some cases they represent formal standard errors, in others an allowance for possible systematic errors is included.

     

The moment of inertia at the saddle point of low energy fission of even-even nuclei

We use the molecular model of low energy fission, which describes the nucleus by two interacting fragments, to calculate the moment of inertia for U²³⁶ in the cranking approximation including BCS theory. We show that the moment of inertia at the saddle point:

1. depends almost linearly on the fragment distance.
2. is influenced only very weakly by the pairing constant and by the fragment deformations.
3. shows, as a function of the distribution of mass between the two fragments (A ₁ ,A ₂ ), a minimum near the magic configurationA ₁=132,Z ₁=50 and depends in this mass region strongly on the term structure near the Fermi energy.
4. is approximately that of a rigid body.

     

Probing of the Higgs-fermion coupling atγγ-colliders

Three possibilities to observe the Higgs-top interation at future γγ-colliders are discussed:

1. associated Higgs production via the \(\gamma \gamma \to t\bar tH\) reaction,
2. Higgs obliged radiative correction to the \(\gamma \gamma \to t\bar t\) channel,
3. Higgs resonance production via γγ→H→ZZ.

The results obtained show windows of the Higgs mass where the Yukawa interaction of the Higgs with the top quark can be studied at γγ-colliders.     

The possibility of using a semiconductor thermal probe to investigate the power flow distribution in waveguides

Conclusions

1. The temperature profile of an absorbing film for a given microwave power flux distribution has been considered.
2. The conditions under which agreement is found between the temperature relief and the flux distribution has been clarified.
3. An experimental investigation has been carried out of the temperature profile in a matched film for the TE₁₀ mode.
4. The possibility of using a semiconductor thermal probe to investigate the microwave power flux distribution has been demonstrated.

     

Some current challenges in space plasma physics

An overview of the subject of space plasma physics is attempted. This encompasses a discussion of various ground-based and satellite studies of the near-Earth space environment, with its marked temporal and spatial variations, theoretical investigations, and numerical simulations. The important distinction is drawn between passive studies of elements of the natural system, aimed at the difficult task of understanding the self-consistent evolution of some natural processes, and active investigations, which either probe or modify natural processes, in order to improve understanding of cause and effect (e.g. of energy transformations) within the system. Linear, nonlinear, and chaotic processes can occur. Attention is paid to:

1. Energetic events on the Sun,
2. Large-scale features of the interplanetary medium, both observed directly and via scintillations of distant radio stars,
3. The magnetosphere in general, and the aurora in particular,
4. Wave-particle interactions, especially cyclotron resonance phenomena, and
5. The ionosphere, particularly when heated by powerful radio waves.

The approach adopted is to place these special topics in the context of the Solar Terrestrial Energy Program (STEP) of ICSU's SCOSTEP. Finally, mention is made of some benefits to humanity of studies of space plasma physics phenomena.     

The process e + e − → bb̅W + W − at the next linear collider in the Minimal Supersymmetric Standard Model

The complete matrix element for e ⁺ e^? → bb?W⁺ W^? is computed at tree-level within the Minimal Supersymmetric Standard Model. Rates of interest to phenomenological analyses at the Next Linear Collider are given. In particular, we study:

• ? tt? production and decay tt? →(bW ⁺)(b?W ^?)
• ? ZH production followed by Z → bb? and H → W ⁺ W^?
• ? AH production followed by A→ bb? and H → W ⁺ W^?
• ? hW ⁺ W^? production followed by h→ bb?.

Top and Higgs finite width effects are included, as well as all those of the irreducible backgrounds.     

Nanoparticle and Nanoporous Carbon Adsorbents for Removal of Trace Organic Contaminants from Water

Removal of a wide range of trace organic contaminants from water to concentrations below USEPA Maximum Contaminant Levels (MCL) remains an important goal for the water industry. Design of advanced carbon based adsorption systems represents a unique approach to solving these problems. A number of successful examples are cited in this paper and are briefly summarized in the following section.

1. Removal of foulants such as humic acid using nanoparticle carbon blacks and chemically activated nanoporous fibers;
2. Removal of trace organic contaminants such as benzene, toluene, ethylbenzene and p-xylene (BTEX) to levels below USEPA MCL using nanoporous carbon fibers;
3. Removal of trace chemical warfare simulants such as diisopropylmethyl phosponate and chloroethylethylsulfide using enlarged nanoporous carbon fibers;
4. Removal of trace chlorinated solvents such as trichloroethylene (TCE) and chloroform using tailored nanoporous carbon fibers;
5. Removal of the trace herbicide, atrazine, to below USEPA MCL level using nanoporous chemically activated fibers.

In this paper the enormous improvement of the above systems over commercially available products in static and dynamic adsorption evaluation is described.     

Correlation inequalities and uniqueness of the equilibrium state for the plane rotator ferromagnetic model

We derive new inequalities for the plane rotator ferromagnetic model and use them to obtain the following results:

1. If the model is isotropic, the derivability of the free energy as function of the magnetic fieldh implies the existence of a unique translation invariant Gibbs state and if furthermoreh=0 all Gibbs states are invariant by rotation of the spins.
2. If the model is anisotropic the above assertion holds forh non-zero.
3. If the model is anisotropic then there are at most two extremal translation invariant Gibbs states for almost all values of the anisotropy parameter.