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.

     

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.     

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.     

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.

     

On continuity of Bowen-Ruelle-Sinai measures in families of one dimensional maps

Let us consider a family of mapsQ _a (x)=ax(1?x) from the unit interval [0,1] to itself, wherea∈[0,4] is the parameter. We show that, for any β<2, there exists a subsetE?4 in [0,4] with the properties

1. Leb([4??,4]?E) < ?^β for sufficiently small ?>0,
2. Q _a admits an absolutely continuous BRS measure µ_a whena∈E, and
3. µ_a converges to the measure µ₄ asa tends to 4 on the setE. Also we give some generalization of this results.

     

Linear spin-zero quantum fields in external gravitational and scalar fields

We give mathematically rigorous results on the quantization of the covariant Klein Gordon field with an external stationary scalar interaction in a stationary curved space-time. We show how, following Segal, Weinless etc., the problem reduces to finding a “one particle structure” for the corresponding classical system. Our main result is an existence theorem for such a one-particle structure for a precisely specified class of stationary space-times. Byproducts of our approach are:

1. A discussion of when a given “equal-time” surface in a given stationary space-time is Cauchy.
2. A modification and extension of the methods of Chernoff [3] for proving the essential self-adjointness of certain partial differential operators.

     

Ambiguities in theη-nucleon scattering length determination

The positive sign of theη-nucleon scattering lengthb _ηN was predicted in [1] assuming the resonance mechanism for theπ ^?p → ηn reaction. We demonstrate that

1. the assumption about thet-channel mechanism of the reaction leads tob _ηN < 0 and
2. the experimental data on theη production cross section are equally compatible with both resonance andt-channel mechanisms.

     

The Mott Anderson metal insulator transition in n orbital models

The interplay of Coulomb interactions and disorder is formulated on the basis of local gauge invariant models withn orbitals per site. Universality classes of correlation-influenced metal insulator transitions are examined from the conducting region of an approximately semi-elliptical band. The microscopic 1/n expansion is brought into direct correspondence with the 1/(k _F ?) expansion of Altshuler et al. Based on1. the assumption that theO(1/n)-expansion can be exponentiated and2. on the renormalization group β-function for finite length scaling, critical exponents are derived in leading order ofd-2 (d is dimensionality). The density of states-at-E _F as the order parameter vanishes at the critical pointE _c like \(\left| {E_F - E_c } \right|^{\beta _{MA} } \) with \(\beta _{MA} = \frac{1}{{4(d - 2)}}\) for the interacting real matrix (orthogonal) ensemble and \(\beta _{MA} = \frac{1}{{2(d - 2)}}\) for the unitary ensemble. If the bare Coulomb interactionU _b (q)∝q ^1-d is replaced by a general long range interactionV _b (q)∝q ^?x withx>0 ford=2, β_MA depends on the “interaction range exponent”x like β_MA(x) = xβ_MA(1). Also in leading order ofd?2, the conductivity exponent ist=1 for both models with or without time reversal invariance respectively. This implies a correlation-induced crossover fromt=1/2 for unitary Anderson localization (broken time reversal invariance) tot=1 at the Mott Anderson transition.     

Continuous measures in one dimension

Families of unimodal maps satisfying

1. T _λ: [?1,1]?[?1,1] withT(±1)=?1 and |T _λ ^′ (1)|>1.
2. T _λ(x) isC ² inx ² and λ, and symmetric inx.
3. T ₀(0)=0,T ₁(0)=1 with \(\frac{d}{{d\lambda }}\) T _λ(0)>0

are considered. The results of Guckenheimer (1982) are extended to show that there is a positive measure of λ for whichT _λ has a finite absolutely continuous invariant measure. The appendix contains general theorems for the existence of such measures for some markov maps of the interval.     

Lifshitz-point behaviour of ferromagnetic superconductors

The critical behaviour of the electromagnetically coupled superconductor magnet system is investigated by means of a generalized mean field theory and a renormalization group analysis. We show that in the presence of a genuine anisotropy in systems with an additional pressure-like parameter (like concentration in pseudo-ternary ferromagnetic superconductors (FMS), e.g. Er_1?x Ho _x Rh₄B₄) the indirect coupling between superconducting and magnetic order parameters (i.e. gauge coupling) can lead to a peculiar kind of critical behaviour characterized by Lifshitz points (LP). These points (quite generally) occur as merging points of three phases: a (magnetically) disordered phase, a homogeneously ordered phase and a modulated phase. In FMS the latter phase may result from exchange screening by supercurrents. This unusual critical behaviour is found in two varieties:

1. a regular LP which may occur on the lower transition line of a reentrant FMS
2. a similar but slightly different critical point which we term modified Lifshitz point (MLP), and which is to be expected at the merging point of the upper and lower superconducting transition lines with the magnetic order disorder transition lines in the (x, T) phase diagrams of FMS's.

     

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.     

On the initial stage of spinodal decomposition

A consistent theory describing the initial stage of spinodal decomposition of a two-component system is proposed. It is shown that the structure factor S(q, t) has two maxima as a function of wavenumber at this stage. The main maximum point q₊ varies with time, first moving from q_saddle to q_m (given by expressions (22) and (12), respectively) and then back after the turning point in time given by (26) is passed. The other maximum point is localized at q ≈ 0, and the corresponding peak amplitude is virtually independent of time. The characteristics of the main maximum are sensitive to the existence of the “zero” peak. Available experimental observations support the predictions of the theory.     

Texture in NdFeB magnets analysed on the basis of the determination of Nd2Fe14B single crystals easy growth axis

We have shown by X-ray analysis and magnetic measurements, that the easy growth axis of Nd₂Fe₁₄B crystals corresponds to the “a” axis of the tetragonal structure while the easy magnetization axis is the “c” axis at temperatures above 135K. This correlation allows to understand some interesting features in NdFeB magnets:

• &#x02022;-anisotropic contraction during sintering in magnets obtained by classical powder metallurgy,
• &#x02022;-orientation mechanism during hot pressing (“die upset”) of magnets based on melt spun ribons.

     

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.

     

Quantum spin chains: Simple models with complex dynamics

The present study highlights some of the complexities observed in the dynamical properties of one-dimensional quantum spin systems. Exact results for zero-temperature dynamic correlation functions are presented for two contrasting situations:

1. a system with a fully ordered ferromagnetic ground state;
2. a system at aT _c=0 critical point.

For both situations it is found that the exact results are considerably more complex than has been anticipated on the basis of approximate approaches which are considered to be appropriate and reliable for such situations. A still higher degree of complexity is expected for the dynamics of quantum spin systems which are nonintegrable. The paper concludes with some observations concerning nonintegrability effects and quantum chaos in spin systems.     

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, $$\phi _\alpha (T) = U_a TU_a *.$$ .     

Jump discontinuities of semilinear,strictly hyperbolic systems in two variables: Creation and propagation

The creation and propagation of jump discontinuities in the solutions of semilinear strictly hyperbolic systems is studied in the case where the initial data has a discrete set, {x _i } _i ⁼¹ⁿ , of jump discontinuities. LetS be the smallest closed set which satisfies:

1. S is a union of forward characteristics.
2. S contains all the forward characteristics from the points {x _i } _i ⁼¹ⁿ .
3. if two forward characteristics inS intersect, then all forward characteristics from the point of intersection lie inS.

We prove that the singular support of the solution lies inS. We derive a sum law which gives a lower bound on the smoothness of the solution across forward characteristics from an intersection point. We prove a sufficient condition which guarantees that in many cases the lower bound is also an upper bound.     

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.

     

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.