On the sign of cos θ at the branch points of a partial wave amplitude in thes-plane

The sign of the cosine of the scattering angle, cos, at the branch points of a relativistic two-body partial wave amplitude with arbitrary masses in the complexs-plane is determined. The results yield that as to the tops-sheet, (i) the sign of cos is the same at the complex conjugated branch points which lie off the reals-axis, and (ii) cos changes sign at the (direct channel) thresholds. The difference between the elastic and inelastic cases is emphasized. It is pointed out that in certain physical energy ranges, for some collisions (e.g. + N + N), the directions near the backward direction can be considered as the most important ones, while for several other collisions (e.g. + N + N) the directions into the forward hemisphere have the strongest influence.The author would like to thank Professor G. Höhler for his kind hospitality at the Institut für theoretische Kernphysik, University of Karlsruhe. He is grateful to him and to the members of that Institute for valuable discussions. Correspondence with Dr. Jens Lyng Petersen, which gave rise to the present investigation, is also acknowledged.     

Three-photon excitation ofp-quaterphenyl with a mode-locked femtosecond Ti:sapphire laser

We observed emission fromp-quaterphenyl (p-QT) at 360 nm when exposed to the focused light from a femtosecond (fs) Ti:sapphire laser at 850 nm. This wavelength is too long to allow two-photon excitation of p-QT. The emission intensity of p-QT was found to depend on the cube of the laser power at 850 nm, suggesting that excitation occurs due to a three-photon process. The same emission spectrum and single exponential decay times were observed for three-photon excitation at 850 nm as for two-photon excitation at 586 nm and for one-photon excitation at 283 nm. The same rotational correlation times were observed for one-, two-, and three-photon excitation, but higher time-zero anisotropies were observed for two- and three-photon excitation. The steady-state anisotropies for one-, two-, and three-photon excitation are precisely consistent with cos², cos⁴, and cos⁶ excitation photoselection, where is the angle between the electric field of the incident light and the absorption dipole. These experiments were performed with 3×10^–5 M solutions of p-QT. Use of such low concentrations was possible because p-QT displays one of the highest apparent cross sections we have observed to date for three-photon excitation. The spatial distribution of the excited fluorescence was less for three-photon excitation than for two-photon excitation of Coumarin 102 at the same 850-nm excitation wavelength. The high cross section, photostability, and clear cos⁶ photoselection of p-QT make it an ideal three-photon standard for spectroscopy and microscopy.     

A Far IR Study of NbN in the Normal and Superconductive State

A thin film of NbN (thickness t = 300 Å), has been deposited on an MgO and a Si wafer. Both samples have been studied by transmission from 10 or 20 to 120 cm^–1, and have exhibited one maximum of transmission at a given frequency like the classical superconductors as Pb, Sn or Hg in the superconductive state. From the Far IR experimental data, the characteristic temperature _c, and the gap frequency (_gap () = 2 (), () being the energy gap) are immediately obtained (for instance for the NbN / MgO sample, _c = 15.5 K; _g (5 K) = 39.7 cm^–1), and it is seen that as expected from the BCS theory for a weak coupling. To fit the data we had to adjust only two additionnal parameters: collision and plasma frequency, _c () and _p (including all carriers). At = 5 K, thebest fit for the NbN / MgO sample is obtained with _c = 371 cm^–1 and _p = 12,600cm^–1.     

Third-order processes and their relation to structural symmetry

We have studied the various nonlinear optical processes that can be described by a fourth-rank ⁽³⁾-tensor: signals of frequency in degenerate four-wave mixing (DFWM), harmonics of frequency 2 and 3, and ⁽³⁾-type difference-frequency generation (DFG) with observation of anti-Stokes emission of a signal of frequency 2₁ — ₂. Structural information in terms of normalized anisotropies is derived in all frequency domains by analysis of the elements of the respective orientation-dependent susceptibility tensor. A novel laser-based technique for the remote orientation analysis of crystalline structures is introduced.     

Symplectic Structures on Moduli Spaces of Parabolic Higgs Bundles and Hilbert Scheme

Parabolic triples of the form (E_*,,) are considered, where (E_*,) is a parabolic Higgs bundle on a given compact Riemann surface X with parabolic structure on a fixed divisor S, and is a nonzero section of the underlying vector bundle. Sending such a triple to the Higgs bundle (E_*,) a map from the moduli space of stable parabolic triples to the moduli space of stable parabolic Higgs bundles is obtained. The pull back, by this map, of the symplectic form on the moduli space of stable parabolic Higgs bundles will be denoted by d. On the other hand, there is a map from the moduli space of stable parabolic triples to a Hilbert scheme Hilb(Z), where Z denotes the total space of the line bundle K_{X X}(S), that sends a triple (E_*,,) to the divisor defined by the section on the spectral curve corresponding to the parabolic Higgs bundle (E_*,). Using this map and a meromorphic one–form on Hilb(Z), a natural two–form on the moduli space of stable parabolic triples is constructed. It is shown here that this form coincides with the above mentioned form d.     

The Anisotropic Free Energy of the Solid-Liquid Phase Boundary in Al

We have performed large-scale molecular dynamics simulations of solid-liquid interfaces in aluminum, in order to calculate their interfacial stiffness and free energy. The anisotropy of these properties, though small, is key for determining the steady-state solutions for solidification in three dimensions. We find that the interfacial free energy, (), can be well represented by the form () = ₀(1 + cos 4, where measures the angle relative to the [100] interface, rotating about a [001] direction. We find values of ₀ = 120 ± 6 mJ/m² and = 1.3 ± 0.4%, in agreement with previous estimates and current experimental results.     

The determination of the parameters of “spherical” motion in a kerr field

The problem of the existence of class M geodesic motions on the surface r=const, all of whose mechanical parameters in the specified Kerr field are determined only from stability conditions, is posed and investigated. A system of equations which determines this class is derived and solved. It is shown that in the general case this motion does not cover the entire surface r=const and is restricted by the condition ₀ }- ₀. Simple algebraic expressions are found for all the parameters of these configurations-energy, momentum, radius, and the angle ₀-as functions of the specific angular momentuma of the Kerr field. It is shown that these motions can exist only in Kerr fields with a value of the parametera larger or equal to r_g/2. In a Kerr field with a fixed value ofa there exist only two configurations with the indicated properties. In conclusion, the properties of the M-solutions associated with the appearance of configurations with negative energies and negativeness of g₀₀ within the limits of some configurations and values ofa larger than r_g/2 are discussed. It is noted that the negative values of the energy occur only in those configurations within whose limits g₀₀ < 0. It is also pointed out that the Kerr field is free of pathological properties associated with the breakdown of causality whena > r_g/2 if one does not made the assumption, unnecessary within the framework of the problem under discussion, that the sources of the Kerr field are in the region r=0.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 17–25, May, 1979.The authors express their gratitude to A. A. Grib for useful discussions.     

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     

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.     

Evaluation of positron annihilation angular correlation curves and line profiles of compton scattering in noble metals

Angular correlation curveN () as well as the Compton line profile I() of Cu, Ag, Au and Pt have been calculated by the assumption, that the coincidence counting rate and Compton line shift intensity are proportional to the area of cuts through the body defined by the Fermi surface. Parametrical expression of the Fermi surface were employed and the results were used to fit some measured curves on Cu, Ag and Au.The authors are indebted to Prof. P.Ry and Dr. I.Volf for enabling the work, Dr. A. íek for supplying the experimental data for Au, Ag and Cu and J. Sedláek for assistance by programming of numerical evaluations.     

On the validity of an einstein relation in models of interface dynamics

We consider models of interface dynamics derived from Ising systems with Kac interactions and we prove the validity of the Einstein relation=, where is the proportionality coefficient in the motion by curvature, is the interface mobility, and is the surface tension.     

On the global behaviour of symmetric Skyrmions

It is shown that the chiral angle, (r), of the hedgehog (symmetric) Skyrmions with an arbitrary baryon number, is a strictly decreasing or increasing function. For large values of r>0, (r) is strictly convex or concave. As r, (r) and (r) approach their limit values at the rate Or ^- for any (0,2).     

Anderson localization for the almost Mathieu equation: A nonperturbative proof

We prove that for any diophantine rotation angle and a.e. phase the almost Mathieu operator (H()) _n = _n–1 + _n+1 +cos(2(+n)) _n has pure point spectrum with exponentially decaying eigenfunctions for 15. We also prove the existence of some pure point spectrum for any 5.4.     

One-dimensional harmonic lattice caricature of hydrodynamics

We derive the hydrodynamic (Euler) approximation for the harmonic time evolution of infinite classical oscillator system on one-dimensional lattice ¹ It is known that equilibrium (i.e., time-invariant attractive) states for this model are translationally invariant Gaussian ones, with the mean 0, which satisfy some linear relations involving the interaction quadratic form. The natural parameter characterizing equilibrium states is the spectral density matrix function (SDMF)F(), [– , ). Time evolution of a space profile of local equilibrium parameters is described by a space-time SDMFF(t;x, ) t, xR ¹. The hydrodynamic equation forF(t; x, ) which we derive in this paper means that the normal mode profiles indexed by are moving according to linear laws and are mutually independent. The procedure of deriving the hydrodynamic equation is the following: We fix an initial SDMF profileF(x, ) and a familyP ,>0 of mean 0 states which satisfy the two conditions imposed on the covariance of spins at various lattice points: (a) the covariance at points close to the value ^–1 x in the stateP is approximately described by the SDMFF(x, ); (b) The covariance (on large distances) decreases with distance quickly enough and uniformly in. Given nonzerotR ¹, we consider the states P _–1 ,>0, describing the system at the time moments ^–1 t during its harmonic time evolution. We check that the covariance at lattice points close to ^–1 x in the state P _–1 is approximately described by a SDMFF(t;x, ) and establish the connection betweenF(t; x, ) andF(x,).     

Temporal optics of resonant transmission of gamma rays through57Fe

The development in time of the transmission through⁵⁷Fe of a broad Lorenztian radiation is calculated numerically. Examples are given for=0 and/2, for the magnetic hyperfine case, and for=/2 for pure quadrupole splitting.     

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     

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.     

Is the Cabibbo Angle a Function of the Weinberg Mixing Parameter?

The (u, c) quarks and (d, s) quarks arerequired to have mass matrices of a certainform. To achieve these mass matrices appropriate Lagrangians are assumed. Theu quark is coupled to the standard Higgs scalar _L. Thec quark has a ₅ couplingwith _L and _R, where _R is the Higgs scalar corresponding to theleft-rightmodel. The u quark has no ₅ coupling. Both u,c quarks have a Yukawa couplingwith a Higgs multiplet. Exactly similar Lagrangians are chosen for thed, s qurks.Using these mass matrices, the Cabibbo angle is found to be 13° 11. The ratiom _c/m _s is shown to be approximately 3.1 with the help of the Weinberg mixingparameter. The mixing angles ₂ and ₁ determine the Cabibbo angle. The ratiotan ₂/ tan ₁ is shown to be a function of the Weinberg mixing parameter.     

A relation between a.c. spectrum of ergodic Jacobi matrices and the spectra of periodic approximants

We study ergodic Jacobi matrices onl ²(Z), and prove a general theorem relating their a.c. spectrum to the spectra of periodic Jacobi matrices, that are obtained by cutting finite pieces from the ergodic potential and then repeating them. We apply this theorem to the almost Mathieu operator: (H _{, ,} u)(n)=u(n+1)+u(n–1)+ cos(2n+)u(n), and prove the existence of a.c. spectrum for sufficiently small , all irrational 's, and a.e. . Moreover, for 0<2 and (Lebesgue) a.e. pair , , we prove the explicit equality of measures: |_ac|=||=4 –2.Work partially supported by the US-Israel BSF