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.     

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.     

Branched polymers in a wedge geometry in three dimensions

We investigate the statistical and dimensional properties of uniform star polymers attached by the branching vertex of degreef in a wedge geometry in three dimensions and described by the wedge angles and. We show that the growth constant is equal to ^f , where is the self-avoiding walk limit. Thef and (, ) dependences of the corresponding critical exponent _f (, ) are studied using Monte Carlo techniques. In the casef=1, our results are compared with existing predictions obtained from series expansion and renormalization group methods. We have also estimated the amplitudes for the mean square radius of gyration and the mean square end-to-end branch length. Our results for the ratio of the mean square radius of gyration of anf-star to that of a linear polymer of the same degree of polymerization attached in a similar wedge, and the analogous ratio for the mean square end-to-end branch length, are consistent with these ratios being lattice-independent quantities.     

On Percolation with Fibers or Layers

We consider site percolation on Z ^d, directed edges going from any sZ ^d to s+A ₁,..., s+A _n, where A ₁,..., A _n are the same for all sites and at least two of them are noncollinear. A site is closed if it belongs to p+Block, where p is a point in a Poisson distribution in R ^dZ ^d with a density and Block={sL: |s|M}+{sR ^d: |s|}, where L is a linear subspace of R ^d, |·| is the Euclidean norm, =max(|A ₁|,..., |A _n|) and M is a parameter. We study the behavior of *, the critical value, and P _closed*, corresponding critical percentage of closed sites, when M. Denote R ^d/L the factor space. Call two nonzero vectors U, V codirected if U=kV, where k>0. Theorem. If there are A _i and A _j whose projections to R ^d/L are not codirected, then *1/M ^dim(L) and P _closed* remains separated both from 0 and 1 when M. If projections of all A ₁,..., A _n to R ^d/L are codirected, then *1/M ^dim(L)+1 and P _closed*1/M when M.     

Some experimental data about the two contributions to magnetoresistance for n-type silicon crystal at 125 K

The transverse magnetoresistance (MR) was measured versus magnetic field strengthB at different rotational angles between the directions of bothB and currentI for n-type silicon crystal with charge carrier concentration of 1·8×10¹⁵cm^–3. The direction of the current through the two samples was chosen so that the angles between the current vector and [100] crystallographic axis were 50° and 70°, respectively. These measurements were done under weak electric and magnetic fields atT=125 K. It was found that the MR exhibits two types of anomalous effects, one of them at two opposite directions ofB at different, and the other at the same angles, when=50° and=70°. This shows that the anomalous behaviour of MR is not onlyB and dependent, but depends also on the current direction. Also the values ofB which are separated between the negative and positive parts of MR curves at the same depend on the magnitude of. These results may be attributed to the anomalous motion of charge carriers ink-space as a result of deviation of current direction from the symmetry axis.     

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     

Superstability estimates for anharmonic systems

We consider an anharmonic crystal described by variablesS _x ,x ^d ,S _x , with one-body interaction ¦S _x ¦ and nearest neighbor (n.n.) two body interaction ¦S _x –S _y ¦. We prove that, for ^d bounded, , where is the correlation function for the free boundary condition Gibbs state in ,>0 and are suitable constants independent of and . This generalizes previous results obtained in the case.Research partially supported by Consiglio Nazionale delle Ricerche.     

Photon-photon angular correlation ine +e− collision in QED

The angular correlation of two monochromatic photons produced ine ⁺e^– collision (annihilation), defined as the average of the cosine of the angle of separation between their outgoing momenta, is studied completely in momentum space to lowest order in the fine structure constant in QED. This is done from the expression of thee ⁺e^–-momentum-spin,-polarization-averaged conditional probability density for the angular distributions of the photons, given that the process has occurred. Although the density is in general nonvanishing for less than as well as greater than/2, the angular correlation is found to be strictly negative for all energies, indicating that the photons tend to travel in opposing directions in a statistical sense. The back-to-back motion, however, is very quickly unfavored as we move to higher energies.     

Characterization of the Weyl solutions

For the Weyl solutions(z, x) of the Schrödinger and Dirac equations, asymptotics for |z| are obtained. This gives a possibility of selecting Weyl solutions by their behaviour when |z| . Some applications are given.     

Conical Quantum Billiard

The conical quantum billiard is examined. Wavefunctions are obtained in an open domain which excludes the polar axis, involving associated Legendre functions of the first and second kind. The first excited state is three-fold degenerate. One wavefunction is nonnodal. The nodal surface of either of the other states is a bisecting plane which includes the axis of the cone. These nodal properties maintain for 0 < ₀ /2, where ₀ is the half vertex angle of the cone. At > /2, the nonnodal state acquires a nodal at = /2. Thus, as with the image problem in two dimensions, there is critical vertex angle about which the nodal structure of one of the eigenstates suffers a topological change. This nodal transition is accompanied by a geometrical transformation of the cone from convex to concave. Solutions obtained are valid for all conical quantum billiards to the limit of the spherical quantum billiard excluding the polar axis.     

Perturbations of flows on Banach spaces and operator algebras

For automorphism groups of operator algebras we show how properties of the difference _t – ' _t are reflected in relations between the generators , . Indeed for a von Neumann algebraM with separable predual we show that if _t – '_t 0.28 for smallt, then = 0(+)°^-1 where is an inner automorphism ofM and is a bounded derivation ofM. If the difference _t – ' _t =O(t) ast ; 0, then = + and if _t – ' _t 0.28 for allt then =. We prove analogous results for unitary groups on a Hilbert space andC ₀,C ₀ ^* groups on a Banach space.This paper subsumes an earlier work of the same title which appeared as a report from Z.I.F. der Universität BielefeldWith partial support of the U.S. National Science Foundation     

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.     

First experiment to test whether space-time is flat. II. Effects of orbit

The gyroscope in an orbiting satellite will be acted on by additional gravitational fields due to the rotation of the earth and due to the orbital velocity of the satellite. According to special relativistic gravitational theory, we deduce _L ^(S) —the gyroscope's precession rate due to the orbital velocity—and _S ^(S) —the gyroscope's precession rate due to the earth's rotation in the polar orbit case. The results are _L ^(S) = (2/3) _L ^(G) , _S ^(S) = (3/2) cos (1 - sin² cos²)^1/2 _S ^(G) , where and are the gyroscope's polar angles, and _L ^(G) and _S ^(G) are the geodetic and frame-dragging precession rates predicted by general relativity, respectively.     

Stochastic modeling of a billiard in a gravitational field: Power law behavior of Lyapunov exponents

We consider the motion of a point particle (billiard) in a uniform gravitational field constrained to move in a symmetric wedge-shaped region. The billiard is reflected at the wedge boundary. The phase space of the system naturally divides itself into two regions in which the tangent maps are respectively parabolic and hyperbolic. It is known that the system is integrable for two values of the wedge half-angle ₁ and ₂ and chaotic for ₁<< ₂. We study the system at three levels of approximation: first, where the deterministic dynamics is replaced by a random evolution; second, where, in addition, the tangent map in each region is, replaced by its average; and third, where the tangent map is replaced by a single global average. We show that at all three levels the Lyapunov exponent exhibits power law behavior near ₁ and ₂ with exponents 1/2 and 1, respectively. We indicate the origin of the exponent 1, which has not been observed in unaccelerated billiards.     

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).     

On Shirokov's “One New Effect of the Einsteinian theory of Gravitation”

In this note we study M.F. Shirokov's One New Effect of Einstein's theory of Gravitation in the Kerr field. We confine ourselves to a circular trajectory (r=const) in the plane=/2. In the limit that terms of the second order and higher ina/r (a is the angular momentum per unit mass) are negligible we find an additional shift betweenT andT _r (orT ) of amount –(8a/r)(m/r) ^3/2. Thus vibrations lie further behindr(or) vibrations in this case than in the Schwarzschild field.     

The spectrum of a Schrödinger operator inL p ℝ v isp-independent

LetH _p =–1/2+V denote a Schrödinger operator, acting inL _p ^v , 1p. We show that (H _p )=(H ₂) for allp[1, ], for rather general potentialsV.     

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     

Angular dependence of the superexchange interaction Fe3+-O2−-Cr3+

The super-exchange interaction parametersI(Fe, Cr) of Fe³⁺ and Cr³⁺ in iron doped rate-earth orthochromitesRCr_0.99Fe_0.01 O₃ (R=La, La_0.5Nd_0.5, Nd, Sm, Gd, Dy, Y, Er, Yb or Lu) have been obtained from⁵⁷Fe magnetic hyperfine structure measurementsvia the Mössbauer effect.The dependence of the experimental valuesI(Fe, Cr) on the Fe–O–Cr average superexchange angle (depending upon the relative size of the rare-earth (RE) ionR ³⁺) is well described by the equationI(d⁵, d ^N ) = _N + _N cos + _N cos² .Within the accessible range of super-exchange angles 142°156°, the Fe³⁺–O^2––Cr³⁺ interaction is negative (antiferromagnetic). However, a theoretical analysis predicts a sign reversal forI(Fe, Cr.) at about 162° and thus ferromagnetic character of the interaction between 162° and 180°.The spin-only super-exchange interaction integrals fore _g andt _2g electrons, separately, are also calculated. Their angular dependence is accounted for by the behaviour of the antiferromagnetic kinetic and ferromagnetic potential exchange which are of different character when passing from 180° to 90° super-exchange geometry. The magnitude and the sign of the spin-only super-exchange integral for an arbitrary 3d cation, pair is predicted.     

Spatial fluctuations in reaction-limited aggregation

A general method is used for describing reaction-diffusion systems, namely van Kampen's method of compounding moments, to study the spatial fluctuations in reaction-limited aggregation processes. The general formalism used here and in subsequent publications is developed. Then a particular model is considered that is of special interest, since it describes the occurrence of a phase transition (gelation). The corresponding rate constants for the reaction between two clusters of sizei and sizej areK _ij=ij (i, j=1, 2,). For thediffusion constants D _j of clusters of sizej the following class of models is considered:D _j=D if 1Js andD _j=0 ifj>s. The casess= ands< are studied separately. For the models= the equal-time and the two-time correlation functions are calculated; this modelbreaks down at the gel point. The breakdown is characterized by a divergence of the density fluctuations, and is caused by the large mobility of large clusters. For all models withs< the density fluctuations remain finite att _c, and the equal-time correlation functions in the pre- and in the post-gel stage are calculated. Many explicit and asymptotic results are given. From the exact solution the upper critical dimension in this gelling model isd _c=2.