The length and the relative length of tangent vectors of finsler spaces

We consider the length of a vector in a Finsler space with the fundamental function L(x,y). The length of a vector X is usually defined as the value L(x,X) of L. On the other hand, we have an essential tensor g_ij(x,y), called the fundamental tensor, and the concept of relative length |X_y| of X may be introduced by |X|_y^y = g_ij(x,y)XⁱX^j with re spect to a supporting element y. The question arises whether is L(x,X) the minimum of |X|_y or not? If there exists a supporting element y satisfying |X|_y < L(x,X), then a curve x(t) in the Finsler space will be measured shorter than the usual length, by integrating |dx/dt|_y with the field of such supporting element y(t) along the curve.     

On a soluble model of an antiferromagnetic chain with Dzyaloshinsky interactions. I

The one-dimensional anisotropic XY model with antisymmetric nearest-neighbour interactions (Dzyaloshinsky interactions) in the presence of a magnetic field B in the z direction is investigated. Special attention is given to the critical behaviour of the system. In the ground state, the susceptibility χ^zz has a logarithmic singularity as B → 1 provided that the strength Δ of the Dzyaloshinsky interaction obeys the inequality |Δ| ≤ |γ|, where γ is the anisotropy parameter. However, if |Δ| #62; |γ|, χ^zz diverges with a power -$\text{1}\text{2}$ singularity as B ↑ (1 + Δ² - γ²)^{$\text{1}\text{2}$}. The specific heat is studied for low temperatures. Furthermore for a few special values of γ and B the static correlation functions 〈S^α_jS^β_k〉 are evaluated in the low-temperature limit, for α, β = x, y, z and |j - k| = 1, 2. Finally we consider the chain with Dzyaloshinsky interactions only.     

All-optical soliton switching for the asymmetric fiber couplers

Coupled nonlinear Schrödinger (CNLS) equations for the fiber couplers with asymmetric self-phase modulation (SPM) and cross-phase modulation (XPM) are studied. With symbolic computation, one- and two-soliton solutions are obtained for the constant- and variable-coefficient CNLS equations. Switching dynamics of the solitons is discussed, and effects of the second-order group-velocity dispersion β ₂, SPM coefficient σ ₁, XPM coefficient σ ₂ and Kerr nonlinear intensity γ on the all-optical switching properties are studied, while other coefficients in those equations are seen not to affect the all-optical switching properties. For the constant-coefficient CNLS equations, we find that |β ₂| is proportional to the optical switching speed, and the optical extinction ratios increase with the decrease of σ ₁/σ ₂ and increase of |β ₂| and γ. A numerical simulation by the split-step Fourier and Runge-Kutta methods is presented on the constant-coefficient CNLS equations to analyse the stability of the one- and two-solitons with the random initial perturbations. For the variable-coefficient CNLS equations, effects of σ ₁/σ ₂, β ₂(z) = a ₂ e ^bz and γ(z) = a ₃ e ^bz on the optical switching are analyzed (where a ₂, a ₃ and b are all constants, and z gives the direction of propagation in the fiber couplers): optical switching speed increases with the increase of |a ₂| and decrease of |b|, and optical extinction ratios increase with the increase of |a ₂| and decrease of σ ₁/σ ₂ and |a ₃|.     

Off-energy-shell continuation of the two-body transition matrix in the impact parameter representation

In the impact parameter representation, the symmetric part σ(k′, b, k) of the half-shell T-matrix, H, can be given arbitrarily. This in turn determines the entire T-matrix. Since σ(k, b, k) is essentially the impact parameter phase shift, the arbitrary part of the T-matrix appears to be a continuation into two dimensions of the phase shift function with symmetry being the only restriction. Since we can work with the T-matrix instead of the potential V, our formalism stays closer to experiments. Only two assumptions are necessary, namely, high energy and small intermediate angles.     

On the measure of gaps and spectra for discrete 1D Schrödinger operators

We study the lebesgue measure of gaps and spectra, of ergodic Jacobi matrices. We show that: |σ/A|+|G|≥v, where: σ is the spectrum,G is the union of the gaps,A is the set of energies where the Lyaponov exponent vanishes andv is an appropriate seminorm of the potential. We also study in more detail periodic Jacobi matrices, and obtain a lower bound and large coupling asymptotics for the measure of the spectrum. We apply the results of the periodic case, to limit periodic Jacobi matrices, and obtain sufficient conditions for |G|≥v and for |σ|>0.     

Scaling form of zero-field-cooled and field-cooled susceptibility in superparamagnet

The scaling form of the normalized ZFC and FC susceptibility of superparamagnets (SPMs) is presented as a function of the normalized temperature y(=k_BT/K_u〈V〉), normalized magnetic field h (=H/H_K), and the width σ of the log-normal distribution of the volumes of nanoparticles, based on the superparamagnetic blocking model with no interaction between the nanoparticles. Here 〈V〉 is the average volume, K_u is the anisotropy energy, and H_K is the anisotropy field. Main features of the experimental results reported in many SPMs can be well explained in terms of the present model. The normalized FC susceptibility monotonically increases as the normalized temperature y decreases. The normalized ZFC susceptibility exhibits a peak at the normalized blocking temperature y_b(=k_BT_b/K_u〈V〉), forming the y_b vs h diagram. For large , y_b starts to increase with increasing h, showing a peak at h=h_b, and decreases with further increasing h. The maximum of y_b at h=h_b is due to the nonlinearity of the Langevin function. For small σ, y_b monotonically decreases with increasing h. The derivative of the normalized FC magnetization with respect to h shows a peak at h=0 for small y. This is closely related to the pinched form of M_FC vs H curve around H=0 observed in SPMs.     

Singularities of the surface magnetisation profile near the critical point

Using renormalised perturbation theory we calculate explicitly the leading singular behaviour of the magnetisation shape function φ(y). To leading order φ(y)?y^σ, where σ=1-$\text{1}\text{6?}$.     

Measurements of elastic scattering in alpha-alpha and alpha-proton collisions at the CERN intersecting storage rings

We measured the elastic scattering of $\text{αα}\text{at}\text{s}\text{= 126}\text{GeV}$ and of αp at $\text{s}\text{= 89}\text{GeV}$. For αα, the differential cross section dσ/dt has a diffractive pattern minima at |t| = 0.10 and 0.38 GeV². At small |t| = 0.05?0.07 GeV², this cross section behaves like exp[(100 ± 10) t]. Extrapolating a fit to the data to the optical point, we obtained for the total cross section α_tot(αα) = 250 ± 50 mb and an integrated elastic cross section σ_e1(αα) = 45 ± mb. Another method of estimating σ_tot(αα), based on measuring the interaction rate, yielded 295 ± 40 mb. For αp, dσ/dt has aminimum at |t| = 0.20 GeV², and for 0.05 < |t| < 0.18 GeV² behaves like exp[(41 ± 2) t]. Extrapolating this slope to |t| = 0, we found σ_tot(αp) = 130 ± 20 and σ_e1(αp) = 20 ± 4mb. Results on pp elastic scattering at $\text{s}\text{= 63}\text{GeV}$ agree with previous ISR experiments.     

Reconstruction of singularities for solutions of Schrödinger's equation

We determine the behavior in time of singularities of solutions to some Schrödinger equations onR ⁿ . We assume the Hamiltonians are of the formH ₀+V, where \(H_0 = 1/2\Delta + 1/2 \sum\limits_{k = 1}^n { \omega _k^2 x_k^2 } \) , and whereV is bounded and smooth with decaying derivatives. When all ω _k =0, the kernelk(t,x,y) of exp (?itH) is smooth inx for every fixed (t,y). When all ω₁ are equal but non-zero, the initial singularity “reconstructs” at times \(t = \frac{{m\pi }}{{\omega _1 }}\) and positionsx=(?1) ^m y, just as ifV=0;k is otherwise regular. In the general case, the singular support is shown to be contained in the union of the hyperplanes \(\{ x|x_{js} = ( - 1)^l js_{y_{js} } \} \) , when ω _j t/π=l _j forj=j ₁,...,j _r .     

Galvanomagnetic effects in graphite—II: The influence of trigonal warping of the constant energy surfaces on σxx(Bz)

The dispersion relationship for the electrons near the region of band overlap in graphite corresponds to the case where the constant energy surfaces are strongly warped in the k_x?k_y plane with three-fold symmetry (trigonal warping). The effects of this warping on the galvanomagnetic tensor component σ_xx(B_z) are examined. In the present calculation the trigonal warping is treated using a simplified mathematical model. Implications with respect to the calculation of the density of free carriers in graphite are discussed.     

Correlation studies in quark jets using combinants

A brief summary of the basic properties of combinants is provided. Their behavior is analysed using the Opal multiplicity data for light quark jets in restricted rapidity bins. For |Δy|≤1 the combinants do not exclude clustering effects with Poisson superposition. For |Δy|≤2 this pattern of correlations is ruled out by the sign-changing oscillations of combinants, as well as other models which predict oscillations alternating in sign. The future experimental possibilities concerning combinants are discussed.     

Magnetotransport properties of untwinned YBa2Cu3Oy single crystals: novel 60-K-phase anomalies in the charge transport

We present the result of our accurate measurements of the a- and b-axis resistivity (ρ_a and ρ_b), magnetoconductivity Δσ/σ, Hall coefficient R_H, and the a-axis thermopower S_a in untwinned YBa₂Cu₃O_y single crystals in a wide range of doping (6.45≤y≤7.0). The systematics of our data reveals a number of novel 60-K-phase anomalies in the charge transport: (i) temperature dependences of ρ_a show anomalous overlap below ∼130 K for 6.65≤y≤6.80, (ii) Hall mobility μ_H shows an enhancement near y?6.65, which is reflected in an anomalous y dependence of σ_xy, (iii) with decreasing temperature R_H shows a marked drop upon approaching T_c only in samples with 6.70≤y≤6.85, (iv) superconducting fluctuation magnetoconductivity is anomalously enhanced near y?6.7, and (v) H_c2 is anomalously reduced near y?6.70. We discuss that the fluctuating charge stripes might be responsible for these anomalies in the charge transport.     

The production of charged particles with high transverse momentum in proton-proton collisions at the CERN ISR

Results are given on the inclusive production of charged pions, kaons and nucleons in high-energy proton-proton collisions in the centre-of-mass rapidity range |y_cm| < 1 and for transverse momenta up to 4.8 GeV/c. The dependence of the composition of produced particles on y_cm, the total energy $\text{s}$, and transverse momentum p_T is discussed.     

On-shell T-matrices in multiple scattering

The transition operator T for the scattering of a particle from N potentials V_j(x) can be expanded into a series featuring the transition operators t_j associated with the individual potentials. For V_j(x) both absolutely and square integrable in x, we show, using an analytic continuation argument, that if T is on-shell, i.e. in 〈k|T(k₀²±i0)|k′〉, |k| = |k′| = k₀, then each t_j is also on-shell.     

Better Entanglement Witness for Genuine Multipartite Entanglement

In the short contribution, we consider inequalities of confirming genuine multipartite entanglement. We have a better entanglement witness for a particular mixed state to test genuine multipartite entanglement. Our physical situation is that we measure Pauli observables σ _x , σ _y , and σ _z per side. If the reduction factor is greater than 0.4, then we can confirm the measured quantum state is genuine multipartite entangled experimentally.     

Comparison between bremsstrahlung cross section measurements at the short wavelenght limit and theoretical results

Recent precise measurements of the electron bremsstrahlung cross section d²σ/dk dΩ_k at the short wavelength limit for an incident electron energy of 1.84 MeV important discrepancies between experimental results and earlier theoretical calculations. A new exact theoretical result, for a point Coulomb potential is presented: descrepancies with experimental results remain.     

Optimized implementations of rational approximations for the Voigt and complex error function

Rational functions are frequently used as efficient yet accurate numerical approximations for real and complex valued functions. For the complex error function w(x+iy), whose real part is the Voigt function K(x,y), code optimizations of rational approximations are investigated. An assessment of requirements for atmospheric radiative transfer modeling indicates a y range over many orders of magnitude and accuracy better than 10⁻⁴. Following a brief survey of complex error function algorithms in general and rational function approximations in particular the problems associated with subdivisions of the x, y plane (i.e., conditional branches in the code) are discussed and practical aspects of Fortran and Python implementations are considered. Benchmark tests of a variety of algorithms demonstrate that programming language, compiler choice, and implementation details influence computational speed and there is no unique ranking of algorithms. A new implementation, based on subdivision of the upper half-plane in only two regions, combining Weideman's rational approximation for small |x|+y<15 and Humlicek's rational approximation otherwise is shown to be efficient and accurate for all x, y.     

Magnetomechanical coupling in Dy0.73Tb0.27Fe2 alloys

Dynamic and static measurements of the magnetomechanical coupling coefficient, k₃₃, have been performed on as cast random polycrystalline terfenol. The values obtained from the two techniques are consistent (k₃₃ ≈ 0.33) but are small in comparison with previously published values from similar material. Although a significant improvement could be achieved by employing refined preparation techniques to produce grain oriented material, the magnetic properties of the present material have been investigated to explore the reasons for low coupling. Data for the relative differential permeability at constant stress, μ^σ, and magnetostrictive strain coefficient, d₃₃, show that the coupling is spoiled by a low maximum permeability and an exceedingly small value for d₃₃. The difficulties in making measurements on samples which give information on material quality alone, regardless of the experimental conditions, are discussed.     

Localization in the ground state of the ising model with a random transverse field

We study the zero-temperature behavior of the Ising model in the presence of a random transverse field. The Hamiltonian is given by $$H = - J\sum\limits_{\left\langle {x,y} \right\rangle } {\sigma _3 (x)\sigma _3 (y) - \sum\limits_x {h(x)\sigma _1 (x)} } $$ whereJ>0,x,y∈Z ^d, σ₁, σ₃ are the usual Pauli spin 1/2 matrices, andh={h(x),x∈Z ^d} are independent identically distributed random variables. We consider the ground state correlation function 〈σ₃(x)σ₃(y)〉 and prove:

1. Letd be arbitrary. For anym>0 andJ sufficiently small we have, for almost every choice of the random transverse fieldh and everyx∈Z ^d, that $$\left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle \leqq C_{x,h} e^{ - m\left| {x - y} \right|} $$ for ally∈Z ^d withC _{x h} <∞.
2. Letd≧2. IfJ is sufficiently large, then, for almost every choice of the random transverse fieldh, the model exhibits long range order, i.e., $$\mathop {\overline {\lim } }\limits_{\left| y \right| \to \infty } \left\langle {\sigma _3 (x)\sigma _3 (y)} \right\rangle > 0$$ for anyx∈Z ^d.