Improved higher order phase-integral approximations of the JWKB type in the vicinity of zeros and singularities of the “wave number”

This paper treats the local behaviour of certain phase-integral approximations (PIA) of arbitrary order. This is done for the vicinities of zeros and poles of the coefficient Q²(z) in the wave-equation d²ψ/dz²+Q²(z)ψ = 0. This coefficient can be complex on the real axis. A simple formula relating the cumulative error of PIA (μ-integral) to the first truncated correction in the phase-integral expansion is derived. For a simple model of a zero or pole of Q²(z), PIA of arbitrary order are determined explicitly. Their phase-integrals exhibit certain symmetry properties which justify the “loop integrals” often used in the JWKB formulae when applied in higher orders. We demonstrate the asymptotic character of the phase-integral expansion explicitly and determine its optimum order and accuracy. The well-known connection formulae are shown to retain their one-directional character in higher orders. Modifications which improve PIA at their critical points are also discussed in detail both at the modification point and elsewhere. Some quantum mechanical applications are also discussed.     

Notes on a paper by Lutzky on the noncanonical symmetries of Hamiltonian systems

We obtain the first integrals Tr(R^k) by using a differential equation of the Lax type of simpler structure than the one obtained in a recent paper. Certain questions raised in this paper on the relation between noncanonical symmetries S and complete integrability are answered. Additional first integrals depending on the derivatives of S of order greater than one are also obtained.     

Monte Carlo studies of triangulated spherical surfaces in the two-dimensional space

We numerically study a triangulated surface model in R²${\mathbf{R}}^2$ by taking into account a viewpoint of string model. The models are defined by a mapping X from a two-dimensional surface M   to R²${\mathbf{R}}^2$, where the mapping X and the metric g of M are the dynamical variables. The sum over g in the partition function is simulated by the sum over bond lengths and deficit angles by using the Regge calculus technique, and the sum over g is defined to be performed independently of the sum over X. We find that the model undergoes a first-order transition of surface fluctuations, which accompanies a collapsing transition, and that the transitions are reflected in the internal geometry of surface. Fluid surface models are also studied on dynamically triangulated surfaces, and the transitions are found to be of second order. The order of the transition remains unchanged from that of the conventional model defined only by the variable X both in the fixed-connectivity and the fluid models.     

Single crystal magnetization studies of DySb

High resolution magnetization measurements in single crystal-spherical DySb samples have been performed versus T in fields to 23.6 kOe. Measurements with H along principal crystallographic and 〈11$\text{2}$〉 directions are interpreted in terms of the intermediate metamagnetic phase having the HoP structure. Magnetization components parallel and perpendicular to the applied field for field rotations in (110) and (111) crystallographic planes have been measured and are interpreted in terms of a simple model with a single critical field. For H ∥ 〈110〉, M and H are collinear. The (M - H - T) phase diagram has been determined for H ∥ 〈110〉. The metamagnetic transition is 1st order below a critical point P_c = (8.5 K, 14.7 kOe) becoming 2nd order above. Field induced order for T >T_N is observed in agreement with the results of Brun et al. The absence of hysteresis in M_∥(θ) for H in (110) and (111) planes is interpreted as evidence for the tunneling model in DySb.     

A classical model of EPR experiment with quantum mechanical correlations and bell inequalities

A simple model of a classical break-up process is given in which the correlation E(a,b) of the components A and B of the spins of the two subsystems along directions a and b gives precisely the quantum mechanical result $\text{?cos(}\text{a·b}\text{)}$. The model is “local”, but the normalization procedure of correlation functions in terms of “hidden variables” is different from that used in deriving Bell's inequalities. A discretization procedure of the classical spins is then given which reproduces fully the dichotomous quantum mechanical results both for probabilities and for correlation functions. This procedure illustrates particularly clearly the difference between quantum and classical spins and provides a possible intuitive picture for the notion of the “reduction of the wave function”.     

From a grain to avalanches: on the physics of granular surface flows

Granular surface flows have still to be fully modelled. Analysing the motion of a single grain can already help us to understand the physical origin of several characteristic angles (starting, stopping, jumping angles). Then looking at layers of grains allows the inference of the velocity profile inside the flowing layer, and the physical origin of the flow depth selection. Then these results can be plugged into a general model of mass and momentum conservation integrated vertically (St-Venant). This model can be tested on stationary flows, but also on transients, such as avalanches. To cite this article: S. Douady et al., C. R. Physique 3 (2002) 177–186.     

Study of two-phonon excitations in superfluid 4He

We explain the second branch of excitations in superfluid ⁴He observed by Cowley and Woods, by accounting for two-phonon contributions to the dynamic structure function, S(k, ω). Our theory gives a good fit with the experimental data in the high energy region for several values of momentum transfer. It is observed that the contribution to S(k, ω) due to two-phonon excitations is of the order of k² as against its k⁴ dependence reported in earlier theories.     

Extinction ratio improvement by an all-optical signal regenerator with a semiconductor optical amplifier and a Sagnac loop

In this paper, we present the operation of an all-optical signal regenerator (AOSR). The AOSR is based on a semiconductor optical amplifier (SOA), which is incorporated in an asymmetric Sagnac loop (ASL). We show experimentally that the AOSR is capable of improving the input signal extinction ratio (ER) considerably. We present a theoretical model, which explains this improvement, and we illustrate a qualitatively similar behavior with a simulation.     

Crystal-field and magnetic moment direction in rare earth-silicon intermetallic compounds RSi of CrB type (R=Tb,Dy, Ho,Er, Tm)

Using a crystal-field calculation within a point charge model, we interpret the rare-earth magnetic moment direction in the equiatomic rare earth-silicon compounds of CrB type. We showed that the 2nd order crystal-field parameter V²₂ is predominant and implies the magnetic moment to the perpendicular to the two-fold quantization axis i.e. b-axis. The calculated magnetic moment direction are in good agreement with neutron diffraction results.     

Electric field controlled higher-order diffraction images of paraelectric potassium lithium tantalate niobate

We report some electric field controlled photorefractive higher-order diffraction phenomena of a paraelectric phase potassium lithium tantalate niobate crystal doped with iron. In experiments, a p-polarized semiconductor laser (532 nm) was used to record grating at a small incident angle. Higher-order diffraction images were observed when the signal beam was focused behind and in front of the crystal. Then the higher-order diffraction images were reconstructed by a p-polarized He–Ne laser (632.8 nm) in the direction perpendicular to the surface. The higher-order diffraction images could be controlled by the external electric field. A theory about the higher-order diffraction images of the K and 2K grating is developed. The results show that the even order diffraction images of the K grating and the odd order diffraction of the 2K grating overlap each other. The odd order diffraction images of the K grating are diffracted in unattached direction. The electric field controlled higher-order diffraction image provides a useful method for optical information processing.     

Field of linear frames as a fundamental self-interacting system

We present some philosophical and physical arguments supporting the hypothesis that the most fundamental self-interacting field in an amorphous space-time is the field of linear frames, i.e. the quadruple of vector bosons. We construct a wide class of Lagrangian dynamical models invariant under the total group of diffeomorphisms and under the natural action of the proper linear group GL⁺ (4, R) on the tetrad field. There exist some links between these models and the Hamiltonian dynamical systems on GL⁺ (3, R) (the mechanics of affinely-rigid bodies [23] [27]). We present the general form of field equations, conservation laws and Bianchi identities. There exist some formal similarities between our Lagrangians and those used in non-linear electrodynamics, in particular in the Born–Infeld theory [21]. We also give a few rough remarks concerning models invariant under natural subgroups of GL⁺ (4, R), i.e. under SL(4, R) and SO(1, 3; R) (special linear group and Lorentz group). The latter class includes the conventional Einstein relativity and the more general metrical-parallelism models. It turns out that there are GL⁺ (4, R)-invariant Lagrangians which are structurally alike the conventional Einstein Lagrangian.We have not derived as yet either mathematical or physical consequences of the presented model. Nevertheless, it seems to follow from our discussion that, a priori, the GL⁺ (4, R)-invariant tetrad models could be competitive with the Einstein theory. The next thing to be done would be a careful mathematical analysis of these models and attempts to compare their consequences with those of the Einstein relativity and of other field theories.     

Strings on pp-waves and massive two-dimensional field theories

We find a general class of pp-wave solutions of type IIB string theory such that the light cone gauge worldsheet Lagrangian is that of an interacting massive field theory. When the light cone Lagrangian has (2,2) supersymmetry we can find backgrounds that lead to arbitrary superpotentials on the worldsheet. We consider situations with both flat and curved transverse spaces. We describe in some detail the background giving rise to the N=2 sine Gordon theory on the worldsheet. Massive mirror symmetry relates it to the deformed CP¹ model (or sausage model) which seems to elude a purely supergravity target space interpretation. To cite this article: J. Maldacena, L. Maoz, C. R. Physique 4 (2003).     

Long-wavelength excitations in a Bose gas at zero temperature

The long-wavelength excitations in a simple model of a dilute Bose gas at zero temperature are investigated from a purely microscopic viewpoint. The role of the interaction and the effects of the condensate are emphasized in a dielectric formulation, in which the response functions are expressed in terms of regular functions that do not involve an isolated single-interaction line nor an isolated single-particle line. Local number conservation is incorporated into the formulation by the generalized Ward identities, which are used to express the regular functions involving the density in terms of regular functions involving the longitudinal current. A perturbation expansion is then developed for the regular functions, producing to a given order in the perturbation expansion an elementary excitation spectrum without a gap and simultaneously response functions that obey local number conservation and related sum rules.Explicit results to the first order beyond the Bogoliubov approximation in a simple one-parameter model are obtained for the elementary excitation spectrum ω_k, the dynamic structure function $\text{S}$(k, ω), the associated structure function $\text{S}$_m(k), and the one-particle spectral function $\text{A}$(k, ω), as functions of the wavevector k and frequency ω. These results display the sharing of the gapless spectrum ω_k by the various response functions and are used to confirm that the sum rules of interest are satisfied. It is shown that ω_k and some of the $\text{S}$_m(k) are not analytic functions of k in the long wavelength limit. The dynamic structure function $\text{S}$(k, ω) can be conveniently separated into three parts: a one-phonon term which exhausts the f sum rule, a backflow term, and a background term. The backflow contribution to the static structure function $\text{S}$₀(k) leads to the breakdown of the one-phonon Feynman relation at order k³. Both $\text{S}$(k, ω) and $\text{A}$(k, ω) display broad backgrounds because of two-phonon excitations. Simple arguments are given to indicate that some of the qualitative features found for various physical quantities in the first-order model calculation might also be found in superfluid helium.     

Effects of band structure and matrix element on RKKY interaction

The effects of band structure and matrix elements on the RKKY interaction J(R) are separately investigated. When the Fermi surface has planes perpendicular to R, effects appear on the period of oscillation, the phase shift and the amplitude of J(R). The applicable region of the asymptotic form for large R and the validity of the free electron approximation are also examined. If there are no tangential planes perpendicular to R, it is found that: 1) when two interacting localized spins are on lattice points in the crystal, exponential damping appears even for the constant matrix element model and the matrix element effects introduce competing terms causing a sign change; 2) when one of the spins is at an interstitial position, the constant matrix model gives a weaker J(R) ∝ R^-2 damping, but the character of this term changes into the exponential damping by taking into account matrix elements.     

Orientational dynamics of superfluid 3He: A “two-fluid” model. II. Orbital dynamics

We present a phenomenological theory of the homogeneous orbital dynamics of the class of “separable” anisotropic superfluid phases which includes the ABM state generally identified with ³He-A. The theory is developed by analogy with the spin dynamics described in the first paper of this series; the basic variables are the orientation of the Cooper-pair wavefunction (in the ABM phase, the l-vector) and a quantity K which we visualize as the “pseudo-angular momentum” of the Cooper pairs but which must be distinguished, in general, from the total orbital angular momentum of the system. In the ABM case l is the analog of d in the spin dynamics and K of the “superfluid spin” S_p. Important points of difference from the spin case which are taken into account include the fact that a rotation of l without a simultaneous rotation of the normal-component distribution strongly increases the energy of the system (“normal locking”), and that the equilibrium value of K is zero even for finite total angular momentum. The theory does not claim to handle correctly effects associated with any intrinsic angular momentum arising from particle-hole asymmetry, but it is shown that the magnitude of this quantity can be estimated directly from experimental data and is extremely small; also, the Landau damping does not emerge automatically from the theory, but can be put in in an ad hoc way. With these provisos the theory should be valid for all frequencies $\text{ω ?}\text{Δ(T)}\text{h}\text{?}$ irrespective of the value of ωτ. (Δ = gap parameter, τ = quasi-particle relaxation time.) It disagrees with all existing phenomenological theories of comparable generality, although the disagreement with that of Volovik and Mineev is confined to the “gapless” region very close to T_c.The phenomenological equations of motion, which are similar in general form to those of the spin dynamics with damping, involve an “orbital susceptibility of the Cooper pairs” χ_orb(T). We give a possible microscopic definition of the variable K and use it to calculate χ_orb(T) for a general phase of the “separable” type. The theory is checked by inserting the resulting formula in the phenomenological equations for ωτ ? 1 and comparing with the results of a fully microscopic calculation based on the collisionless kinetic equation; precise agreement is obtained for both the ABM and the (real) polar phase, showing that the complex nature of the ABM phase and the associated “pair angular momentum” is largely irrelevant to its orbital dynamics. We note also that the phenomenological theory gives a good qualitative picture even when ω ～ Δ(T), e.g., for the flapping mode near T_c. Our theory permits a simple and unified calculation of (1) the Cross-Anderson viscous torque in the overdamped regime, (2) the flapping-mode frequency near zero temperature, (3) orbital effects on the NMR, both at low temperatures and near T_c, (4) the orbit wave spectrum at zero temperature (this requires a generalization to inhomogeneous situations which is possible at T = 0 but probably not elsewhere). We also discuss the possibility of experiments of the Einstein-de Haas type. Generally speaking, our results for any one particular application can be also obtained from some alternative theory, but in the case of orbital and spin relaxation very close to T_c (within the “gapless” region) our predictions, while somewhat tentative and qualitative, appear to disagree with those of all existing theories. We discuss briefly how our approach could be extended to apply to more general phases.     

Non-perturbative calculation of the mass-gap in the Gross-Neveu model

We calculate a fully renormalizable effective action for local composite operators in the U(N) Gross-Neveu model, recently introduced by one of us, to two loop order. We obtain results for the massgap in one and two loops which are optimized using the Grunberg method of effective charges. At one loop the accuracy is of the order of 2% or less (except for N = 2). At two loops the accuracy is significantly improved for N ≥ 5.     

A study of some methods for measuring CKM CP violating phases

We study the influence of penguin (especially, electroweak penguin) effects on some methods of measuring the angles α, β, and γ in the CKM unitarity triangle. We use next-to-leading order effective Hamiltonian, and present numerical estimates based on the factorization approximation. We find that some techniques suggested in the literature, especially for α determination, are not workable in light of the electroweak penguin effects. Nevertheless, there are methods that would work for each angle determination. For angle β we consider B → D ⁺D^{～ -} mode and estimate the penguin contamination. For angle γ we consider a method based on SU(3) symmetry and carefully consider SU(3) breaking effects. We point out regions in the parameter space where this method could be used reliably.     

On the solution of S(ω)x=0 by a Newtonian procedure

The method [1] developed for the solution of (E ? λ A)x=0, where E and A are real symmetric matrices, and A is positive definite, is extended to deal with S(ω)x=0, where S is a real symmetric structural dynamic stiffness matrix whose elements are trancendental functions of ω, the radian natural frequency. The method enables all natural frequencies (latent roots [2]) and mode shapes (latent vectors, x) across a prescribed frequency range to be determined infallibly and in ascending frequency order at a speed approaching twice that associated with bisection and sign counting methods [3]. It is ideally suited for use on micro- and minicomputers where single precision working is the norm, and on the Commodore 4032 computer can cope with matrices, S, of order n and bandwidth p provided that np < 4200. Much larger problems, of course, may be dealt with on mainframe machines.     

Collisional-radiative model for non-Maxwellian inductively coupled argon plasmas using detailed fine-structure relativistic distorted-wave cross sections

Our recently developed collisional-radiative model which included fine-structure cross sections calculated with a fully relativistic distorted-wave method [R.K. Gangwar, L. Sharma, R. Srivastava, A.D. Stauffer, J. Appl. Phys. 111, 053307 (2012)] has been extended to study non-Maxwellian inductively coupled argon plasmas. We have added more processes to our earlier collisional-radiative model by further incorporating relativistic distorted-wave electron impact cross sections from the 3p ⁵4sJ = 0, 2 metastable states, (1s ₃, 1s ₅ in Paschen’s notation) to the 3p ⁵5p (3p _i ) excited states. The population of various excited levels at different pressures in the range of 1–25 mTorr for an inductively coupled argon plasma have been calculated and compared with the recent optical absorption spectroscopy measurements as well as emission model results of Boffard et al. [Plasma Sources Sci. Technol. 19, 065001 (2010)]. We have also calculated the intensities of two emission lines, 420.1 nm (3p ₉ → 1s ₅) and 419.8 nm (3p ₅ → 1s ₄) and compared with measured intensities reported by Boffard et al. [J. Phys. D 45, 045201 (2012)]. Our results are in good agreement with the measurements.     

Dimer adsorption on square surfaces with first- and second-neighbor interactions

Dimer adsorption on surfaces simulates the adsorption of particles that bind onto two nearest-neighbor sites. In 1993, we constructed a transfer matrix (T-matrix) for the study of dimers on stepped surfaces, consisting of M-sites wide square terraces, considering only first-neighbor interaction energies. Here, we consider a more realistic model by including both first- and second-neighbor interaction energies, V and W. The non-trivial construction of the T-matrix to include second-neighbor interactions is used to obtain the low-temperature energy phase diagrams of the dimer system for any M, when first-neighbors are attractive, and for values of M<7 when first-neighbors are repulsive. New crystallization patterns and phases are observed and extrapolated to infinite M. Monte Carlo simulation techniques confirm our T-matrix results, but the T-matrix method is found to be computationally more efficient and more precise. However, Monte Carlo parallel tempering simulations combined with finite-size scaling, while limited in precision, are more efficient to obtain the critical temperature of the various order-disorder transitions as a function of W/|V|, from the study of the heat capacity and the order parameter as functions of temperature. We also discuss the relevance of these results to experiments.