Nuclear mean fields through self-consistent semiclassical calculations

Semiclassical expansions derived in the framework of the Extended Thomas-Fermi approach for the kinetic energy density τ( r) and the spin-orbit density J( r) as functions of the local density ρ( r) are used to determine the central nuclear potentials V _n( r) and V _p( r) of the neutron and proton distribution for effective interactions of the Skyrme type. We demonstrate that the convergence of the resulting semiclassical expansions for these potentials is fast and that they reproduce quite accurately the corresponding Hartree-Fock average fields. Received: 12 February 2000 / Accepted: 14 March 2002     

Existence of Noncompact Static Spherically Symmetric Solutions of Einstein SU(2)-Yang–Mills Equations

We consider static spherically symmetric solutions of the Einstein equations with cosmological constant Λ coupled to the SU(2)-Yang–Mills equations that are smooth at the origin r=0. We prove that all such solutions have a radius r _c at which the solution in Schwarzschild coordinates becomes singular. However, for any positive integer N, there exists a small positive Λ _N such that whenever 0<Λ<Λ _N , there exist at least N distinct solutions for which the singularity is only a coordinate singularity and the solution can be extended to r≥r _c . Received: 5 June 2000 / Accepted: 13 March 2001     

Hausdorff Dimension of Measures¶via Poincaré Recurrence

We study the quantitative behavior of Poincaré recurrence. In particular, for an equilibrium measure on a locally maximal hyperbolic set of a C ^1+α diffeomorphism f, we show that the recurrence rate to each point coincides almost everywhere with the Hausdorff dimension d of the measure, that is, inf{k>0 :f ^k x∈B(x,r)}∼r ^{− d} . This result is a non-trivial generalization of work of Boshernitzan concerning the quantitative behavior of recurrence, and is a dimensional version of work of Ornstein and Weiss for the entropy. We stress that our approach uses different techniques. Furthermore, our results motivate the introduction of a new method to compute the Hausdorff dimension of measures. Received: 17 July 2000 / Accepted: 20 December 2000     

On the confining potential in 4D SU(N_{\mathrm c}) gauge theory with dilaton

Using the formal analogy between the Dick superstring inspired model and the problem of the building of an Eguchi–Hanson metric in 4D N = 2 harmonic superspace (HS), we derive a general formula for the quark–quark interaction potential V(r) including the Dick confining potential. The interquark potential V(r) depends on the dilaton–gluon coupling and may be related to the parameterization of confinement by the quark and gluon vacuum condensates. It is also shown how the axion field may be incorporated in agreement with 10D type IIB superstring requirements. Others features are also discussed. Received: 23 December 1999 / Published online: 6 March 2000     

No or Infinitely Many A.C.I.P.¶for Piecewise Expanding Cr Maps¶in Higher Dimensions

We modify Tsujii's example [9] to show that in contrast with the one-dimensional case, piecewise uniformly expanding and C ^r maps of the plane may: (1) either have no absolutely continuous invariant probability measures (a.c.i.p. for short) and be such that {\bf every point} is statistically attracted to a fixed repelling point;? (2) or have infinitely many ergodic a.c.i.p. Received: 6 September 2000 / Accepted: 15 May 2001     

Theoretical study of stereodynamics for the O（3P） ＋ H2 → OH ＋ H reaction

This paper employs the quasi-classical trajectory calculations to study the influence of collision energy on the title reaction on the potential energy surface of the ground ³A' triplet state developed by Rogers et al. (J. Phys. Chem. A 2000 104 2308). It calculates the product angular distribution of P(θ_r), P(φ_r) and P(θ_r, φ_r) which reflects vector correlation. The distribution P(θ_r) shows that product rotational angular momentum vectors j' of the products are strongly aligned along the relative velocity direction k. The distribution of P(φ_r) implies a preference for left-handed product rotation in planes parallel to the scattering plane. Four different polarisation-dependent cross-sections are also presented in the centre-of-mass frame. Results indicate that OH is sensitively affected by collision energies of H₂.     

The Klein-Gordon equation with the Kratzer potential in <Emphasis Type="Italic">d</Emphasis> dimensions

We apply the Asymptotic Iteration Method to obtain the bound-state energy spectrum for the d-dimensional Klein-Gordon equation with scalar S(r) and vector potentials V(r). When S(r) and V(r) are both Coulombic, we obtain all the exact solutions; when the potentials are both of Kratzer type, we obtain all the exact solutions for S(r) = V(r); if S(r) > V(r) we obtain exact solutions under certain constraints on the potential parameters: in this case, a possible general solution is found in terms of a monic polynomial, whose coefficients form a set of elementary symmetric polynomials.      

An Inverse Scattering Problem with Part of the Fixed-Energy Phase Shifts

Assume that q(r) is a real-valued, compactly supported potential, q(r)=0 for , . Let be an arbitrary fixed subset of non-negative integers such that , and be fixed-energy phase shifts corresponding to q(r). The main result is: Theorem. The data determine q(r) uniquely. Received: 3 March 1999 / Accepted: 27 April 1999     

Ehrenfest’s Paradox and Radial Electric Field in Quasi-Neutral Tokamak Plasma

A relation between physical consequences of the so-called Ehrenfest’s Paradox and the radial electric field E _r (r) in the classical quasi-neutral tokamak plasma is shown. Basic author’s approach to the relativistic nature of the tokamak E _r (r) has been described in Romannikov (J. Exp. Theor. Phys. 108:340–348, 2009). The experiment which can resolve the Ehrenfest’s Paradox is presented.     

The Pair Correlation Function of Fractional Parts of Polynomials

We show that a smooth interval map satisfying the Collet-Eckmann condition at some critical point is not structurally stable in C ^r topology for any r. Received: 17 October 1996 / Accepted: 16 April 1997     

The correlation between expansion speed and magnetic field in solar flare ribbons

In this paper, we study the correlation between the expansion speed of two-ribbon flares and the magnetic field measured in the ribbon location, and compare such correlation for two events with different magnetic configurations. These two events are: an M1.0 flare in the quiet sun on September 12, 2000 and an X2.3 flare in Active Region NOAA 9415 on April 10, 2001. The magnetic configuration of the M1.0 flare is simple, while that of X2.3 event is complex. We have derived a power-law correlation between the ribbon expansion speed (V _r ) and the longitudinal magnetic field (B _z ) with an empirical relationship V _r = A×B- _z ^−δ , where A is a constant and δ is the index of the power-law correlation. We have found that δ for the M1.0 flare in the simple magnetic configuration is larger than that for the X2.3 flare in the complex magnetic configuration.     

Spectra of Random Hermitian Matrices with a Small-Rank External Source: The Critical and Near-Critical Regimes

Random Hermitian matrices are used to model complex systems without time-reversal invariance. Adding an external source to the model can have the effect of shifting some of the matrix eigenvalues, which corresponds to shifting some of the energy levels of the physical system. We consider the case when the n×n external source matrix has two distinct real eigenvalues: a with multiplicity r and zero with multiplicity n−r. For a Gaussian potential, it was shown by Péché (Probab. Theory Relat. Fields 134:127–173, 2006) that when r is fixed or grows sufficiently slowly with n (a small-rank source), r eigenvalues are expected to exit the main bulk for |a| large enough. Furthermore, at the critical value of a when the outliers are at the edge of a band, the eigenvalues at the edge are described by the r-Airy kernel. We establish the universality of the r-Airy kernel for a general class of analytic potentials for r=O(n^g)r=\mathcal{O}(n^{\gamma}) for 0≤γ<1/12.     

On the Distribution of Free Path Lengths for the Periodic Lorentz Gas III

 For r(0,1), let Z _r ={xR ² |dist(x,Z ²)>r/2} and define τ _r (x,v)=inf{t>0|x+tv∂Z _r }. Let Φ _r (t) be the probability that τ _r (x,v)≥t for x and v uniformly distributed in Z _r and §¹ respectively. We prove in this paper that

Z-scan measurements of photorefractive nonlinearities for a SBN: Ce crystal

 In this paper, we derived the Z-scan formula for a photorefractive crystal sample under an external applied electric field. The far-field diffraction pattern of a Gaussian beam wavefront through a photorefractive crystal is calculated by considering spatial-phase perturbation induced by the space-charge field. The photorefractive drift nonlinearities and correspondingly, the electro-optic coefficients r ₃₃, r ₁₃, (r ₂₃) and the characteristic ratio n ³ _e r ₃₃/n ³ _o r ₁₃ for a cerium-doped Sr_0.61Ba_0.39Nb₂O₆ crystal are determined from the Z-scan experiments. Z-scan with enhanced sensitivity is also realized by measuring the normalized transmittance at the off-axis position in the far field. A deviation between the off-axis Z-scan experimental results and the theoretical prediction is discussed too. Received: 22 July 1996/Revised version: 7 October 1996     

Clusters of cycles

A cluster of cycles (or (r,q)-polycycle) is a simple planar 2-connected finite or countable graph G of girth r and maximal vertex-degree q, which admits an (r,q)-polycyclic realization P(G) on the plane. An (r,q)-polycyclic realization is determined by the following properties: (i) all interior vertices are of degree q; (ii) all interior faces (denote their number by p_r) are combinatorial r-gons; (iii) all vertices, edges and interior faces form a cell-complex.An example of (r,q)-polycycle is the skeleton of (r^q), i.e. of the q-valent partition of the sphere, Euclidean plane or hyperbolic plane by regular r-gons. Call spheric pairs (r,q)=(3,3),(4,3),(3,4),(5,3),(3,5). Only for those five pairs, P((r^q)) is (r^q) without exterior face; otherwise, P((r^q))=(r^q).Here we give a compact survey of results on (r,q)-polycycles. We start with the following general results for any (r,q)-polycycle G: (i) P(G) is unique, except of (easy) case when G is the skeleton of one of the five Platonic polyhedra; (ii) P(G) admits a cell-homomorphism f into (r^q); (iii) a polynomial criterion to decide if given finite graph is a polycycle, is presented.Call a polycycle proper if it is a partial subgraph of (r^q) and a helicene, otherwise. In [ARS Comb. A 29 (1990) 5], all proper spheric polycycles are given. An (r,q)-helicene exists if and only if p_r>(q−2)(r−1) and (r,q)≠(3,3). We list the (4,3)-, (3,4)-helicenes and the number of (5,3)-, (3,5)-helicenes for first interesting p_r. Any outerplanar (r,q)-polycycle G is a proper (r,2q−2)-polycycle and its projection f(P(G)) into (r^2q−2) is convex. Any outerplanar (3,q)-polycycle G is a proper (3,q+2)-polycycle.The symmetry group Aut(G) (equal to Aut(P(G)), except of Platonic case) of an (r,q)-polycycle G is a subgroup of Aut((r^q)) if it is proper and an extension of Aut(f(P(G))), otherwise. Aut(G) consists only of rotations and mirrors if G is finite, so its order divides one of the numbers 2r, 4 or 2q. Almost all polycycles G have trivial AutG.Call a polycycle G isotoxal (or isogonal, or isohedral) if AutG is transitive on edges (or vertices, or interior faces); use notation IT (or IG, or IH), for short. Only r-gons and non-spheric (r^q) are isotoxal. Let T^*(l,m,n) denote Coxeter’s triangle group of a triangle on S², E² or H² with angles π/l, π/m, π/n and let T(l,m,n) denote its subgroup of index 2, excluding motions of 2nd kind. We list all IG- or IH-polycycles for spheric (r,q) and construct many examples of IH-polycycles for general case (with AutG being above two groups for some parameters, including strip and modular groups). Any IG-, but not IT-polycycle is infinite, outerplanar and with same vertex-degree, we present two IG-, but not IH-polycycles with (r,q)=(3,5),(4,4) and AutG=T(2,3,∞)PSL(2,Z), T^*(2,4,∞). Any IH-polycycle has the same number of boundary edges for each its r-gon. For any r≥5, there exists a continuum of quasi-IH-polycycles, i.e. not isohedral, but all r-gons have the same 1-corona.On two notions of extremal polycycles:

1. We found for the spheric (r,q) the maximal number n_int of interior points for an (r,q)-polycycle with given p_r; in general case, (p_r/q)≤n_int<(rp_r/q) if any r-gon contains an interior point.

2. All non-extendible (r,q)-polycycles (i.e. not a proper subgraph of another (r,q)-polycycle) are (r^q), four special ones, (possibly, but we conjecture their non-existence) some other finite (3,5)-polycycles, and, for any (r,q)≠(3,3),(3,4),(4,3), a continuum of infinite ones.

On isometric embedding of polycycles into hypercubes Q_m, half-hypercubes and, if infinite, into cubic lattices Z_m, : for (r,q)≠(5,3),(3,5), there are exactly three non-embeddable polycycles (including (4³)−e, (3⁴)−e); all non-embeddable (5,3)-polycycles are characterized by two forbidden sub-polycycles with p₅=6.     

The structure of carbodiimide,HNCNH

An experimentally determined r _s -type structure of HNCNH is reported: r _NH = 1.0074 Å, r _CN = 1.2242 Å, ∠HNC = 118.63°, ∠NCN = 170.63°, ∠HN ··· NH = 88.99°. The number of digits quoted allow for errors with two significant figures. In order to obtain these values we recorded rotational—torsional spectra of HN¹³CNH, H¹⁵NC¹⁵NH and DNCND, by using isotopically enriched cyanamide. A chemical equilibrium exists between carbodiimide, HNCNH, and the more stable isomer cyanamide, H₂NCN, which strongly favours cyanamide (approximately 1:115 at 110 °C). The expensive C- and N-substituted isotopomers could only be investigated in the millimetre wave region, while for DNCND the far infrared spectrum between 10–350 cm^?1 was also recorded. Rotational constants of the three isotopomers, as well as of the parent species, were determined by fitting the assigned spectral transitions to the Watson Hamiltonian in S reduction. Using fitting programs written by Schwendeman and Rudolph, r _o, r_s and r^ρ _m structures of HNCNH were derived. The experimentally determined structural parameters are compared with an ab initio r_e structure.     

Andreev-Lifshitz supersolid revisited for a few electrons on a square lattice. I

In 1969, Andreev and Lifshitz have conjectured the existence of a supersolid phase taking place at zero temperature between the quantum liquid and the solid. In this and a succeeding paper, we re-visit this issue for a few polarized electrons (spinless fermions) interacting via a U/r Coulomb repulsion on a two dimensional L×L square lattice with periodic boundary conditions and nearest neighbor hopping t. This paper is restricted to the magic number of particles N = 4 for which a square Wigner molecule is formed when U increases and to the size L = 6 suitable for exact numerical diagonalizations. When the Coulomb energy to kinetic energy ratio r _s = UL/(2t ) reaches a value r _s ^F ≈ 10, there is a level crossing between ground states of different momenta. Above r _s ^F, the mesoscopic crystallization proceeds through an intermediate regime ( r _s ^F < r _s < r _s ^W ≈ 28) where unpaired fermions with a reduced Fermi energy co-exist with a strongly paired, nearly solid assembly. We suggest that this is the mesoscopic trace of the supersolid proposed by Andreev and Lifshitz. When a random substrate is included, the level crossing at r _s ^F is avoided and gives rise to a lower threshold r _s ^F(W) < r _s ^F where two usual approximations break down: the Wigner surmise for the distribution of the first energy excitation and the Hartree-Fock approximation for the ground state. Received 21 June 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: jpichard@cea.fr     

The microwave spectrum and structure of carbonyl fluoride

The ground state microwave rotational spectra of four isotopic species of carbonyl fluoride have been measured between 18 GHz and 77 GHz, and analyzed to obtain the quartic and some sextic centrifugal constants. The rotational constants have been used to obtain a r₀ structure and, using a harmonic force field, a r_z structure is also obtained: r_z(C---F) = 1.3166 (10) Å, r_z(C---O) = 1.1700 (26) Å.These values are considerably more precise than those of the previously estimated average structure.     

Higher order terms in the inflaton potential and the lower bound on the tensor to scalar ratio r

The MCMC analysis of the CMB + LSS data in the context of the Ginsburg–Landau approach to inflation indicated that the fourth degree double-well inflaton potential in new inflation gives an excellent fit of the present CMB and LSS data. This provided a lower bound for the ratio r of the tensor to scalar fluctuations and as most probable value r ? 0.05, within reach of the forthcoming CMB observations. In this paper we systematically analyze the effects of arbitrarily higher order terms in the inflaton potential on the CMB observables: spectral index n_s and ratio r. Furthermore, we compute in close form the inflaton potential dynamically generated when the inflaton field is a fermion condensate in the inflationary universe. This inflaton potential turns out to belong to the Ginsburg–Landau class too. The theoretical values in the (n_s, r) plane for all double well inflaton potentials in the Ginsburg–Landau approach (including the potential generated by fermions) fall inside a universal banana-shaped region B. The upper border of the banana-shaped region B is given by the fourth order double-well potential and provides an upper bound for the ratio r. The lower border of B is defined by the quadratic plus an infinite barrier inflaton potential and provides a lower bound for the ratio r. For example, the current best value of the spectral index n_s = 0.964, implies r is in the interval: 0.021 < r < 0.053. Interestingly enough, this range is within reach of forthcoming CMB observations.     

Magnetic impurities in gapless Fermi systems: perturbation theory

We consider a symmetric Anderson impurity model with a soft-gap hybridization vanishing at the Fermi level, with r>0. Three facets of the problem are examined. First the non-interacting limit, which despite its simplicity contains much physics relevant to the U>0case: it exhibits both strong coupling (SC) states (for r<1) and local moment states (for r>1), with characteristic signatures in both spectral properties and thermodynamic functions. Second, we establish general conditions upon the interaction self-energy for the occurence of a SC state for U>0. This leads to a pinning theorem, whereby the modified spectral function is pinned at the Fermi level for any U where a SC state obtains; it generalizes to arbitrary r the pinning condition upon familiar in the normal r=0 Anderson model. Finally, we consider explicitly spectral functions at the simplest level: second order perturbation theory in U, which we conclude is applicable for and r>1 but not for . Characteristic spectral features observed in numerical renormalization group calculations are thereby recovered, for both SC and LM phases; and for the SC state the modified spectral functions are found to contain a generalized Abrikosov-Suhl resonance exhibiting a characteristic low-energy Kondo scale with increasing interaction strength. Received 26 August 1999