Stretched exponential relaxation in the Coulomb glass

The relaxation of the specific heat and the entropy to their equilibrium values is investigated numerically for the three-dimensional Coulomb glass at very low temperatures. The long time relaxation follows a stretched exponential function, f (t) = f ₀exp - (t/τ)^β , with the exponent β increasing with the temperature. The relaxation time diverges as an Arrhenius law when T→ 0. Received 24 May 2001 and Received in final form 12 September 2001     

Current-voltage characteristics for a Peierls-conducting point contact

Current-voltage (J-V) and differential-conductivity-voltage ( dJ/dV-V) characteristics are analytically calculated at zero temperature for a point contact consisting of: two Peierls conductors P ( = 1, 2) separated by an insulator (I). Here P is a conductor with charge density wave (CDW). The J-V and dJ/dV-V characteristics depend on the CDW phases ( = 1, 2) in the mean field approximation. To calculate them analytically we assumed, = ≡Δ where ( = 1, 2) are the energy gaps of P ( = 1, 2). The current J has a discontinuous jump at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The differential conductivity dJ/dV has a singularity at eV = 2Δ for ϕ ₁ = ϕ ₂≠ 0. The relation J(V,ϕ ₁,ϕ ₂) = - J(- V,ϕ ₁ + π,ϕ ₂ + π) is obtained. Received 4 July 2001 and Received in final form 13 September 2001     

Universality in diffusion front growth dynamics

We have studied the scaling properties of diffusion fronts by numerical calculations based on the mean field approach in the context of a lattice gas model, performed in a triangular lattice. We find that the height-height correlation function scales with time t and length l as C(l, t) ≈l ^α f (t/l ^α/β) with α = 0.62±0.01 and β = 0.39±0.02. These exponent values are identical to those characterising the roughness of the diffusion fronts evolving through a square lattice [1,2], thus confirming their universality. Received 14 November 2001 / Received in final form 20 April 2002 Published online 31 July 2002     

Short-range plasma model for intermediate spectral statistics

We propose a plasma model for spectral statistics displaying level repulsion without long-range spectral rigidity, i.e. statistics intermediate between random matrix and Poisson statistics similar to the ones found numerically at the critical point of the Anderson metal-insulator transition in disordered systems and in certain dynamical systems. The model emerges from Dysons one-dimensional gas corresponding to the eigenvalue distribution of the classical random matrix ensembles by restricting the logarithmic pair interaction to a finite number k of nearest neighbors. We calculate analytically the spacing distributions and the two-level statistics. In particular we show that the number variance has the asymptotic form Σ²(L) ∼χL for large L and the nearest-neighbor distribution decreases exponentially when s→∞, P(s) ∼ exp(- Λs) with Λ = 1/χ = kβ + 1, where β is the inverse temperature of the gas (β = 1, 2 and 4 for the orthogonal, unitary and symplectic symmetry class respectively). In the simplest case of k = β = 1, the model leads to the so-called Semi-Poisson statistics characterized by particular simple correlation functions e.g. P(s) = 4s exp(- 2s). Furthermore we investigate the spectral statistics of several pseudointegrable quantum billiards numerically and compare them to the Semi-Poisson statistics. Received 13 September 2000     

Monte Carlo calculations of angular momentum projected many-body matrix elements in the Pairing Plus Quadrupole Model

We extend the recently presented formalism for Monte Carlo calculations of the partition function, for both even and odd particle number systems (Phys. Rev. C 59, 2500 (1999)), to the calculation of many-body matrix elements of the type <ψ| e ^{- βℋ}|ψ> where |ψ> is a many-body state with a definite angular momentum, parity, neutron and proton numbers. For large β such matrix elements are dominated by the lowest eigenstate of the many-body Hamiltonian ℋ, corresponding with a given angular momentum parity and particle number. Emphasis is placed on odd-mass nuclei. Negligible sign fluctuations in the Monte Carlo calculation are found provided the neutron and proton chemical potentials are properly adjusted. The formalism is applied to the J ^π = 0⁺ state in ¹⁶⁶ Er and to the J ^π = 9/2^-, 13/2⁺, 5/2^- states in ¹⁶⁵ Er using the pairing-plus-quadrupole model. Received: 28 April 2000 / Accepted: 20 September 2000     

Two-particle dispersion in model two-dimensional velocity fields

We consider two-particle dispersion in a velocity field, where the relative two-point velocity scales according to v ²(r) ∝r ^α and the corresponding correlation time scales as τ(r) ∝r ^β, and fix α = 2/3, as typical for turbulent flows. We show that two generic types of dispersion behavior arize: For α/2 + β < 1 the correlations in relative velocities decouple and the diffusion approximation holds. In the opposite case, α/2 + β > 1, the relative motion is strongly correlated. The case of Kolmogorov flows corresponds to a marginal, nongeneric situation. In this case, depending on the particular parameters of the flow, the dispersion behavior can be rather diffusive or rather ballistic. Received 13 March 2001     

New transitions in the β-decay of 36Ca

The β-decay of the T _z = - 2 nucleus ³⁶Ca was studied at the LISE3 magnetic spectrometer at GANIL. Two new proton-emitting states have been detected and the other nine known βp and βγ transitions have been remeasured with improved resolution. A simulation with the GEANT code has been applied to this experimental setup. A comparison with shell model calculations is given. Received: 19 September 2000 / Accepted: 28 February 2001     

Momentum transport and torque scaling in Taylor-Couette flow from an analogy with turbulent convection

We generalize an analogy between rotating and stratified shear flows. This analogy is summarized in Table 1. We use this analogy in the unstable case (centrifugally unstable flow vs. convection) to compute the torque in Taylor-Couette configuration, as a function of the Reynolds number. At low Reynolds numbers, when most of the dissipation comes from the mean flow, we predict that the non-dimensional torque G = T/ν² L, where L is the cylinder length, scales with Reynolds number R and gap width η, G = 1.46η^3/2(1 - η)^-7/4 R ^3/2. At larger Reynolds number, velocity fluctuations become non-negligible in the dissipation. In these regimes, there is no exact power law dependence the torque versus Reynolds. Instead, we obtain logarithmic corrections to the classical ultra-hard (exponent 2) regimes: G = 0.50 . These predictions are found to be in excellent agreement with avail-able experimental data. Predictions for scaling of velocity fluctuations are also provided. Received 7 June 2001 and Received in final form 7 December 2001     

Spectral determinant on graphs with generalized boundary conditions

The spectral determinant of the Schr?dinger operator ( - Δ + V(x)) on a graph is computed for general boundary conditions. (Δ is the Laplacian and V(x) is some potential defined on the graph). Applications to restricted random walks on graphs are discussed. Received 9 July 2001     

Energy landscapes, lowest gaps, and susceptibility of elastic manifolds at zero temperature

We study the effect of an external field on (1 + 1) and (2 + 1) dimensional elastic manifolds, at zero temperature and with random bond disorder. Due to the glassy energy landscape the configuration of a manifold changes often in abrupt, “first order”-type of large jumps when the field is applied. First the scaling behavior of the energy gap between the global energy minimum and the next lowest minimum of the manifold is considered, by employing exact ground state calculations and an extreme statistics argument. The scaling has a logarithmic prefactor originating from the number of the minima in the landscape, and reads ΔE ₁∼L ^θ[ln(L _z L ^{- ζ})]^-1/2, where ζ is the roughness exponent and θ is the energy fluctuation exponent of the manifold, L is the linear size of the manifold, and L_z is the system height. The gap scaling is extended to the case of a finite external field and yields for the susceptibility of the manifolds ∼L ^{2D + 1 - θ}[(1 - ζ)ln(L)]^1/2. We also present a mean field argument for the finite size scaling of the first jump field, h ₁∼L ^{d - θ}. The implications to wetting in random systems, to finite-temperature behavior and the relation to Kardar-Parisi-Zhang non-equilibrium surface growth are discussed. Received December 2000 and Received in final form April 2001     

High frequency sound and the boson peak in amorphous silica

We present the results of extensive molecular dynamics computer simulations in which the high frequency dynamics of silica, i.e. for frequencies ν > 0.5 THz, is investigated in the viscous liquid state as well as in the glass state. We characterize the properties of high frequency sound modes by analyzing J _l(q,ν) and J _t(q,ν), the longitudinal and transverse current correlation function, respectively. For wave-vectors q > 0.4 ?^-1 the spectra are sitting on top of a flat background. The dynamic structure factor S(q,ν) exhibits for q > 0.23 ?^-1 a boson peak which is located nearly independent of q around 1.7 THz and for which the intensity scales approximately linearly with temperature. We show that the low frequency part of the boson peak is mainly due to the elastic scattering of transverse acoustic modes with frequencies around 1 THz. The strength of this scattering depends on q and is largest around q = 1.7 ?^-1, the location of the first sharp diffraction peak in the static structure factor. By studying S(q,ν) for different system sizes we show that strong finite size effects are present in the low frequency part of the boson peak in that for small systems part of its intensity is missing. We discuss the consequences of these finite size effects for the structural relaxation. Received 27 June 2000 and Received in final form 9 January 2001     

The 130Nd↦130Pr↦130Ce decay chain revisited

An investigation of low-lying energy levels of ¹³⁰Pr and ¹³⁰Ce has been made via β-decay. The radioactive parent nuclei were produced via ^94,96Mo + ⁴⁰Ca reactions at 6.8 MeV/nucleon and transported by a He-jet system. Gamma-γ-t, γ-X-t, γ-e^--t coincidence measurements were performed. Internal conversion coefficients have been measured with a magnetic spectrometer. The new β-decay half-life of ¹³⁰Nd has been determined to be 21(3) s. A partial level scheme of ¹³⁰Pr at low-spin has been constructed. The β-decay of ¹³⁰Pr to ¹³⁰Ce suggests the existence of three β-instable isomeric states in ¹³⁰Pr, while only one half-life T _1/2 = 40(4) s has been measured. Based on the present work and low-lying excited states in neighbouring odd-mass nuclei, the spins and parities of isomeric states in ¹³⁰Pr are proposed to be 2⁺, (4,5)⁺ and (7,8^±). The ground state in ¹³⁰Pr is still undetermined. Received: 20 August 2001 / Accepted: 6 November 2001     

Random quantum magnets with broad disorder distribution

We study the critical behavior of Ising quantum magnets with broadly distributed random couplings (J), such that P(ln J) ∼ | ln J|^{-1 - α}, α > 1, for large | ln J| (Lévy flight statistics). For sufficiently broad distributions, α < , the critical behavior is controlled by a line of fixed points, where the critical exponents vary with the Lévy index, α. In one dimension, with = 2, we obtained several exact results through a mapping to surviving Riemann walks. In two dimensions the varying critical exponents have been calculated by a numerical implementation of the Ma-Dasgupta-Hu renormalization group method leading to ≈ 4.5. Thus in the region 2 < α < , where the central limit theorem holds for | ln J| the broadness of the distribution is relevant for the 2d quantum Ising model. Received 6 December 2000 and Received in final form 22 January 2001     

Vertically shaken column of spheres. Onset of fluidization

The onset of surface fluidization of granular material in a vertically vibrated container, z = A cosωt , is studied experimentally. Recently, for a column of spheres it has been theoretically found (see T. P?schel, T. Schwager, C. Salue na, Phys. Rev. E 62, 1361 (2000)) that the particles lose contact if a certain condition for the acceleration amplitude ≡Aω²/g = f (ω) holds. This result is in disagreement with other findings where the criterion = = const was found to be the criterion of fluidization. We show that for a column of spheres a critical acceleration is not a proper criterion for fluidization and compare the results with theory. Received 21 August 2000 and Received in final form 30 October 2000     

Beta-decay of the N = Z nucleus 72Kr

The beta-decay of the N = Z, even-even nucleus ⁷²Kr has been studied at the ISOLDE PSB facility at CERN. Measurements of βγ and βγγ coincidences have enriched the decay scheme of the daughter nucleus ⁷²Br with 27 new low spin levels. A more precise half-life of T _1/2 = 17.1(2) s has been determined. Strong feeding to the ⁷²Br ground state is established yielding an unambiguous J ^π = 1⁺ assignment for this state. Candidates for the ⁷²Br g.s. wave function are discussed in the framework of a self-consistent deformed mean-field calculation with SG2 Skyrme force and pairing correlations. A search for beta-delayed particle emission was made and an upper limit of 10^-6 for this decay branch obtained. The cumulated experimental level density of 1⁺ states has been fitted with the constant temperature formula. The comparison indicates that most likely all 1⁺ levels up to 1.2 MeV have been observed in this investigation. The corresponding nearest-neighbour level spacing does not follow a Poisson distribution. The Gamow-Teller strength distribution is compared, in terms of nuclear deformation, with different calculations made in the framework of the quasiparticle random phase approximation. Received: 7 February 2002 / Accepted: 31 October 2002 / Published online: 6 March 2003 RID="a" ID="a"e-mail: borge@pinar2.csic.es RID="b" ID="b"Present address: Centre d' Etudes Nucléaires de Bordeaux-Gradignan, Le Haut Vigneau, F-33175 Gradignan Cedex, France. RID="c" ID="c"Present address: University Mentouri, 25000 Constantine, Algeria. Communicated by J. ?yst?     

Neighborhood preferences in random matching problems

We consider a class of random matching problems where the distance between two points has a probability law which, for a small distance l, goes like l^r. In the framework of the cavity method, in the limit of an infinite number of points, we derive equations for p_k, the probability for some given point to be matched to its kth nearest neighbor in the optimal configuration. These equations are solved in two limiting cases: r = 0 -- where we recover p _k = 1/2^k, as numerically conjectured by Houdayer et al. and recently rigorously proved by Aldous -- and r→ + ∞. For 0 < r < + ∞, we are not able to solve the equations analytically, but we compute the leading behavior of p_k for large k. Received 14 February 2001     

A cluster Monte Carlo algorithm for 2-dimensional spin glasses

A new Monte Carlo algorithm for 2-dimensional spin glasses is presented. The use of clusters makes possible global updates and leads to a gain in speed of several orders of magnitude. As an example, we study the 2-dimensional ±J Edwards-Anderson model. The new algorithm allows us to equilibrate systems of size 100² down to temperature T = 0.1. Our main result is that the correlation length diverges as an exponential ( ξ∼e ^2βJ) and not as a power law as T↦T _c = 0. Received 10 January 2001 and Received in final form 29 May 2001     

Low-spin states of doubly odd 182Au

Low-lying states in the odd-odd light gold isotope ¹⁸²Au have been populated by the β⁺/EC decay of the ¹⁸²Hg nuclei. Level energies, spin and parity values were determined using on-line γ-ray and e^- spectroscopy measurements. No isomeric state with a long half-life was found in the ¹⁸²Au nucleus. Spin and parity I ^π = 2⁺ can be very likely assigned to the ¹⁸²Au ground state. Received: 19 December 2000 / Accepted: 28 February 2001     

Ground-state spin of 59Mn

Beta-decay of ⁵⁹Mn has been studied at PSB-ISOLDE, CERN. The intense and pure Mn beam was produced using the Resonance Ionization Laser Ion Source (RILIS). Based on the measured β-decay rates the ground-state spin and parity are proposed to be J ^π = 5/2^-. This result is consistent with the systematic trend of the odd-A Mn nuclei and extends the systematics one step further towards the neutron drip line. Received: 17 November 2000 / Accepted: 16 February 2001