Numerical study of local and global persistence in directed percolation

The local persistence probability P _l (t) that a site never becomes active up to time t, and the global persistence probability P _g (t) that the deviation of the global density from its mean value does not change its sign up to time t are studied in a (1+1)-dimensional directed percolation process by Monte-Carlo simulations. At criticality, starting from random initial conditions, P _l (t) decays algebraically with the exponent . The value is found to be independent of the initial density and the microscopic details of the dynamics, suggesting is an universal exponent. The global persistence exponent is found to be equal or larger than . This contrasts with previously known cases where . It is shown that in the special case of directed-bond percolation, P _l (t) can be related to a certain return probability of a directed percolation process with an active source (wet wall). Received: 15 December 1997 / Revised: 6 April 1998 / Accepted: 29 May 1998     

On charged mesoscopic metallic bubbles

We investigate the existence of stable charged metallic bubbles using the shell correction method. We find that for a given mesoscopic system of n atoms of a given metal and (positive) elementary charges, a metallic bubble turns out to have a lower total energy than a compact spherical cluster, whenever the charge number q is larger than a critical charge number q_c. For a magic number (n-q) of free electrons, the spherical metallic bubble may become stable against fission. Received: 17 November 1997 / Revised: 28 May 1998 / Accepted: 20 July 1998     

Comparing mean field and Euclidean matching problems

Combinatorial optimization is a fertile testing ground for statistical physics methods developed in the context of disordered systems, allowing one to confront theoretical mean field predictions with actual properties of finite dimensional systems. Our focus here is on minimum matching problems, because they are computationally tractable while both frustrated and disordered. We first study a mean field model taking the link lengths between points to be independent random variables. For this model we find perfect agreement with the results of a replica calculation, and give a conjecture. Then we study the case where the points to be matched are placed at random in a d-dimensional Euclidean space. Using the mean field model as an approximation to the Euclidean case, we show numerically that the mean field predictions are very accurate even at low dimension, and that the error due to the approximation is O(1/d ² ). Furthermore, it is possible to improve upon this approximation by including the effects of Euclidean correlations among k link lengths. Using k=3 (3-link correlations such as the triangle inequality), the resulting errors in the energy density are already less than at . However, we argue that the dimensional dependence of the Euclidean model's energy density is non-perturbative, i.e., it is beyond all orders in k of the expansion in k-link correlations. Received: 1st December 1997 / Revised: 6 May 1998 / Accepted: 30 June 1998     

Is NaI soluble in water clusters?

clusters (solvents being , or ) have been studied by resonance enhanced two photons ionization, leading to the detection of clusters. When water is the solvent, large clusters up to n>50 can be observed, whereas for and no clusters larger than 10 could be evidenced. Because the first step in the ionization process is the excitation from the ground solvated () ion pair state to a covalent excited state, the differences in the cluster size distribution for different solvent may be interpreted as a difference in cluster structures leading to a difference in the charge separation in the ground state. Received: 30 September 1997 / Revised in final form: 30 October 1997 / Accepted: 30 October 1997     

Can we rationalize the structure of small silicon-carbon clusters?

A theoretical study of clusters with using density functional theory is presented. Tests of various functionals demonstrate that local spin density approximation (LSDA) is the most adequate functional for the study of these systems. Structures, vibrational frequencies, and IR intensities of the lowest energy isomer of the studied clusters obtained using LSDA are described, and the unusual properties of the Si-C clusters are discussed. A quantitative analysis of the obtained structures was carried out, and relations between the coordinations, interatomic distances, and angles observed in the Si-C clusters were obtained through introduction of the notion of coordination. This analysis also shows that the carbon atoms mainly exhibit sp and sp² hybridizations, and that a majority of silicon atoms do not hybridize. This study is the fi rst step of the implementation of a semi-empirical potential, which would describe the moderately small Si-C clusters. Received: 20 October 1997 / Received in final form: 16 December 1997 / Accepted: 17 December 1997     

Simulation of small positively charged MgO clusters and study of their electronic densities

With the help of ab initio methods the clusters [(MgO)₁₃Mg] ^Q+ are simulated for Q = 0, 1, 2. Then, vacancy clusters [(MgO)₁₂Mg₂] ^Q+ obtained by removing one oxygen atom are computed for Q running from 0 to 4. These clusters exhibit a slight sphericity and generally shorter interatomic distances than in the crystal. The electronic densities variations are studied in function of Q. In particular, it is observed that the electronic density in the oxygen vacancy goes to a maximum when Q = 2. The ionisation potentials vary from approximately 4 to 14 eV when Q varies from 0 to 3, with a more rapid increase from Q = 1 to Q = 2. The stability study of vacancy clusters show that they experience a phase transition when their charge becomes equal to 2, in accordance with the features mentioned above. Received 14 September 1999 and Received in final form 2 December 1999     

Aqueous mixtures of spherical and rodlike (flexible) macroparticles: structure and dynamics of latex spheres in saltfree solutions

This paper resumes light scattering investigations of saltfree aqueous solutions of two component mixtures of charged spheres by extending those measurements to systems in which one component is replaced by essentially stiff rodlike particles. In a second step of investigations these were replaced by linear flexible particles. Fd-virus particles (length l=883 nm) or macromolecules of NaPSS of four different contour lengths have been used as representatives. Mostly the concentration of latex spheres was fixed at 0.02 Vol%. The concentration of the other component was varied over a wide range. Concerning the scattering intensity, the contribution of the latex spheres dominates, in particular in the systems containing NaPSS particles. This simplifies the interpretation of data considerably. A rearrangement of the spheres is observed, depending on the shape of the other sort of particles. These conclusions can be drawn from the shift of measured static structure factor with concentration c. A power law is found for the q-value of the maximum. The exponent depends on the properties of the second component. For the lower molecular weight (MW) samples of NaPSS below a critical concentration, the exponent is smaller than 1/3, decreasing the more the smaller the MW of the samples is. A tentative explanation in terms of charge number of NaPSS particles is given. The short time dynamics has been explored too. From the data a “dynamically determined structure factor” can be derived, that can be compared with the measured static structure factor. Good (fd) and fair (NaPSS) agreement is obtained respectively. Only at small wavenumbers below the maximum of deviations occur which increase with concentration; they are consistent with hydrodynamic interaction. Received 30 July 1998 and Received in final form 14 December 1998     

Fermi liquid theory: a renormalization group approach

We show how Fermi liquid theory results can be systematically recovered using a renormalization group (RG) approach. Considering a two-dimensional system with a circular Fermi surface, we derive RG equations at one-loop order for the two-particle vertex function in the limit of small momentum () and energy () transfer and obtain the equation which determines the collective modes of a Fermi liquid. The density-density response function is also calculated. The Landau function (or, equivalently, the Landau parameters F _l ^s and F _l ^a ) is determined by the fixed point value of the -limit of the two-particle vertex function (). We show how the results obtained at one-loop order can be extended to all orders in a loop expansion. Calculating the quasi-particle life-time and renormalization factor at two-loop order, we reproduce the results obtained from two-dimensional bosonization or Ward Identities. We discuss the zero-temperature limit of the RG equations and the difference between the Field Theory and the Kadanoff-Wilson formulations of the RG. We point out the importance of n-body () interactions in the latter. Received: 27 June 1997 / Received in final form: 17 December 1997 / Accepted: 26 January 1998     

Electronic structural and magnetic properties of cadmium chalcogenide beryllosilicate sodalites

Density functional self-consistent spin-polarized calculations with the Discrete Variational Method were performed to obtain the electronic structures of cadmium chalcogenide beryllosilicate sodalites Cd₈[BeSiO₄]₆Z₂ and their bulk materials CdZ (Z = S, Se, Te). Similar as their bulk materials, these sodalites are also semiconductors. From their density of states and charge distributions, it was found that there is greater localization of the electron density in the sodalites compared with that of the bulk. The band gaps in their bulk compounds are different from those in the sodalite structures due to the electrons of Si, Be and O filled in. Different from their bulk materials, the d electrons of Cd play an important role to form an unseparated valence band with all orbitals of other elements. The calculated magnetic moments of these three materials are very small since all d atomic orbitals are fully occupied. Received: 28 March 1997 / Revised: 18 July 1997 / Accepted: 9 September 1997     

Ionization of metal clusters by ions in the Fermi velocity range

We simulate excitation of metal clusters by highly charged, energetic ions, analyzing electron emission in terms of discrete ionization probabilities. Our test case is the collision of on the cluster at velocities around the electronic Fermi velocity of bulk sodium. The calculations are performed with a density-functional approach, using the time-dependent local density approximation. We find that ionization takes place on an extremely short time scale of less than 5 fs. The preferred final charge state depends sensitively on the impact parameter. High ionization can easily be achieved in sufficiently close collisions. Direct trapping through the by-passing ion is found to be of little importance at the velocities considered. Received: 28 July 1997 / Received in final form: 23 December 1997 / Accepted: 8 January 1998     

Atomic beam deflection by coherent momentum transfer and the dependence on weak magnetic fields

The deflection of Ne atoms in the metastable state ³ P ₂ by coherent transfer of the momenta of 4 or 8 photons is demonstrated, based on the technique developed for coherent population transfer with delayed pulses (STIRAP). After deflection the intensity profile of the isotope of mass 20 is fully seperated from that for the undeflected atoms of mass 22. It is furthermore shown, how the interplay of Larmor precession of the electronic magnetic moment and the sequential deflection in two spatially separated zones can be used to measure the magnetic field, integrated over the flight-path between the transfer zones. Received: 1 October 1997 / Revised: 22 December 1997 / Accepted: 11 March 1998     

Electronic properties and Compton profiles of molybdenum dichalcogenides

We present the first ever experimental Compton profiles of molybdenum dichalcogenides (MoX₂; X=S and Te) using 20 Ci ¹³⁷Cs Compton spectrometer. To interpret our experimental data, we have computed the theoretical profiles, energy bands and density of states using linear combination of atomic orbitals method in the framework of density functional theory and its hybridisation with Hartree Fock. The energy bands and density of states using full potential linearised augmented plane wave method have also been computed. Both theories show the existence of the indirect band gap. In addition, the relative nature of bonding is explained in terms of equal-valence-electron-density profiles and valence band charge densities.     

Study of the O(N) linear \sigma model at finite temperature using the 2PPI expansion

We show that a new expansion, which sums seagull and bubble graphs to all orders, can be applied to the O(N) linear -model at finite temperature. We prove that this expansion can be renormalized with the usual counterterms in a mass independent scheme and that Goldstone's theorem is satisfied at each order. At the one loop order of this expansion, the Hartree result for the effective potential (daisy and superdaisy graphs) is recovered. We show that at one loop 2PPI order, the self-energy of the -meson can be calculated exactly and that diagrams are summed beyond the Hartree approximation. Received: 22 March 2001 / Revised version: 3 September 2001 / Published online: 14 December 2001     

Evolution from BCS superconductivity to Bose condensation: analytic results for the crossover in three dimensions

We provide an analytic solution for the mean-field equations and for the relevant physical quantities at the Gaussian level, in terms of the complete elliptic integrals of the first and second kinds, for the crossover problem from BCS superconductivity to Bose-Einstein condensation of a three-dimensional system of free fermions interacting via an attractive contact potential at zero temperature. This analytic solution enables us to follow the evolution between the two limits in a particularly simple and transparent way, as well as to verify the absence of singularities during the evolution. Received: 9 May 1997 / Revised: 4 August 1997 / Accepted: 6 November 1997     

Electrostatics of DNA-cationic lipid complexes: isoelectric instability

We propose a Poisson-Boltzmann electrostatic theory for DNA/cationic lipid complexes modeled as a stack of aligned DNA chains intercalated with lipid bilayers, a structure suggested by the recent X-ray synchrotron studies of Radler et al. Poisson-Boltzmann theory is shown to predict that the isoelectric point - where the DNA and cationic lipid charges are in balance - is unstable against absorption of extra DNA or lipid material. The instability is caused by the entropy gain obtained following the release of small ions inside the complex and is manifested by singular behavior of the rod-rod spacing near the isoelectric point. We apply the theory to a discussion of the results of Radler et al. Received: 21 July 1997 / Received in final form: 19 January 1998 /Accepted: 5 March 1998     

Cavitation in superfluid helium-4 at low temperature

We have studied the nucleation of bubbles in pure superfluid helium-4 at temperatures down to 65 mK. We have found that the nucleation is a stochastic process, and that at temperatures below 600 mK the nucleation rate is independent of temperature. These results are consistent with the assumption that the nucleation takes place via quantum tunneling. Received: 15 November 1997 / Received in final form: 19 December 1997 / Accepted: 22 January 1998     

Sonic stop-bands for cubic arrays of rigid inclusions in air

Extensive band structures have been computed for cubic arrays of rigid spheres and cubes in air. Complete stop bands are obtained for the face-centered-cubic (fcc) structure; however, there is no gap for the body-centered-cubic (bcc) and simple-cubic (sc) structures. These gaps start opening up for a filling fraction of (27%) for spherical (cubic) inclusions and tend to increase with the filling fraction, exhibiting a maximum at the close-packing. We also propose a tandem structure that allows the achievement of an ultrawideband filter for environmental or industrial noise in the desired frequency range. This work is motivated by the recent experimental measurement of sound attenuation on the sculpture, by Eusebio Sempere, exhibited at the Juan March Foundation in Madrid (Nature 378, 241 (1995)) and complements the corresponding theoretical work (Appl. Phys. Lett. 70, 3218 (1997)). Received: 24 October 1997 / Revised: 1 December 1997 and 26 January 1998 / Accepted: 6 March 1998     

Cesium ordering and electron localization-delocalization phenomena in the quasi-one-dimensional diphosphate tungsten bronzes: Cs1‒xP8W8O40

We present a structural investigation of the family of quasi-one-dimensional (quasi-1D) conductors, which exhibit intriguing charge transport properties where, for x small, the conductivity exhibits a crossover from a semiconducting to a metallic like regime when the temperature decreases. In these materials the double zig-zag chains, together with the diphosphate groups, delimit channels which are partially filled with the ions. It is found, from an X-ray diffuse scattering investigation, that at room temperature the ions are locally ordered on a lattice of well-defined sites in the channel direction and not ordered between neighboring channels. These ions form 1D incommensurate concentration waves whose periodicity depends on the stoichiometry. In upon cooling, the intrachannel order increases significantly, and an interchannel order between the 1D concentration waves develops. But, probably because of kinetic effects, no tridimensional (3D) long range order of the ions is achieved at low temperature. The 3D low-temperature local order has been determined and it is found that the phase shift between the concentration waves minimizes their Coulomb repulsions. This local order is increasingly reduced as the Cs concentration diminishes. We interpret the intriguing features of the electrical conductivity in relationship with the thermal evolution of the Cs ordering effects. We suggest that in , for x small, a localization-delocalization transition of the Anderson type occurs due to the thermal variation of the Cs disorder. When x increases, the enhancement of the disorder leads to a localization of the electronic wave function in the whole temperature range measured. Finally, and probably because of the disorder, no charge density wave instability is revealed by our X-ray diffuse scattering investigation. Received: 10 October 1997 / Received in final form: 11 December 1997 / Accepted: 16 December 1997     

Multiple conformations in polyampholytes

We study the configurational statistics of a ring polyampholyte chain made of N randomly charged monomers with elementary charge .To a large extent, the overall structure of a polyampholyte is controlled by a total sum Q of all charges. When the total charge is smaller than , the polyampholyte has a compact globular structure. At charges larger than , the configuration has the form of a ring of small globules (beads) connected by strings. Between Q₁ and Q₂ we find a remarkable diversity of meta-stable configurations having the shapes of irregular clusters of small globules connected by the strings. We estimate the number of these configurations and the energy barriers between them. Between Q₁ and Q₂, the minimum energy configurations are completely controlled by randomness in the charge distribution along the chain. There are hysteresis effects in the shapes of the clusters. As the total charge increases, the linearly extended configurations become dynamically more preferable. When the charge decreases, the circular shapes are preferred. We remark on the probable connection with the multiple phase transitions observed in polyampholyte gels. Received: 10 July 1997 / Accepted: 13 October 1997