Dielectric resonances in disordered media

Binary disordered systems are usually obtained by mixing two ingredients in variable proportions: conductor and insulator, or conductor and super-conductor. They present very specific properties, in particular the second-order percolation phase transition, with its fractal geometry and the multi-fractal properties of the current moments. These systems are naturally modeled by regular bi-dimensional or tri-dimensional lattices, on which sites or bonds are chosen randomly with given probabilities. The two significant parameters are the ratio h = σ ₁/σ of the complex conductances, σ and σ ₁, of the two components, and their relative abundances p (or, respectively, 1 - p). In this article, we calculate the impedance of the composite by two independent methods: the so-called spectral method, which diagonalises Kirchhoff's Laws via a Green function formalism, and the Exact Numerical Renormalization method (ENR). These methods are applied to mixtures of resistors and capacitors (R-C systems), simulating e.g. ionic conductor-insulator systems, and to composites constituted of resistive inductances and capacitors (LR-C systems), representing metal inclusions in a dielectric bulk. The frequency dependent impedances of the latter composites present very intricate structures in the vicinity of the percolation threshold. In this paper, we analyse the LR-C behavior of compounds formed by the inclusion of small conducting clusters (“n-legged animals”) in a dielectric medium. We investigate in particular their absorption spectra who present a pattern of sharp lines at very specific frequencies of the incident electromagnetic field, the goal being to identify the signature of each animal. This enables us to make suggestions of how to build compounds with specific absorption or transmission properties in a given frequency domain. Received 16 August 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: laurent.raymond@l2mp.fr RID="b" ID="b"e-mail: steffen.schaefer@l2mp.fr RID="c" ID="c"UMR CNRS 6137     

Enhanced conductivity in ionic conductor-insulator composites: numerical models in two and three dimensions

We describe a two-dimensional (2D) and a three-dimensional (3D) percolation model for ionic conductor-insulator composites such as copper(I) bromide-titanium dioxide (CuBr-TiO₂) or lithium iodide-alumina (LiI-Al₂O₃). These composites present an enhanced conductivity closely related to the insulator concentration. This effect is explained by the formation of highly conducting space charge regions near the phase boundaries which are represented by good conductor bonds. Our numerical model takes into account grain size and correlation effects. The dimension has a leading role for the conduction properties. In the 2D case, the good conductor bonds do not percolate, whatever the insulator concentration, and the maximum conductivity of the composite samples is of the same order as that of the ionic conductor grains. The behavior of the system is very different in the 3D case where, for a large domain of composition, the good conductors percolate through the regions between the conductor grains. For the CuBr-TiO₂ composites the conductivity versus composition curve is bell-shaped. Conversely, in the LiI-Al₂O₃ system, a linear relation between the conductivity and the insulator volume fraction is obtained in the experiments. Our model gives a plausible interpretation of the conductivity in both systems. Received 10 April 2001     

Transmission resonances in magnetic-barrier structures

Quantum transport properties of electrons in simple magnetic-barrier (MB) structures and in finite MB superlattices are investigated in detail. It is shown that there exists a transition of transmission resonances, i.e., from incomplete transmission resonances in simple MB structures consisting of unidentical blocks, to complete transmission resonances in comparatively complex MB structures (, n is the number of barriers). In simple unidentical block arrangements in double- and triple-MB structures we can also obtain complete transmission by properly adjusting parameters of the building blocks according to k_y-value (k_y is the wave vector in y direction). Strong suppression of the transmission and of the conductance is found in MB superlattices which are periodic arrangements of two different blocks. The resonance splitting effect in finite MB superlattices is examined. It is confirmed that the rule (i.e., for n-barrier tunneling the splitting would be (n-1)-fold) obtained in periodic electric superlattices can be extended to periodically arranged MB superlattices of identical blocks through which electrons with tunnel, and it is no longer proper for electrons with k _y <0 to tunnel. Received: 18 August 1997 / Revised: 20 September 1997 / Accepted: 13 October 1997     

Plaquette ground state in the two-dimensional SU(4) spin-orbital model

In order to understand the properties of Mott insulators with strong ground state orbital fluctuations, we study the zero temperature properties of the SU(4) spin-orbital model on a square lattice. Exact diagonalizations of finite clusters suggest that the ground state is disordered with a singlet-multiplet gap and possibly low-lying SU(4) singlets in the gap. An interpretation in terms of plaquette SU(4) singlets is proposed. The implications for LiNiO₂ are discussed. Received 6 July 2000     

Vibrational Feshbach resonances in electron attachment to carbon dioxide clusters

Using a high resolution ( meV) laser photoelectron attachment method, we have studied the formation of (CO ₂) _q ⁻ ions (q = 4−22) in collisions of low energy electrons (1−180 meV) with (CO₂) _N () clusters. The previously reported “zero energy resonance”, observed at much larger electron bandwidths, actually consists of several narrow vibrational Feshbach resonances of the type [(CO ₂) _{N −1}CO which involve a vibrationally-excited molecular constituent ( denotes vibrational mode) and a diffuse electron weakly bound to the cluster by long range forces. The resonances occur at energies below those of the vibrational excitation energies of the neutral clusters [(CO ₂) _{N −1}CO ]; the redshift rises with increasing cluster ion size q by about 12 meV per unit; these findings are recovered by a simple model calculation for the size dependent binding energies. The size distribution in the cluster anion mass spectrum, resulting from attachment of very slow electrons, mainly reflects the amount of overlap of solvation-shifted vibrational resonances with zero energy; the cluster anion size q is identical with or close to that of the attaching neutral cluster. Received 11 January 2000 and Received in final form 10 April 2000     

Random walk statistics on fractal structures

We consider some statistical properties of simple random walks on fractal structures viewed as networks of sites and bonds: range, renewal theory, mean first passage time, etc. Asymptotic behaviors are shown to be controlled by the fractal (¯d) and spectral (¯d) dimensionalities of the considered structure. A simple decimation procedure giving the value of (¯d) is outlined and illustrated in the case of the Sierpinski gaskets. Recent results for the trapping problem, the self-avoiding walk, and the true-self-avoiding walk are briefly reviewed. New numerical results for diffusion on percolation clusters are also presented.     

Noise and conductance in one-dimensional systems

Summary We derive an explicit form for the current correlation function of a Fermi gas in a finite sample at arbitrary degree of degeneracy. The expression so found enables a continuous investigation from diffusive to ballistic transport regimes to be carried out. For degenerate one-dimensional conductors under ballistic regime we find that the noise spectral density exhibits characteristic geometrical resonances and its low-frequency value has the universal formS _I (0)=8e ² KT/h, implying a universal conductanceG=2e ²/h.     

Transport in dispersed ionic conductors: Effect of insulating particle size

Dispersed ionic conductors are random mixtures of a solid salt, e.g. AgI, LiI, with fine particles of an insulating second phase, like Al₂O₃ or SiO₂. These composites can show a dramatic increase in ionic conductivity compared to the pure homogeneous system. Generally, this observation is attributed to an increased conductivity along the internal interface between the conducting salt and the insulating material. In this work a three-component random resistor network (RRN) model for dispersed ionic conductors is reviewed. In the model, the ionic conductor is represented by normally conducting bonds, the insulating material by non-conducting bonds and the interface between the two phases by highly conducting bonds. A special feature of the model is the existence of two critical concentrations of the insulating phase, p′_c and p″_c , for interface percolation and bulk conduction, respectively, where critical transport properties corresponding to conductor/superconductor and conductor/insulator networks are predicted. The model describes satisfactorily the dependence on composition of the conductivity and activation energy of dispersed ionic conductors. Furthermore, the observed effect on the conductivity of the size of dispersed particles can be described qualitatively well by a generalized version of the RRN model, which in addition predicts a sensitive dependence of the critical thresholds on particle size. Non-universality features in the critical exponents for the conductivity are also discussed within a continuum percolation analog of the model.     

A stochastic multi-cluster model of freeway traffic

A stochastic approach based on the Master equation is proposed to describe the process of formation and growth of car clusters in traffic flow in analogy to usual aggregation phenomena such as the formation of liquid droplets in supersaturated vapour. By this method a coexistence of many clusters on a one-lane circular road has been investigated. Analytical equations have been derived for calculation of the stationary cluster distribution and related physical quantities of an infinitely large system of interacting cars. If the probability per time (or p) to decelerate a car without an obvious reason tends to zero in an infinitely large system, our multi-cluster model behaves essentially in the same way as a one-cluster model studied before. In particular, there are three different regimes of traffic flow (free jet of cars, coexisting phase of jams and isolated cars, highly viscous heavy traffic) and two phase transitions between them. At finite values of p the behaviour is qualitatively different, i.e., there is no sharp phase transition between the free jet of cars and the coexisting phase. Nevertheless, a jump-like phase transition between the coexisting phase and the highly viscous heavy traffic takes place both at and at a finite p. Monte-Carlo simulations have been performed for finite roads showing a time evolution of the system into the stationary state. In distinction to the one-cluster model, a remarkable increasing of the average flux has been detected at certain densities of cars due to finite-size effects. Received 17 September 1999     

Cluster formation in mesoscopic systems

Graph-theoretical approach is used to study cluster formation in mesocsopic systems. Appearance of these clusters is due to discrete resonances which are presented in the form of a multigraph with labeled edges. This presentation allows to construct all non-isomorphic clusters in a finite spectral domain and generate corresponding dynamical systems automatically. Results of MATHEMATICA implementation are given and two possible mechanisms of cluster destroying are discussed.     

Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)⁵ for the one-particle Green function in arbitrary dimension. The spectral weight is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented. Received 25 October 1999     

(Li3N)n(n=1—5)团簇结构与性质的密度泛函研究

用密度泛函理论(DFT)的杂化密度泛函B3LYP方法在6-31G*基组水平上对(Li₃N)_n(n=1—5)团簇各种可能的构型进行几何结构优化,预测了各团簇的最稳定结构. 并对最稳定结构的振动特性、成键特性、电荷特性等进行了理论研究. 结果表明,(Li₃N)_n(n=1—5)团簇中N原子的配位数以4,5较多见,Li—Li键长为0.210—0.259nm,Li原子在桥位时Li—N键长为0.185—0.204nm,Li原子在端位时Li—N键长为0.172—0.178nm;团簇中N原子的平均自然电荷为-2.01e,Li原子的平均自然电荷为+0.67e;Li₃N,(Li₃N)₅团簇有相对较高的动力学稳定性. 关键词： 3N)_n(n=1—5)团簇')" href="#">(Li₃N)_n(n=1—5)团簇 密度泛函理论 结构与性质 储氢材料     

Simulating the thermal stability and phase changes of small carbon clusters and fullerenes

The thermal stability, phases and phase changes of small carbon clusters and fullerenes are investigated by constant energy Molecular Dynamics simulations performed over a wide range of temperatures, i.e., from to above the melting point of graphitic carbon. The covalent bonds between the carbon atoms in the clusters are represented by the many-body Tersoff potential. The zero temperature structural characteristics of the clusters, i.e., the minimum energy structures as well as the isomer hierarchy can be rationalized in terms of the interplay between the strain energy (due to the surface curvature) and the number of dangling bonds in the cluster. Minimization of the strain energy opposes the formation of cage structures whereas minimization of the number of dangling bonds favors it. To obtain a reliable picture of the processes experienced by carbon clusters as a function of temperature, both thermal and dynamical characteristics of the clusters are carefully analyzed. We find that higher excitation temperatures are required for producing structural transformations in the minimum energy structures than in higher lying isomers. We have also been able to unambiguously identify some structural changes of the clusters occurring at temperatures well below the melting-like transition. On the other hand, the melting-like transition is interrupted before completion, i.e., the thermal decomposition of the clusters (evaporation or ejection of or units) occurs, from highly excited configurations, before the clusters have fully developed a liquid-like phase. Comparison with experiments on the thermal decomposition of and a discussion of the possible implications of our results on the growth mechanisms leading to the formation of different carbon structures are included. Received: 25 March 1998 / Received in final form: 30 October 1998     

Electronic structure and magnetism in 4d-transition metal clusters

We analyze the stability of magnetic states obtained within the tight-binding model for cubooctahedral (O_h) and icosahedral (I_h) clusters of early 4d (Y, Zr, Nb, Mo, and Tc) transition metals. Several metastable magnetic clusters are identified which suggests the existence of multiple magnetic solutions in realistic systems. A bulk-like parabolic behavior is observed for the binding energy of O_h and I_h clusters as a function of the atomic number along the 4 d-series. The charge transfer on the central atom changes sign, while the average magnetic moments present an oscillatory behavior as a function of the number of d electrons in the cluster. Our results are in agreement with other theoretical calculations. Received: 20 November 1997 / Received in final form: 9 March 1998 / Accepted: 30 March 1998     

Influence of covalence and anion symmetry on the structure of small metal hydroxide clusters: Sodium versus silver hydroxide

An ab initio study of the Na_n(OH)_n, Na_n(OH)_n-1 ⁺, Ag_n(OH)_n, and Ag_n(OH)_n-1 ⁺ clusters with n up to four is presented. The results of this study show that, in accordance with experimental observations, the sodium hydroxide clusters are almost purely ionic, while the Ag-O bond exhibits a significant covalent character. The perturbation caused by the non-spherical OH^- group relatively to an atomic anion, as well as the influence on structures and energies of the covalent character of the metal-oxygen bond are determined. The appearance of metal-metal bonds in the silver hydroxide clusters is also discussed. Finally, the theoretical results obtained on the Na-OH clusters are compared to experimental results available on the dissociation of the Na_n(OH)_n-1 ⁺ clusters. Received 9 August 1999 and Received in final form 1st December 1999     

Effect of deuteration on the electronic and electron-vibrational properties of the organic conductor k-(D8-BEDT-TTF)2[Hg(SCN)2Br]

We present here for the first time polarized reflection spectra and optical conductivity spectra of single crystals of the newly deuterated organic conductor k-(D₈-BEDT-TTF)₂[Hg(SCN)₂Br] at room temperature. The spectral region investigated is 700–40 000 cm⁻¹. We examined the effect of deuteration on electronic and electron-vibrational transitions observed in the spectra. The observed shift of the electron “dimer” transition in the infrared toward lower frequencies upon deuteration is linked with an increase in the interaction between neighboring, mutually perpendicular dimers in the structure of the deuterated crystal. A lowering of the symmetry of the BEDT-TTF molecule is demonstrated in crystals similar to k-(BEDT-TTF)₂[Hg(SCN)₂Br], relative to the symmetry D _2h of the free molecule. We refine the assignment of the spectral features determined by the interaction of electrons with the fully-symmetric intramolecular vibrations of the C=C, C-S, and C-C-H bonds of the BEDT-TTF molecule. Fiz. Tverd. Tela (St. Petersburg) 40, 1595–1598 (September 1998)     

Helicity amplitudes and electromagnetic decays of hyperon resonances

We present results for the helicity amplitudes of the lowest-lying hyperon resonances Y^*, computed within the framework of the Bonn Constituent-Quark model, which is based on the Bethe-Salpeter approach. The seven parameters entering the model were fitted to the best-known baryon masses. Accordingly, the results for the helicity amplitudes are genuine predictions. Some hyperon resonances are seen to couple more strongly to a virtual photon with finite Q² than to a real photon. Other Y^*'s, such as the S₀₁(1670) Λ-resonance or the S₁₁(1620) Σ-resonance, couple very strongly to real photons. We present a qualitative argument for predicting the behaviour of the helicity asymmetries of baryon resonances at high Q².-1     

A Mixed-Transfer-Matrix Method for Simulating Normal Conductor/Perfect Insulator/Perfect Conductor Random Networks

We develop a mixed-transfer-matrix approach for computing the macroscopic conductivity of a three-constituent normal conductor/perfect insulator/perfect conductor random network. This is applied to two-dimensional and three-dimensional samples at a percolation threshold. Such networks are simulated in order to test whether a diluted percolating network of normal conducting bonds remains in the same universality class of critical behavior when a finite fraction of those bonds have been replaced by perfectly conducting bonds. Also tested by such simulations is whether a percolating mixture of normal and perfectly conducting bonds remains in the same universality class of critical behavior when a finite fraction of the normal bonds are replaced by perfectly insulating bonds. These questions are crucial for some recently published exact results which connect the macroscopic electrical and elastic responses of percolating networks.     

Copolymer at a selective interface and two-dimensional wetting: a grand canonical approach

We consider two different problems involving the localization of a single polymer chain: (i) a periodic AB copolymer at a selective fluid-fluid interface, with the upper (resp. lower) fluid attracting A (resp. B) monomers (ii) a homopolymer chain attracted to a hard wall (wetting). Self avoidance is neglected in both models, which enables us to study their localization transition in a grand canonical approach. We recover the results obtained in previous studies via transfer matrix methods. Moreover, we calculate in this way the loop length distribution functions in the localized phase. Some finite size effects are also determined and tested numerically. Received 13 April 2000