Energetics of carbon nanotubes

We have investigated the energetics of carbon nanotubes. Calculations have been performed by using the empirical many-body potential energy function developed by Tersoff for carbon. Received: 30 March 1998 / Accepted: 28 July 1998     

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     

Filling carbon nanotubes with metals by the arc-discharge method: the key role of sulfur

Various filled carbon nanotubes have recently been successfully produced by the arc-discharge method by doping a 99.4% graphite anode with a transition metal like Cr, Ni, a rare earth like Yb, Dy, or a covalent element like S, Ge. In this work, the structural characteristics of these encapsulated nanowires were studied by High Resolution Transmission Electron Microscopy and their chemical composition was investigated using Electron Energy-Loss Spectroscopy with high spatial resolution: this analysis mode provides elemental concentration profiles across or along the filled nanotubes. Except in the case of Ge for which only pure Ge fillings were identified, surprising amounts of sulfur, which was present as an impurity ( 0.25%) in the graphite rods, were found within numerous filling materials. When using high purity carbon rods, no filled nanotube was obtained. We chose the case of Cr to clearly evidence that the addition of sulfur in catalytic quantity is responsible for the formation of filled nanotubes, including sulfur free encapsulated nanowires. A growth mechanism based on a catalytic process involving three elements, i.e. carbon, a metal and sulfur, and taking into account the experimental results is proposed. Received: 20 January 1998 / Received in final form and accepted: 9 April 1998     

Specific heat jump in non-Fermi superconductors

We derive the jump in the specific heat at T=T _c for a superconductor in a non-Fermi liquid model. We took into consideration the two possible limits in this problem: the spin-charge separation model for a Fermi liquid and the usual non-Fermi liquid model which satisfies the homogeneity relation for the spectral function , ). We also derive the order parameter behavior for these two cases in the vecinity of the critical temperature. Received: 25 January 1998 / Revised: 25 March 1998 / Accepted: 25 March 1998     

Elliptic curves from finite order recursions or non-involutive permutations for discrete dynamical systems and lattice statistical mechanics

We study birational mappings generated by matrix inversion and permutations of the entries of matrices. For q=3 we have performed a systematic examination of all the birational mappings associated with permutations of matrices in order to find integrable mappings and some finite order recursions. This exhaustive analysis gives, among 30 462 classes of mappings, 20 classes of integrable birational mappings, 8 classes associated with integrable recursions and 44 classes yielding finite order recursions. An exhaustive analysis (with a constraint on the diagonal entries) has also been performed for matrices: we have found 880 new classes of mappings associated with integrable recursions. We have visualized the orbits of the birational mappings corresponding to these 880 classes. Most correspond to elliptic curves and very few to surfaces or higher dimensional algebraic varieties. All these new examples show that integrability can actually correspond to non-involutive permutations. The analysis of the integrable cases specific of a particular size of the matrix and a careful examination of the non-involutive permutations, shed some light on the integrability of such birational mappings. Received: 9 February 1998 / Revised: 13 March 1998 / Accepted: 17 March 1998     

Mixed spin transverse Ising model with longitudinal random crystal field interactions

The effect of a longitudinal random crystal field interaction on the phase diagrams of the mixed spin transverse Ising model consisting of spin-1/2 and spin-1 is investigated within the finite cluster approximation based on a single-site cluster theory. In order to expand a cluster identity of spin-1, we transform the spin-1 to spin-1/2 representation containing Pauli operators. We derive the state equations applicable to structures with arbitrary coordination number N. The phase diagrams obtained in the case of a honeycomb lattice (N=3) and a simple-cubic lattice (N=6), are qualitatively different and examined in detail. We find that both systems exhibit a variety of interesting features resulting from the fluctuation of the crystal field interactions. Received: 13 February 1998 / Accepted: 17 March 1998     

Optical conductivity of the Bechgaard salts: the sum rules revisited

The validity of the optical sum rules has been addressed eversince and was always matter of debate. Particularly controversial is the proof that the partial sum rules can be extended to both optical conductivity and energy loss function. We show in this paper that for both transverse (optical conductivity) and longitudinal (energy loss function) absorption processes the corresponding sum rule can be theoretically established and through appropriate conditions for the integration limits exactly verified. We also focus our attention on the one-dimensional case within the microscopic Hubbard model. An application of these concepts to the quasi one-dimensional systems, for which we have chosen the organic (TMTSF)₂PF₆ material, will also be presented. Received: 19 December 1997 / Received in final form: 9 March 1998 / Accepted: 23 March 1998     

Random-phase approximation for the grand-canonical potential of composite fermions in the half-filled lowest Landau level

We reconsider the theory of the half-filled lowest Landau level using the Chern-Simons formulation and study the grand-canonical potential in the random-phase approximation (RPA). Calculating the unperturbed response functions for current- and charge-density exactly, without any expansion with respect to frequency or wave vector, we find that the integral for the ground-state energy converges rapidly (algebraically) at large wave vectors k, but exhibits a logarithmic divergence at small k. This divergence originates in the k^-2 singularity of the Chern-Simons interaction and it is already present in lowest-order perturbation theory. A similar divergence appears in the chemical potential. Beyond the RPA, we identify diagrams for the grand-canonical potential (ladder-type, maximally crossed, or a combination of both) which diverge with powers of the logarithm. We expand our result for the RPA ground-state energy in the strength of the Coulomb interaction. The linear term is finite and its value compares well with numerical simulations of interacting electrons in the lowest Landau level. Received: 19 February 1998 / Revised: 25 March 1998 / Accepted: 17 April 1998     

Mechanisms of CVD diamond nucleation and growth on mechanically scratched Si(100) surfaces

The diamond nucleation has been studied on scratched Si(100) both by surface analyses (XPS, AES, ELS) and microstructural probes (AFM, SEM). Two pathways for diamond formation and growth are detected: A seeding pathway occurs by direct growth from part of diamond seeds left by the mechanical pretreatment. Not all of these seeds however are prone to diamond growth as they can be either dissolved or carburized. A nucleation pathway occurs through a stepwise process including the formation of extrinsic (pretreatment) or intrinsic (in situ) nucleation sites, followed by formation of carbon-based precursors. It is believed that nucleation sites could be either grooves of scratching lines or protrusions produced by etching-redeposition. The size of these protrusions is not larger than 100 nm. On top of these protrusions as well as on the bare substrate, a thin layer of silicon carbide rapidly forms and DLC carbon likely. This complex process on top of protrusions may constitute carbon-based embryos for further diamond nucleation. Received 21 December 1998     

Ascending air bubbles in protein solutions

We report measurements of the ascending velocity of air bubbles in protein (bovine serum albumin) solutions. We show that, because of the protein molecules adsorbed on their surface, the terminal ascending velocity of bubbles is strongly reduced compared to the terminal velocity in pure water: protein- covered bubbles behave hydrodynamically as solid spheres. From the evolution of the ascending velocity with time, we can derive the amount of protein needed to immobilize the bubble interface which is 0.5 mg m^-2, i.e. only one fifth of the amount adsorbed at equilibrium in the range of used bulk concentrations. Received: 6 March 1998 / Revised and accepted: 6 May 1998     

Fringe contrast in three grating Mach-Zehnder atomic interferometers

Several three-grating Mach-Zehnder atomic interferometers have been built and operated in recent years but no general theory of the contrast of the fringes produced by these apparatus is available. The purpose of this paper is to develop this theory, based on the Fresnel-Kirchoff approximate treatment of diffraction. Such a theory has been developed by Turchette et al. [JOSA B 9, 1601 (1992)] but because the necessary multiple integrals were evaluated in a purely numerical way, this treatment was not fully general. We show here how to reduce the computation by analytic means and we are thus able to calculate the contrast with a modest numerical effort. Moreover, we get a simple insight of the contrast reduction related to several defects of a real apparatus. We apply our calculations to existing interferometers as well as to an apparatus working with lithium which is under construction in our laboratory. Received: 24 April 1998 / Revised: 25 October 1998 / Accepted: 11 December 1998     

Stability of the Haldane state against the antiferromagnetic-bond randomness

Ground-state phase diagram of the one-dimensional bond-random S=1 Heisenberg antiferromagnet is investigated by means of the loop-cluster-update quantum Monte-Carlo method. The random couplings are drawn from a rectangular uniform distribution. We found that even in the case of extremely broad bond distribution, the magnetic correlation decays exponentially, and the correlation length is hardly changed; namely, the Haldane phase continues to be realized. This result is accordant with that of the exact-diagonalization study, whereas it might contradict the conclusion of an analytic theory founded in a power-law bond distribution instead. The latter theory predicts that a second-order phase transition occurs at a certain critical randomness, and the correlation length diverges for sufficiently strong randomness. Received: 31 March 1998 / Revised and Accepted: 7 July 1998     

Crystallized vortex crystals

Numerical simulations of the equations of motion of 300 charged particles confined to a plane with an additional magnetic field orthogonal to the plane reproduce recently observed self-organization of non-neutral plasmas into a small number of interacting vortices. In the presence of damping we observe crystallized vortices, i.e. vortices with regular internal structure. We also observe crystallized vortex crystals, i.e. geometric patterns of crystallized vortices. Fractal vortex arrangements are investigated and found to be stable. Our results are relevant for quantum dots and artificial atoms. Received: 24 February 1998 / Revised: 4 March 1998 / Accepted: 4 May 1998     

Fragmentation of fast positive and negative C ions in collisions with rare gas atoms

The fragmentation of anions and cations resulting from 50 keV collisions with rare gas targets is studied. Positive ion fragment patterns are recorded, and dramatic changes in these patterns are observed as a function of target atom number. The fragment pattern dependence on the target atom size is investigated within a simple model, normally used for stopping power calculations. Fair agreement is obtained between calculated and experimental spectra. From these comparisons we conclude that the range of the screened atomic potentials, as e.g., the Thomas-Fermi potential, is an essential parameter in the collisional induced fragmentation process. Received: 13 February 1998 / Revised: 27 October 1998 / Accepted: 29 October 1998     

Field theoretical calculation of the specific heat exponent for a classical N-vector model in a random external field

We calculate using diagrammatic perturbation theory in the two-loop approximation, the specific heat exponent for the classical N-vector model in a random external field for spatial dimension (D) lying between four and six. The calculation supports the modified hyperscaling , where is the correlation length exponent. Received: 18 March 1998 / Revised: 17 April 1998 / Accepted: 21 April 1998     

Influence of hydrodynamics on the dynamics of a homopolymer

We present an analytical approach of the dynamics of a polymer when it is quenched from a solvent into a good or bad solvent. The dynamics is studied by means of a Langevin equation, first in the absence of hydrodynamic effect, then taking into account the hydrodynamic interactions with the solvent. The variation of the radius of gyration is studied as a function of time. In both cases, for the first stage of collapse or swelling, the evolution is described by a power law with a characteristic time proportional to N ^4/3 (N), where N is the number of monomers, without (with) hydrodynamic interactions. At larger times, scaling laws are derived for the diffusive relaxation time. Received: 10 March 1998 / Received in final form: 15 September 1998 / Accepted: 25 September 1998     

Some remarks on Yang-Baxter algebras

We point out the existence of an alternative algebraic structure in Yang-Baxter algebra with trigonometric R-matrix, which appears to be the generalization of the Yangian in Yang-Baxter algebras with rational R-matrix and which is described most naturally by q-commutators. Some properties are presented, in particular in the case of the well-known symmetric six-vertex model. Received: 13 February 1998 / Revised: 16 March 1998 / Accepted: 17 April 1998     

The new identity for the scattering matrix of exactly solvable models

We discovered a simple quadratic equation, which relates scattering phases of particles on Fermi surface. We consider one-dimensional Bose gas and XXZ Heisenberg quantum spin chain. Received: 4 December 1997 / Accepted: 17 March 1998     

Squeezed two-mode lasers without and with inversion

On the basis of the nondegenerate quantum-beat laser model, we introduce a coherent field which drives the transition between the upper lasing level and an auxiliary level. We demonstrate that such a four-level system can produce squeezed two-mode laser without and with inversion. When the laser is operated well above threshold, the intensity fluctuation in the average mode is reduced below the shot noise with an optimum Mandel parameter Q=- 1/2. At the same time, the noises in the relative amplitude and the relative phase drop to their vaccum noise levels. Furthermore, regardless of inversion, noninversion, and transition between inversion and noninversion, the optimum Mandel Q parameter of Q=- 1/2 is retained when the system operates well above threshold. A simple physical explanation of the squeezing mechanism for two-mode squeezing is given. Received: 22 December 1997 / Revised: 25 March 1998 / Accepted: 9 September 1998     

Long and short range spin-spin interactions in ErBaCuO

Dipolar spin-spin interactions play a crucial role as for the magnetic order in the compounds of the RBa₂Cu₃O_6+x family, (R = Dy, Er, Nd). However, inelastic neutron scattering data observed in ErBa₂Cu₃O₇ can be explained only if exchange interactions in addition to dipolar ones are taken into account. Received: 12 January 1998 / Received in final form: 26 March 1998 / Accepted: 10 April 1998