Landau diamagnetism within Tsallis thermostatistics and quantum groups

In this study, using the base of coherent states, Landau diamagnetism has been generalized within Tsallis Thermostatistics. As far as we know, this is the first attempt to introduce coherent states in this formalism. The magnetization and the susceptibility of the system have been obtained and compared with the standard result to illustrate the effect of nonextensivity. Then, adding a perturbation term to the Hamiltonian of the system, nonextensive effects on diamagnetic susceptibility have been investigated. In addition to this, making use of the -deformed partition function of the -oscillator system, the magnetization for -deformed Landau diamagnetism has been derived, with the aim of comparing the results obtained within both formalisms. Received: 21 July 1997 / Revised: 12 December 1997 / Accepted: 23 January 1998     

Sensitivity to initial conditions in the Bak-Sneppen model of biological evolution

We consider biological evolution as described within the Bak and Sneppen 1993 model. We exhibit, at the self-organized critical state, a power-law sensitivity to the initial conditions, calculate the associated exponent, and relate it to the recently introduced nonextensive thermostatistics. The scenario which here emerges without tuning strongly reminds of that of the tuned onset of chaos in say logistic-like one-dimensional maps. We also calculate the dynamical exponent z. Received: 5 November 1997 / Received in final form: 11 November 1997 / Accepted: 19 November 1997     

Canonically invariant formulation of Langevin and Fokker-Planck equations

We present a canonically invariant form for the generalized Langevin and Fokker-Planck equations. We discuss the role of constants of motion and the construction of conservative stochastic processes. Received : 24 July 1997 / Revised : 30 October 1997 / Accepted : 26 January 1998     

Effect of hydrodynamic flow on kinetics of nematic-isotropic transition in liquid crystals

We investigate kinetics of nematic-isotropic transition by solving the hydrodynamic equations for the nematic tensor order parameter and the fluid velocity in two space dimension (x-y plane). Numerical results indicate that nematic directors tend to align parallel to the x-y plane when hydrodynamic flow is incorporated. Late stage growth exponents, for the correlation length and for the number of topological defects, are not significantly altered by hydrodynamic flow. However, in contrast to the case without flow, the relation holds well, which may indicate the validity of dynamical scaling for the case with hydrodynamic flow. Received: 8 September 1997 / Received in final form: 23 October 1997 /Accepted: 3 November 1997     

Fragmentation of grains in a two-dimensional packing

A numerical model of fragmentation of a two-dimensional granular medium under pressure is investigated. The fragmentation process is found to be strongly dependent on the type of force used as the criterion for breaking the grains. The fragmentation mode affects the process less dramatically. There is a power-law divergence in the pressure when the medium approaches the full packing limit, . Both log-normal and power-law fragment-size distributions are found. Gravity is demonstrated to be an important factor. Received: 14 December 1997 / Accepted: 17 March 1998     

Topology invariance in percolation thresholds

An universal invariant for site and bond percolation thresholds ( and respectively) is proposed. The invariant writes where and are positive constants, and d the space dimension. It is independent of the coordination number, thus exhibiting a topology invariance at any d. The formula is checked against a large class of percolation problems, including percolation in non-Bravais lattices and in aperiodic lattices as well as rigid percolation. The invariant is satisfied within a relative error of for all the twenty lattices of our sample at d=2, d=3, plus all hypercubes up to d=6. Received: 7 July 1997 / Accepted: 5 November 1997     

Dynamic behaviour of electron interference in the two-mode SU(1,1) coherent state field

Aharonov-Bohm-type electron interference in the presence of the two-mode SU(1,1) coherent state(CS) field is investigated. The visibility of the time-averaged interference pattern is discussed for this state, and a comparison with classical cases is made. It is shown that the time evolution of the intensity of electron interference exhibits collapse and revival (CR) phenomenon for this state. The fluctuation in electron interference, and its relation to CR phenomenon are also discussed. Received: 22 August 1997 / Accepted: 15 January 1998     

Metastability of a circular o-ring due to intrinsic curvature

An o-ring takes spontaneously the shape of a chair when strong enough torsion is applied in its tangent plane. This state is metastable, since work has to be done on the o-ring to return to the circular shape. We show that this metastable state exists in a Hamiltonian where curvature and torsion are coupled via an intrinsic curvature term. If the o-ring is constrained to be planar (2d case), this metastable state displays a kink-anti-kink pair. This state is metastable if the ratio is less than , where C and A are the torsion and the bending elastic constants [#!landau!#]. In three dimensions, our variational approach shows that . This model can be generalized to the case where the bend is induced by a concentration field which follows the variations of the curvature. Received: 27 August 1997 / Revised: 23 October 1997 / Accepted: 12 November 1997     

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     

Stability and vibrations of catenoid-shaped smectic films

Catenoid-shaped smectic films are spanned between two coaxial circular frames separated by a distance H. It is shown that there exists a critical height H^* such that below it two shapes of the catenoid are possible. The stability of these two shapes is analysed in terms of their vibrations. The spectrum of eigenfrequencies is calculated as a function of the catenoid height. It is shown that the frequency of the fundamental mode is real for the stable shape and imaginary for the other shape. Experimental study of vibrational eigenmodes performed on stable SCE4 films confirms this theoretical prediction. Received: 25 November 1997 / Received in final form: 30 January 1998 / Accepted: 9 March 1998     

Dynamics of a single particle in a horizontally shaken box

We study the dynamics of a particle in a horizontally and periodically shaken box as a function of the box parameters and the coefficient of restitution. For certain parameter values, the particle becomes regularly chattered at one of the walls, thereby loosing all its kinetic energy relative to that wall. The number of container oscillations between two chattering events depends in a fractal manner on the parameters of the system. In contrast to a vertically vibrated particle, for which chattering is claimed to be the generic fate, the horizontally shaken particle can become trapped on a periodic orbit and follow the period-doubling route to chaos when the coefficient of restitution is changed. We also discuss the case of a completely elastic particle, and the influence of friction between the particle and the bottom of the container. Received: 19 September 1997 / Received in final form: 9 December 1997 / Accepted: 17 December 1997     

Two-dimensional polymer networks at a mixed boundary: Surface and wedge exponents

We provide general formulae for the configurational exponents of an arbitrary polymer network connected to the surface of an arbitrary wedge of the two-dimensional plane, where the surface is allowed to assume a general mixture of boundary conditions on either side of the wedge. We report on a comprehensive study of a linear chain by exact enumeration, with various attachments of the walk's ends to the surface, in wedges of angles and , with general mixed boundary conditions. Received: 20 October 1997 / Accepted: 13 May 1998     

Scaling with respect to disorder in time-to-failure

We revisit a simple dynamical model of rupture in random media with long-range elasticity to test whether rupture can be seen as a first-order or a critical transition. We find a clear scaling of the macroscopic modulus as a function of time-to-rupture and of the amplitude of the disorder, which allows us to collapse neatly the numerical simulations over more than five decades in time and more than one decade in disorder amplitude onto a single master curve. We thus conclude that, at least in this model, dynamical rupture in systems with long-range elasticity is a genuine critical phenomenon occurring as soon as the disorder is non-vanishing. Received: 11 July 1997 / Revised: 6 November 1997 / Accepted: 10 November 1997     

Existence, stability and structure of a hexagonal phase doped with nanoparticles

We describe and study by small-angle X-ray scattering (SAXS) a new type of hybrid system. It is composed of a swollen lyotropic hexagonal phase into the cylinders of which solid magnetic particles of nanometric size have been incorporated. It has been found to be stable for volume fractions of particles up to 2% provided the cylinders are sufficiently large. A unidimensionnal magnetic liquid is thus realized. The structural properties of this colloidal assembly have been investigated by SAXS, and the specific features of the scattering spectra are analysed and interpreted. One of the remarkable results is the evidence of depletion interactions between the particles and the inner walls of the cylinders inside which particles are located. Received: 4 September 1997 / Revised: 14 October 1997 / Accepted: 19 November 1997     

Quantum fluctuations and ground state of weakly interacting helix spin chains in a magnetic field

Ferromagnetic spin chains of a hexagonal lattice coupled by a weak antiferromagnetic interaction J₁ develop a helix arrangement if the intrachain antiferromagnetic NNN exchange J₂ is sufficiently large. We show that the classical minimum energy spin configuration is an umbrella when an external magnetic field is applied. The scenario is dramatically changed by quantum fluctuations. Indeed we find that the zero point motion forces the spins in a plane containing the magnetic field so that classical expectation is deceptive for our model. Our result is obtained by controlled expansion in the low field-long wavelength modulation limit. Received: 9 September 1997 / Revised: 15 October 1997 / Accepted: 17 November 1997     

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     

Concerning the first-order phase transition in the low-dimensional organic superconductor (BEDO—TTF)2ReO4 · H2O. Crystal and electronic band structures below the phase transition (T = 170 K)

The effect of the first-order phase transition occurring around 220 K on the crystal and electronic structure of the molecular superconductor (BEDO-TTF) has been studied. The crystal structure at 170 K has been determined and it is found that the main structural change resulting from the phase transition is connected with a rotation of the anions. This rotation leads to changes in the SS and SO intermolecular contacts within the BEDO-TTF donor layers. How these structural changes affect the electronic structure of the salt is studied by comparing the transfer integrals for the different donordonor intermolecular interactions calculated for the room temperature and 170 K crystal structures. It is shown that Fermi surfaces for the 170 K and room temperature structures are very similar, do not exhibit nesting properties, and can be described as resulting from the hybridization of superposing ellipses. Received: 4 September 1997 / Received in final form: 2 December 1997 / Accepted: 3 December 1997     

Elastic property of bilayer membrane in copolymer-homopolymer mixtures

We study the domain morphology in a phase separated state of diblock copolymer-homopolymer mixtures. In the situation that one of the blocks of copolymers is incompatible with homopolymers, formation of a bilayer membrane of block copolymers is shown to be possible in the matrix of homopolymers. Starting with the free energy functional in terms of the local volume fractions of each monomer, we derive the bending and curvature rigidities in the Helfrich free energy for a membrane. It is found that the curvature modulus is negative only in a limited region of the parameters, where a closed shape of a membrane like a vesicle is possibly formed. We establish a method to calculate the rigidities without a molecular picture in a consistent way with the field theoretic model free energy. Stability of a bilayer membrane compared with micelles is also investigated. Received: 22 July 1997 / Received in final form: 1 December 1997 / Accepted: 22 January 1998     

Polymer adsorption on heterogeneous surfaces

The adsorption of a single ideal polymer chain on energetically heterogeneous and rough surfaces is investigated using a variational procedure introduced by Garel and Orland (Phys. Rev. B 55, 226 (1997)). The mean polymer size is calculated perpendicular and parallel to the surface and is compared to the Gaussian conformation and to the results for polymers at flat and energetically homogeneous surfaces. The disorder-induced enhancement of adsorption is confirmed and is shown to be much more significant for a heterogeneous interaction strength than for spatial roughness. This difference also applies to the localization transition, where the polymer size becomes independent of the chain length. The localization criterion can be quantified, depending on an effective interaction strength and the length of the polymer chain. Received: 29 October 1997 / Revised: 19 December 1997 / Accepted: 6 March 1998     

Axialisation, cooling and quenching of ions in a Penning trap

On the basis of a macroscopic ground state population it was argued recently that Bose-Einstein condensation should occur in a one-dimensional harmonic potential. We examine this situation by drawing analogies to bosons in a two-dimensional box, where the thermodynamic limit is well-defined. We show that in both systems although the ground state populations show sharp onsets at the critical temperature, the behaviour of the specific heat is analytic, which proves the absence of a phase transition in these systems. Received: 17 February 1997 / Revised: 3 September 1997 / Accepted: 13 October 1997