Fluctuations and finite-size effect in the Bak-Sneppen model

The self-organized criticality in the nearest-neighbor version of the Bak-Sneppen model is investigated from the event-by-event fluctuations of the mean fitness. The finite-size effect on the evolution of the critical state is shown, and a scaling solution to the gap equation for an infinite one-dimensional lattice is given numerically for the first time. The mean lifetime of avalanches is presented as a function of the gap from the solution. The critical value of the gap and an exponent are calculated from the solution. Received 10 December 2000 and Received in final form 18 January 2001     

The DLCA-RLCA transition arising in 2D-aggregation: simulations and mean field theory

A sticking probability model based on the average cluster lifetime is employed for deducing a kernel capable to describe the kinetics of computer simulated irreversible aggregation processes in two dimensions. The deduced kernel describes not only the time evolution of the cluster size distribution for diffusion limited aggregation (DLCA) and reaction limited aggregation (RLCA) but also for the entire transition region between both regimes. The model predicts a crossover to diffusion limited cluster aggregation for all sticking probabilities at long aggregation times. The time needed for reaching the DLCA limit increases for decreasing sticking probability. Received 16 April 2001 and Received in final form 24 May 2001     

Reaction-diffusion system with self-organized critical behavior

We describe the construction of a conserved reaction-diffusion system that exhibits self-organized critical (avalanche-like) behavior under the action of a slow addition of particles. The model provides an illustration of the general mechanism to generate self-organized criticality in conserving systems. Extensive simulations in d = 2 and 3 reveal critical exponents compatible with the universality class of the stochastic Manna sandpile model. Received 16 November 2000     

Renormalized tricritical behaviour for wetting transitions

In this paper we study tricritical wetting behaviour in three dimensions. In particular we concentrate on systems with short-ranged forces and apply linear functional renormalization group techniques to elucidate the effect of fluctuations upon tricriticality. In comparison with studies of critical wetting we identify an additional fluctuation regime which is relevant for values of the capillary parameter between 2/9 and 1/2. We demonstrate that this regime essentially provides a crossover from mean-field like behaviour, in which tricritical exponents are always distinct from their critical counterparts, from intermediate- and strong-fluctuation behaviour where the critical exponents for tricritical and critical wetting are found to always coincide. We conclude by discussing briefly the possible relevance of these results for experimental studies of wetting. Received 4 January 2001 and Received in final form 11 May 2001     

Magnetic scattering effects on magnetoresistance in a quasi-two-dimensional disordered electron system

Magnetic-impurity-scattering effects in a quasi-2D disordered electron system have been investigated theoretically with the diagrammatic techniques in perturbation theory. The analytical expressions for magnetoconductivities due to weak-localization effects have been obtained as functions of elastic, inelastic and magnetic scattering times. The relevant dimensional crossover behavior from 3D to 2D with decreasing the interlayer coupling has been discussed, and the condition for the crossover has been obtained. Received 20 March 2001 and Received in final form 28 June 2001     

Nature of the Peierls- to Mott-insulator transition in 1D

In order to clarify the physics of the crossover from a Peierls band insulator to a correlated Mott-Hubbard insulator, we analyze ground-state and spectral properties of the one-dimensional half-filled Holstein-Hubbard model using quasi-exact numerical techniques. In the adiabatic limit the transition is connected to the band to Mott insulator transition of the ionic Hubbard model. Depending on the strengths of the electron-phonon coupling and the Hubbard interaction the transition is either first order or evolves continuously across a narrow intermediate phase with finite spin, charge, and optical excitation gaps. Received 7 July 2002 / Received in final form 21 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: holger.fehske@physik.uni-greifswald.de     

Jump of the minimal site and a new correlation function in the Bak-Sneppen model

A new type of spatio-temporal correlation function for the process approaching the self-organized criticality is investigated within the Bak-Sneppen model for biological evolution. In terms of the “directional shorter distance” between the two sites with minimum fitness at two successive updates, the correlation function is defined and studied numerically for the nearest- and random-neighbor versions of the model. Qualitatively different behaviors of the jump of the minimal site in the two models are presented, and the behaviors of the correlation functions are shown also different. Received 14 April 2001 and Received in final form 28 June 2001     

A minimal model for vorticity and gradient banding in complex fluids

A general phenomenological reaction-diffusion model for flow-induced phase transitions in complex fluids is presented. The model consists of an equation of motion for a nonconserved composition variable, coupled to a Newtonian stress relation for the reactant and product species. Multivalued reaction terms allow for different homogeneous phases to coexist with each other, resulting in banded composition and shear rate profiles. The one-dimensional equation of motion is evolved from a random initial state to its final steady state. We find that the system chooses banded states over homogeneous states, depending on the shape of the stress constitutive curve and the magnitude of the diffusion coefficient. Banding in the flow gradient direction under shear rate control is observed for shear-thinning transitions, while banding in the vorticity direction under stress control is observed for shear-thickening transitions. Received 1 April 2001 and Received in final form 16 June 2001     

Fractionally charged excitations in the charge density wave state of a quarter-filled t-J chain with quantum phonons

Elementary excitations of the 4k _F charge density wave state of a quarter-filled strongly correlated electronic one-dimensional chain are investigated in the presence of dispersionless quantum optical phonons using Density Matrix Renormalization Group techniques. Such excitations are shown to be topological solitons carrying charge e/2 and spin zero. Relevance to the 4k _F charge density wave instability in (DI - DCNQI)₂ A g or recently discovered in (TMTTF)₂X ( X=PF ₆, AsF₆) is discussed. Received 30 March 2001 and Received in final form 11 May 2001     

Painlevé integrability and multi-dromion solutions of the 2+1 dimensional AKNS system

The Painlevé integrability of the 2+1 dimensional AKNS system is proved. Using the standard truncated Painlevé expansion which corresponds to a special B?cklund transformation, some special types of the localized excitations like the solitoff solutions, multi-dromion solutions and multi-ring soliton solutions are obtained. Received 31 January 2001 and Received in final form 15 May 2001     

Localized modes in a one-dimensional sphalerite-structure lattice with anharmonicity

The nonlinear localized vibrational modes of a one-dimensional atomic chain with two periodically alternating masses and force constants are analytically investigated using a discrete multiple-scale expansion method. This model simulates a row of atoms in the <1 1 1>-direction of sphalerite, or zinc blende, crystals. Owing to the structural asymmetry, the vibrational amplitude is governed by a perturbed nonlinear Schr?dinger equation instead of the standard one found in one-dimensional lattices with two alternating masses but uniform force constant. Although the stationary localized modes with carrier wavevector at the Brillouin-zone boundary are similar to those of ionic lattices, the moving localized modes with wavevectors within the zone are different owing to the perturbation. The calculation shows that the height of the moving localized modes in this lattice dampens with time. Received 14 May 2001 and Received in final form 12 July 2001     

Spike autosolitons and pattern formation scenarios in the two-dimensional Gray-Scott model

We performed an extensive numerical study of pattern formation scenarios in the two-dimensional Gray-Scott reaction-diffusion model. We concentrated on the parameter region in which there exists a strong separation of length and/or time scales. We found that the static one-dimensional autosolitons (stripes) break up into two-dimensional radially-symmetric autosolitons (spots). The traveling one-dimensional autosolitons (wave fronts) can be stable or undergo breakup. The static two-dimensional radially-symmetric autosolitons may break up and self-replicate leading to the formation of space-filling patterns of spots, wave fronts, or spatio-temporal chaos due to the competition of self-replication and annihilation of spots upon collision. Received 6 November 2000 and Received in final form 27 February 2001     

Interplay between spin-density-wave and superconducting states in quasi-one-dimensional conductors

The interference between spin-density-wave and superconducting instabilities in quasi-one-dimensional correlated metals is analyzed using the renormalization group method. At the one-loop level, we show how the interference leads to a continuous crossover from a spin-density-wave state to unconventional superconductivity when deviations from perfect nesting of the Fermi surface exceed a critical value. Singlet pairing between electrons on neighboring stacks is found to be the most favorable symmetry for superconductivity. The consequences of non uniform spin-density-wave pairing on the structure of phase diagram within the crossover region is also discussed. Received 3 January 2001 and Received in final form 1st March 2001     

Distribution of the delay time and the dwell time for wave reflection from a long random potential

We re-examine and correct an earlier derivation of the distribution of the Wigner phase delay time for wave reflection from a long one-dimensional disordered conductor treated in the continuum limit. We then numerically compare the distributions of the Wigner phase delay time and the dwell time, the latter being obtained by the use of an infinitesimal imaginary potential as a clock, and investigate the effects of strong disorder and a periodic (discrete) lattice background. We find that the two distributions coincide even for strong disorder, but only for energies well away from the band-edges. Received 11 June 2001 and Received in final form 30 July 2001     

Dimensional crossover of quantum interference effects in thin quasicrystalline Al-Cu-Fe films

We present a study of the electrical transport properties of thin i-Al-Cu-Fe films. We observe clear signatures of a dimensional crossover in the temperature and magnetic field dependence of the conductivity for films thinner that ≃ 10³?. In particular for the thinnest sample the magnetoconductivity is strongly anisotropic, as is expected for the weak localisation contribution in two dimensions. These experiments show direct qualitative manifestations of the disorder induced quantum interference effects occurring in quasicrystals. Estimates of the electronic microscopic parameters are in accordance with those obtained in bulk samples. Their values and significance are discussed. Received 16 February 2001 and Received in final form 20 June 2001     

The modified nonlinear Schrödinger equation: facts and artefacts

We argue that the integrable modified nonlinear Schr?dinger equation with the nonlinearity dispersion term is the true starting point to analytically describe subpicosecond pulse dynamics in monomode fibers. Contrary to the known assertions, solitons of this equation are free of self-steepening and the breather formation is possible. Received 29 September 2001 / Received in final form 25 January 2002 Published online 2 October 2002 RID="a" ID="a"doktorov@dragon.bas-net.by     

Onset of instabilities in self-pulsing semiconductor lasers with delayed feedback

We consider the deterministic dynamics of a semiconductor laser with saturable absorber that is subject to delayed optical feedback. Alone, both the saturable absorber and delayed feedback cause the CW output to become unstable to periodic output via Hopf bifurcations. We examine the combined effects of these two destabilizing mechanisms to determine new conditions for the Hopf bifurcations. We also describe the transient as the unstable CW output evolves to the oscillatory state. A main result is that the presence of a saturable absorber can increase the sensitivity of the laser to delayed feedback. Received 1st August 2001 and Received in final form 28 November 2001     

Statistical confidentiality tests for a quantum transmission using continuous variables

We describe a cryptographic protocol consisting of two entangled beams of squeezed light which makes use of statistical tests to deduce the secret key bit. The sender (Alice) encrypts a secret key by modulating the phase of the beam sent in public by the receiver (Bob) who keeps the other beam private. The knowledge of the degree of non classical correlation between the beam quadrature components measured in private and in public allows only Bob to decrypt the secret key. With a view towards absolute security, we formally prove that any external intervention from an eavesdropper (Eve) during the communication process introduces necessarily some modification susceptible to be detected. Statistical confidentiality tests are proposed to detect the presence of Eve. Received 12 July 2001 and Received in final form 11 November 2001     

Double entanglement and quantum cryptography

We propose a quantum transmission based on bi-photons, which are doubly-entangled both in polarisation and phase. This scheme finds a natural application in quantum cryptography, where we show that an eventual eavesdropper is bound to introduce a larger error on the quantum communication than for a single entangled bi-photon communication, when he steels the same information. Received 23 July 2001 / Received in final form 30 November 2001 Published online 24 September 2002