Non-homogeneous random walks, generalised master equations, fractional Fokker-Planck equations, and the generalised Kramers-Moyal expansion

A generalised random walk scheme for random walks in an arbitrary external potential field is investigated. From this concept which accounts for the symmetry breaking of homogeneity through the external field, a generalised master equation is constructed. For long-tailed transfer distance or waiting time distributions we show that this generalised master equation is the genesis of apparently different fractional Fokker-Planck equations discussed in literature. On this basis, we introduce a generalisation of the Kramers-Moyal expansion for broad jump length distributions that combines multiples of both ordinary and fractional spatial derivatives. However, it is shown that the nature of the drift term is not changed through the existence of anomalous transport statistics, and thus to first order, an external potential Φ(x) feeds back on the probability density function W through the classical term ∝/ x (x)W(x, t), i.e., even for Lévy flights, there exists a linear infinitesimal generator that accounts for the response to an external field. Received 30 June 2000 and Received in final form 12 November 2000     

Convective amplification of parametrically generated acoustic wave in a piezoelectric semiconductor plasma

Using hydrodynamic model of semiconductor plasmas and coupled-mode theory of interacting waves, we have analytically investigated parametric interaction in a magnetised piezoelectric semiconductor plasma in non-relativistic domain. The temperature dependence of momentum transfer collision frequency of electrons due to their heating by the pump is assumed to induce nonlinearity in the medium. We have derived a dispersion relation which finally gives four unstable acoustic modes; two forward amplifying modes and two backscattered attenuating modes. We have also obtained an expression for the critical pump amplitude ( ) at and around which gains and phase velocities of amplifying acoustic modes become least dependent on the pump amplitude and static magnetic field . The required can be readily obtained from a pulsed 10.6 μm CO₂ laser. The magnetic field is found to shift the critical point towards lower pump amplitudes. Received 5 September 2000 and Received in final form 5 March 2001     

Generation of zonal flows by interchange modes in a plasma

The generation of zonal flows by flute-like interchange modes in a nonuniform magnetoplasma is considered. The guiding center particle drifts are then used to derive a system of coupled mode equations. The latter are Fourier analyzed to obtain a nonlinear dispersion relation, which exhibits the excitation of zonal flows by the ponderomotive force of the interchange modes. The growth rate of the parametrically driven zonal flows is obtained. Received 26 July 2002 Published online 24 September 2002 RID="a" ID="a"e-mail: ps@tp4.ruhr-uni-bochum.de     

Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation

We discuss the mode spectrum in both the deterministic and noisy Burgers equations in one dimension. Similar to recent investigations of vortex depinning in superconductors, the spectrum is given by a non-Hermitian eigenvalue problem which is related to a `quantum' problem by a complex gauge transformation. The soliton profile in the Burgers equation serves as a complex gauge field engendering a mode transmutation of diffusive modes into propagating modes and giving rise to a dynamical pinning of localized modes about the solitons. Received 8 November 2000     

Envelope solitons induced by high-order effects of light-plasma interaction

The nonlinear coupling between light beams and non-resonant ion density perturbations in a plasma is considered, taking into account the relativistic particle mass increase and the light beam ponderomotive force. A pair of equations comprising a nonlinear Schr?dinger equation for light beams and a driven (by the light beam pressure) ion-acoustic wave response is derived. It is shown that the stationary solutions of our nonlinear equations can be represented in the form of a bright and dark/gray soliton for the one-dimensional problem. We also present numerical results which exhibit that our bright soliton solutions are stable exclusively for the values of the parameters compatible with our theory. Received 24 July 2002 Published online 31 October 2002 RID="a" ID="a"Permanent address: Dipartimento di Scienze Fisiche, Universitá Federico II and INFN, Complesso Universitario di M.S. Angelo, Via Cintia, 80126 Napoli, Italy e-mail: renato.fedele@na.infn.it RID="b" ID="b"Permanent address: Dipartimento di Fisica Generale, Universitá di Torino, Via Pietro Giuria 1, 10125 Torino, Italy RID="c" ID="c"Permanent address: Institute of Physics, Georgian Academy of Sciences, Tbilisi 380077, Georgia     

Integrable correlated electron model with next-nearest-neighbour interactions

The exactly solvable model of supersymmetric t - J chains (STJC) of correlated electrons with next-nearest-neighbour (NNN) interactions is proposed and studied. The model with interactions between nearest neighbours and NNN interactions in one chain can also be considered as a two-chain model with zigzag-like coupling between the chains. The NNN interaction (coupling between chains) causes the onset of additional Dirac seas for low-lying charge and/or spin excitations. These Dirac seas change the low-energy (conformal) behavior of the model. The filling of those seas depends on the values of the NNN coupling (interactions between chains), external magnetic field and applied voltage. We identify the new ground state phases which appear due to the NNN as incommensurate ones. The NNN coupling in the incommensurate phases induces spontaneous magnetization and/or spontaneous filling of the Dirac sea for charge excitations (“spontaneous charge ordering”). The onset of this order implies a first order quantum phase transition driven by the field with hysteresis phenomena. Received 13 September 2000     

Solitary waves in the Madelung's fluid: Connection between the nonlinear Schrödinger equation and the Korteweg-de Vries equation

An investigation to deepen the connection between the family of nonlinear Schr?dinger equations and the one of Korteweg-de Vries equations is carried out within the context of the Madelung's fluid picture. In particular, under suitable hypothesis for the current velocity, it is proven that the cubic nonlinear Schr?dinger equation, whose solution is a complex wave function, can be put in correspondence with the standard Korteweg-de Vries equation, is such a way that the soliton solutions of the latter are the squared modulus of the envelope soliton solution of the former. Under suitable physical hypothesis for the current velocity, this correspondence allows us to find envelope soliton solutions of the cubic nonlinear Schr?dinger equation, starting from the soliton solutions of the associated Korteweg-de Vries equation. In particular, in the case of constant current velocities, the solitary waves have the amplitude independent of the envelope velocity (which coincides with the constant current velocity). They are bright or dark envelope solitons and have a phase linearly depending both on space and on time coordinates. In the case of an arbitrarily large stationary-profile perturbation of the current velocity, envelope solitons are grey or dark and they relate the velocity u₀ with the amplitude; in fact, they exist for a limited range of velocities and have a phase nonlinearly depending on the combined variable x-u_{0 s} (s being a time-like variable). This novel method in solving the nonlinear Schr?dinger equation starting from the Korteweg-de Vries equation give new insights and represents an alternative key of reading of the dark/grey envelope solitons based on the fluid language. Moreover, a comparison between the solutions found in the present paper and the ones already known in literature is also presented. Received 20 February 2002 and Received in final form 22 April 2002 Published online 6 June 2002     

Electrodynamics of the vortex lattice in untwinned YBaCuO by complex impedance measurements

We report complex impedance measurements in an untwinned YBaCuO crystal. Our broad frequency range covers both the quasi static response and the resistive response of the vortex lattice. It allow us to characterize the irreversibility line without the need of any frequency dependent pinning parameters. We confirm the validity of the two modes model of vortex dynamic, and extract both the surface critical current and the flux flow resistivity around the first order transition T_m. This latter is identified by the abrupt loss of pinning and by an unexpected step of (T) at T_m. Received 22 November 2002 / Received in final form 17 February 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: alain.pautrat@ismra.fr RID="b" ID="b"UMR 6508 associée au CNRS     

Nonlinear interactions between drift waves and zonal flows

Phase coherent interactions between drift waves and zonal flows are considered. For this purpose, mode coupling equations are derived by using a two-fluid model and the guiding center drifts. The equations are then Fourier analyzed to deduce the nonlinear dispersion relations. The latter depict the excitation of zonal flows due to the ponderomotive forces of drift waves. The flute-like zonal flows with insignificant density fluctuations have faster growth rates than those which have a finite wavelength along the magnetic field direction. The relevance of our investigation to drift wave driven zonal flows in computer simulations and laboratory plasmas is discussed. Received 5 April 2002 Published online 28 June 2002     

Frequency-dependent fluctuational conductivity above in anisotropic superconductors: effects of a short wavelength cutoff

We discuss the excess conductivity at nonzero frequencies in a superconductor above T_c within the Gaussian approximation. We focus the attention on the temperature range not too close to T_c: within a time-dependent Ginzburg-Landau formulation, we phenomenologically introduce a short wavelength cutoff (of the order of the inverse coherence length) in the fluctuational spectrum to suppress high momentum modes. We treat the general cases of thin wires, anisotropic thin films and anisotropic bulk samples. We obtain in all cases explicit expressions for the finite frequency fluctuational conductivity. The dc case directly follows. Close to T_c the cutoff has no effect, and the known results for Gaussian fluctuations are recovered. Above T_c, and already for ε = ln(T/T _c) > 10^-2, we find strong suppression of the paraconductivity as compared to the Gaussian prediction, in particular in the real part of the paraconductivity. At high ε the cutoff effects are dominant. We discuss our results in comparison with data on high-T_c superconductors. Received 19 March 2002 Published online 25 June 2002     

Acousto-optic modulation in magnetised diffusive semiconductors

The modulation of an intense electromagnetic beam induced by the acousto-optic (AO) effect has been analysed in a transversely magnetised semiconductor-plasma medium. The effect of carrier diffusion on the threshold field and gain profile of the modulated wave has been extremely investigated using coupled mode theory. The origin of the AO interaction is assumed to lie in the induced nonlinear diffusion current density of the medium. By considering the modulation process as a four wave parametric interaction an expression for effective third-order AO susceptibility describing the phenomena has been deduced. The modulation is greatly modified by propagation characteristics such as dispersion and diffraction due to dielectric relaxation of the acoustic mode. The threshold pump field and the steady state growth rates are estimated from the effective third-order polarisation in the plasma medium. Analytical estimation reveals that in the presence of enhanced diffusion due to excess charge carriers the modulated beam can be effectively amplified in a dispersionless acoustic wave regime. The presence of an external dc magnetic field is found to be favourable for the onset of diffusion induced modulational amplification of the modulated wave in heavily doped regime. Received 5 November 2001     

Classical spin liquid properties of the infinite-component spin vector model on a fully frustrated two dimensional lattice

Thermodynamic quantities and correlation functions (CFs) of the classical antiferromagnet on the checkerboard lattice are studied for the exactly solvable infinite-component spin-vector model, D↦∞. In contrast to conventional two-dimensional magnets with continuous symmetry showing extended short-range order at distances smaller than the correlation length, r ξ _c∝ exp(T ^*/T), correlations in the checkerboard-lattice model decay already at the scale of the lattice spacing due to the strong degeneracy of the ground state characterized by a macroscopic number of strongly fluctuating local degrees of freedom. At low temperatures, spin CFs decay as < >∝ 1/r ² in the range a ₀≪r≪ξ _c∝T ^-1/2, where a₀ is the lattice spacing. Analytical results for the principal thermodynamic quantities in our model are very similar with MC simulations, exact and analytical results for the classical Heisenberg model (D = 3) on the pyrochlore lattice. This shows that the ground state of the infinite-component spin vector model on the checkerboard lattice is a classical spin liquid. Received 16 November 2001 and Received in final form 12 February 2002     

Ginzburg-Landau theory and effects of pressure on a two-band superconductor: application to MgB <Emphasis Type="Bold">2</Emphasis>

We present a model of pressure effects of a two-band superconductor based on a Ginzburg-Landau free energy with two order parameters. The parameters of the theory are pressure as well as temperature dependent. New pressure effects emerge as a result of the competition between the two bands. The theory then is applied to MgB₂. We identify two possible scenaria regarding the fate of the two σ subbands under pressure, depending on whether or not both subbands are above the Fermi energy at ambient pressure. The splitting of the two subbands is probably caused by the E_2g distortion. If only one subband is above the Fermi energy at ambient pressure (scenario I), application of pressure diminishes the splitting and it is possible that the lower subband participates in the superconductivity. The corresponding crossover pressure and Gr neisen parameter are estimated. In the second scenario both bands start above the Fermi energy and they move below it, either by pressure or via the substitution of Mg by Al. In both scenaria, the possibility of electronical topological transition is emphasized. Experimental signatures of both scenaria are presented and existing experiments are discussed in the light of the different physical pictures. Received 3 September 2002 / Received in final form 16 December 2002 Published online 14 February 2003 RID="a" ID="a"e-mail: joseph.betouras@ua.ac.be RID="b" ID="b"On leave from N.S. Kurnakov Institute of General and Inorganic Chemistry of the Russian Academy of Sciences, 31 Leninskii prospekt, 117915, Moscow, Russia     

The influence of mode coupling on the non-linear evolution of tearing modes

On the basis of tearing mode theory a simple but physically explicit model of the evolution of toroidally coupled rotating magnetic islands has been developed. The basic mechanism identified by the model in the island evolution is the locking in phase of rotating islands that leads to rapid destabilisation of an initially stable mode. Destabilisation of marginally stable (2, 1) and (3, 1) modes is analysed in several scenarios. It is shown that mode coupling is an effective way of destabilising a m=3 island in a low- plasma. The numerical examples presented show the individual roles of coupling, inertia and a resistive wall. The model was applied for the analysis of MHD observations of an ASDEX discharge. Received 4 May 1999 and Received in final form 23 July 1999     

Vector potential gauge for superconducting regular polygons

An approach to the Ginzburg-Landau problem of superconducting polygons is developed, based on the exact fulfillment of superconducting boundary conditions along the boundary of the sample. To this end an analytical gauge transformation for the vector potential A is found which gives A _n = 0 for the normal component along the boundary line of an arbitrary regular polygon. The use of the new gauge reduces the Ginzburg-Landau problem of superconducting polygons in external magnetic fields to an eigenvalue problem in a basis set of functions obeying Neumann boundary conditions. The advantages of this approach, especially for low magnetic fields, are illustrated and novel vortex patterns are obtained which can be probed experimentally. Received 28 February 2002 and Received in final form 12 April 2002 Published online 6 June 2002     

Vortex matter in lead nanowires

Theoretical and experimental magnetizations of lead nanowire arrays well below the superconducting transition temperature T_c are described. The magnetic response of the array was investigated with a SQUID magnetometer. Hysteretic behaviour and phase transitions have been observed in sweeping up and down the external magnetic field at different temperatures. The Meissner and Abrikosov states were also experimentally observed in this apparently type-I superconductor. This fact brings to the fore the non-trivial behaviour of the critical boundary κ _c ( = 1/ in bulk materials) between type-I and type-II phase transitions at mesoscopic scales. The time-independent Ginzburg-Landau equations particularized to cylindrically symmetric configurations enable one to explain and reproduce the experimental magnetization curves within 10% of error. Received 16 January 2003 / Received in final form 27 March 2003 Published online 23 May 2003 RID="a" ID="a"e-mail: stenuit@fynu.ucl.ac.be     

The two dimensional classical anisotropic Heisenberg ferromagnetic model with nearest- and next-nearest neighbor interactions

We use the self-consistent harmonic approximation (SCHA) to study the two-dimensional classical Heisenberg anisotropic (easy-plane) ferromagnetic model including nearest- and next-nearest neighbor exchange interactions. For temperatures much lower than the Kosterlitz-Thouless phase transition temperature T _KT, spin waves must be the most relevant excitations in the system and the SCHA must account for its behavior. However, for temperatures near T _KT, we should expect vortex pairs to be quite important. The effect of these vortex excitations on the phase transition temperature is included in our theory as a renormalization of the exchange interactions. Then, combining the SCHA theory to the renormalization effect due to vortex pairs, we calculate the dependence of T _KT as a function of the easy-plane anisotropies and exchange interactions. Received 3 April 2001 and Received in final form 20 September 2001     

Phase transition and random-field induced domain wall response of SrTi O 3

The dielectric permittivity ε^′ - i of SrTi ¹⁸O ₃ (STO18) is studied under a dc electric field E as a function of the temperature, T. In ε^′ vs. T, a double-peak is found when 0 < E < 30 KV/m. While the peak at high-T is attributed to the smeared ferroelectric phase transition, the low-T one is induced by domain wall motion. The transverse Ising model including an external homogeneous and quenched random-fields is successfully used to describe both the smeared phase transition and the domain wall response in the low-T domain state. The calculations are in good agreement with the experimental results. Received 4 January 2002 / Received in final form 25 March 2002 Published online 19 July 2002     

Generation of 3rd and 5th harmonics in a thin superconducting film by temperature oscillations and isothermal nonlinear current response

The generation of harmonics of the voltage response is considered when an AC current is applied through a superconducting film above T_c. It is shown that almost at all temperatures the mechanism of the temperature oscillations created by the AC current and the temperature dependence of the resistance dominates over the isothermal nonlinear electric conductivity. Only in a narrow critical region close to T_c the latter is essential for the generation of the harmonics. A detailed investigation of harmonics generation provides an accurate method for measuring the thermal boundary conductance between the film and the insulating substrate. The critical behaviour of the third harmonic will give a new method for the determination of the lifetime of metastable Cooper pairs above T_c. The comparison of the calculated fifth harmonics of the voltage with the experiment is proposed as an important test for the applicability of the employed theoretical models. Received 8 September 2001     

Electron teleportation with quantum dot arrays

An electron teleportation protocol, inspired by the scenario by Bennett et al., is proposed in a mesoscopic set-up. A superconducting circuit allows to both inject and measure entangled singlet electron pairs in an array of three normal quantum dots. The selection of the teleportation process is achieved in the steady state with the help of two superconducting dots and appropriate gating. Teleportation of the electron spin is detected by measuring the spin-polarized current through the normal dot array. This current is perfectly correlated to the pair current flowing inside the superconducting circuit. The classical channel required by Bennett's protocol, which signals the completion of a teleportation cycle, is identified with the detection of an electron pair charge in the superconducting circuit. Received 10 December 2002 / Received in final form 14 March 2003 Published online 7 May 2003