On N-wave type systems and their gauge equivalent

The class of nonlinear evolution equations (NLEE) - gauge equivalent to the N-wave equations related to the simple Lie algebra are derived and analyzed. They are written in terms of (x, t) ∈ satisfying r = rank nonlinear constraints. The corresponding Lax pairs and the time evolution of the scattering data are found. The Zakharov-Shabat dressing method is appropriately modified to construct their soliton solutions. Received 20 October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: gerjikov@inrne.bas.bg     

Exciton-polariton solitary waves

Effects of the exciton and polariton dispersions and the nonlinear exciton and photon interactions on the properties of polariton solitons in molecular crystals are investigated. Higher-order terms and phase-modulation (chirp) are taken into account. Bright- and dark-soliton solutions of the resulting modified nonlinear Schr?dinger (NLS) equation are presented. Nonlinearity- and dispersion-induced critical points on the polariton dispersion curve are obtained, separating regions with different solutions. Received 2 October 2001 / Received in final form 23 May 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: Stoychev@issp.bas.bg     

Effect of phase shift in shape changing collision of solitons in coupled nonlinear Schrödinger equations

Soliton interactions in systems modelled by coupled nonlinear Schr?dinger (CNLS) equations and encountered in phenomena such as wave propagation in optical fibers and photorefractive media possess unusual features: shape changing intensity redistributions, amplitude dependent phase shifts and relative separation distances. We demonstrate these properties in the case of integrable 2-CNLS equations. As a simple example, we consider the stationary two-soliton solution which is equivalent to the so-called partially coherent soliton (PCS) solution discussed much in the recent literature. Received 1st October 2001 / Received in final form 4 February 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: lakshman@bdu.ernet.in     

Properties of supersymmetric integrable systems of KP type

The recently proposed supersymmetric extensions of reduced Kadomtsev-Petviashvili (KP) integrable hierarchies in N = 1, 2 superspace are shown to contain in the purely bosonic limit new types of ordinary non-supersymmetric integrable systems. The latter are coupled systems of several multi-component non-linear Schr?dinger-like hierarchies whose basic nonlinear evolution equations contain additional quintic and higher-derivative nonlinear terms. Also, we obtain the N = 2 supersymmetric extension of Toda chain model as Darboux-B?cklund orbit of the simplest reduced N = 2 super-KP hierarchy and find its explicit solution. Received 13 September 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: nissimov@inrne.bas.bg RID="b" ID="b"e-mail: svetlana@inrne.bas.bg     

New geometries associated with the nonlinear Schrödinger equation

We apply our recent formalism establishing new connections between the geometry of moving space curves and soliton equations, to the nonlinear Schr?dinger equation (NLS). We show that any given solution of the NLS gets associated with three distinct space curve evolutions. The tangent vector of the first of these curves, the binormal vector of the second and the normal vector of the third, are shown to satisfy the integrable Landau-Lifshitz (LL) equation = ×, ( = 1). These connections enable us to find the three surfaces swept out by the moving curves associated with the NLS. As an example, surfaces corresponding to a stationary envelope soliton solution of the NLS are obtained. Received 5 December 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: radha@imsc.ernet.in     

Full counting statistics of a general quantum mechanical variable

We present a quantum mechanical framework for defining the statistics of measurements of , A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes to observe the so defined statistics experimentally.Received: 30 June 2003, Published online: 15 October 2003PACS: 73.50.Td Noise processes and phenomena - 73.23.-b Electronic transport in mesoscopic systems - 74.40.+k Fluctuations (noise, chaos, nonequilibrium superconductivity, localization, etc.)     

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     

Thermal instability of a rotating saturated porous medium heated from below and submitted to rotation

In this work, we study the problem of onset of thermal convection in a rotating saturated porous medium heated from below. The effect of rotation is restricted to the Coriolis force, neglecting thus the centrifugal effects, the porous medium is described by Brinkman's model. The linear eigenvalue problem is solved by means of a modified Galerkin method. The behavior of the critical temperature gradient is discussed in terms of various parameters of the system for both stationary and overstable convections. Finally a weakly nonlinear analysis is provided to derive amplitude equations and to study the onset of Küppers-Lortz instability. Received 24 June 2002 / Received in final form 11 September 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: tdesaive@ulg.ac.be     

Soliton dynamics in chiral molecular chains with first- and third-neighbour interactions

We investigate the propagation and interaction of solitons associated with circularly polarized vibrations in gyrotropic media. The chirality of the structure yields different dispersion laws and hence different phase and group velocities for the left- and right-handed modes. The helical arrangement of the monomers is modelled through first- and third-neighbour interactions. The dynamics of the excitations is governed by a system of coupled discrete nonlinear Schr?dinger equations which is studied both analytically and numerically. Depending on the initial conditions and the interaction constants, different evolutionary patterns are obtained corresponding to unbound or bound one- and two-soliton solutions. The results can be applied to the process of energy transfer in helical polymers. Received 1st October 2001 / Received in final form 30 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: krad@issp.bas.bg     

Off-center Li ions: solid state rotators described by Mathieu's nonlinear-oscillator equation

Substitutional impurity ions in crystals are known to displace off-center and to perform hindered rotations around the ideal lattice positions. The vibronic theory to describe both the off-center displacements and the hindered rotations by a single angular equation incorporates terms up to 3rd order in the off-center displacement coordinates. When the rotation is confined to a single plane, the corresponding vibronic equation is equivalent to Mathieu's equation. Extending our earlier work, we derive here the dipole-dipole coupling to take into account cooperative phenomena. We also derive the optical absorption band arising from dipolar transitions across “Mexican Hat” surfaces, and we show that hindered rotations gives rise to magnetic moments quantized in rotational bands. Received 18 October 2001 / Received in final form 5 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: allxrose@hotmail.com     

Electron transport in a mesoscopic superconducting / ferromagnetic hybrid conductor

We present electrical transport experiments performed on submicron hybrid devices made of a ferromagnetic conductor (Co) and a superconducting (Al) electrode. The sample was patterned in order to separate the contributions of the Co conductor and of the Co-Al interface. We observed a strong influence of the Al electrode superconductivity on the resistance of the Co conductor. This effect is large only when the interface is highly transparent. We characterized the dependence of the observed resistance decrease on temperature, bias current and magnetic field. As the differential resistance of the ferromagnet exhibits a non-trivial asymmetry, we claim that the magnetic domain structure plays an important role in the electron transport properties of superconducting / ferromagnetic conductors. Received 9 July 2002 / Received in final form 22 October 2002 Published online 27 January 2003 RID="a" ID="a"e-mail: herve.courtois@grenoble.cnrs.fr RID="b" ID="b"associated to Université Joseph Fourier     

Interaction of coupled higher order nonlinear Schrödinger equation solitons

The novel inelastic collision properties of two-soliton interaction for an n-component coupled higher order nonlinear Schr?dinger equation are studied. Some interesting features of three soliton interactions, related to the integrability of the n-component coupled higher order nonlinear Schr?dinger equation are also discussed. Received 17 April 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: abhijit@iitg.ernet.in RID="b" ID="b"e-mail: sasanka@iitg.ernet.in RID="c" ID="c"e-mail: sudipta@iitg.ernet.in     

Method of group foliation and non-invariant solutions of partial differential equations

Using the heavenly equation as an example, we propose the method of group foliation as a tool for obtaining non-invariant solutions of PDEs with infinite-dimensional symmetry groups. The method involves the study of compatibility of the given equations with a differential constraint, which is automorphic under a specific symmetry subgroup and therefore selects exactly one orbit of solutions. By studying the integrability conditions of this automorphic system, i.e. the resolving equations, one can provide an explicit foliation of the entire solution manifold into separate orbits. The new important feature of the method is the extensive use of the operators of invariant differentiation for the derivation of the resolving equations and for obtaining their particular solutions. Applying this method we obtain exact analytical solutions of the heavenly equation, non-invariant under any subgroup of the symmetry group of the equation. Received 13 September 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: sheftel@gursey.gov.tr     

Cyclotron resonance of polarons in ternary mixed crystals

Rayleigh-Schr?dinger perturbation theory and an improved Wigner-Brillouin perturbation theory has been used to study the cyclotron resonance of the polarons in ternary mixed crystals in the zero-temperature limit. The interaction between an electron and two branches of longitudinal optical phonon modes is taken into account in the framework of the random-element-isodisplacement model. The numerical results for several ternary mixed crystals show that the polaronic cyclotron energy and mass split successively twice related to the higher and lower branches of longitudinal optical phonon modes of ternary mixed crystals. A non-linear dependence of the polaronic cyclotron energy and mass on the composition x is found. Received 19 March 2002 / Received in final form 21 March 2003 Published online 20 June 2003 RID="a" ID="a"e-mail: xxliang@imu.edu.cn     

Balance-equation approach to impact ionization induced by an intense terahertz radiation: Application to InAs/AlSb heterojunctions

We have extended the balance equations to account for conduction-valence interband impact ionization (II) process induced by an intense terahertz (THz) electromagnetic irradiation in semiconductors, and applied them to study the II effect on electron transport and electron-hole pair generation-recombination rate in THz-driven InAs/AlSb heterojunctions (HJ). As many as needed multiphoton channels are self-consistently taken into account for yielding a given accuracy. The time evolution of transport state including THz-radiation-induced II process are monitored in details by an extensive time-dependent analysis. Two different physical stages, the quasi-steady state and the complete steady-state, are clearly identified from the present calculations. Intersubband electron transfer rate and net electron-hole generation rate are derived as functions of the THz radiation strength E _ac for various radiation frequencies from f _ac = 0.42 to 6 THz at lattice temperatures T = 6 K. It's indicated that the THz radiation with a larger E _ac or a lower f _ac, has a stronger effect on electron transport and II process. Qualitative agreement is obtained between the calculated electron-hole generation rate and the available experimental data for InAs/AlSb HJ's at T = 6 K. Received 24 May 2002 / Received in final form 26 August 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: jccao8@hotmail.com     

ZnSe films deposited on crystalline GaAs and amorphous quartz substrates by means of pulsed laser ablation technique

ZnSe films were deposited by pulsed laser ablation on a crystalline GaAs substrate and on an amorphous quartz substrate. The deposition process was performed with the same growth parameters. The films were investigated by means of X-ray diffraction, reflectance and photoluminescence spectroscopy. The X-ray diffraction spectra have demonstrated that the films grow in a highly oriented way but having different orientations, i.e. the films deposited on GaAs grow (100)-oriented and the films deposited on quartz grow (111)-oriented. Reflectance spectra as a function of the temperature have been analysed by means of the classical oscillator model, in order to obtain the temperature dependence of the band gap energy. This gives results comparable to those of ZnSe single crystals for ZnSe on GaAs, but it is red-shifted for ZnSe on quartz, because of lattice and thermal strains. The photoluminescence measurements at T = 10 K confirm the better quality of ZnSe deposited on GaAs and show that pulsed laser ablation is a promising technique to grow films having intrinsic luminescence even on an amorphous substrate. Received 29 May 2002 Published online 31 October 2002 RID="a" ID="a"e-mail: giuseppe.perna@ba.infn.it     

solitons in quantum Hall systems

We present here an elementary pedagogical introduction to CP_N solitons in quantum Hall systems. We begin with a brief introduction to both CP_N models and to quantum Hall (QH) physics. We then focus on spin and layer-spin degrees of freedom in QH systems and point out that these are in fact CP_N fields for N = 1 and N = 3. Excitations in these degrees of freedom will be shown to be topologically non-trivial soliton solutions of the corresponding CP_N field equations. We conclude with a brief summary of our own recent work in this area, done with Sankalpa Ghosh. Received 17 November 2001 Published online 2 October 2002 RID="a" ID="a"e-mail: doug0700@mail.jnu.ac.in     

Dichromatic squeezing generation

We propose a novel scheme for the joint generation of two squeezed beams at arbitrary frequencies ω ₁ and ω ₂. The scheme consists of two successive steps, both involving nonlinear interactions in χ⁽²⁾ crystals. The dynamics of the setup is analyzed both quantum mechanically and classically within the parametric approximation. An experimental implementation involving the fundamental and the harmonics of a Nd:YAG laser pulse, and β-BaB ₂ O ₄ nonlinear crystals is suggested. Received 17 May 2000 and Received in final form 9 October 2000     

Dynamics of modulated and composite aperiodic crystals

We compare within an unifying formalism the dynamical properties of modulated and composite aperiodic (incommensurate) crystals. We discuss the concept of inner polarization and we define an inner polarization parameter β that distinguishes between different acoustic modes of aperiodic crystals. Although this concept has its limitations, we show that it can be used to extract valuable information from neutron coherent inelastic scattering experiments. Within certain conditions, the ratio between the dynamic and the static structure factors at various Bragg peaks depends only on β. We show how the knowledge of β for modes of an unknown structure can be used to decide whether the structure is composite or modulated. The same information can be used to predict scattered intensity within unexplored regions of the reciprocal space, being thus a guide for experiments. Received 9 June 2002 Published online 14 October 2002 RID="a" ID="a"e-mail: Ovidiu.Radulescu@univ-rennes1.fr     

Carrier-induced changes in the phase resolved reflection of GaAs quantum wells

The influence of thermalized non-coherent carriers on the dielectric function of GaAs/AlAs quantum wells is investigated by reflection spectroscopy. Experiments are performed using the method of spectral interferometry, where both amplitude and phase of reflected pulses can be determined. For low excitation density the complex coefficient of reflection can be described using as dielectric function a broadened Elliot formula. With increasing carrier density pronounced nonlinearities appear in both amplitude and phase due to many-body effects between excited carriers. The nonlinear behavior fits very well to the results of a many-body theory based on the Semiconductor Bloch equations including memory effects in the scattering processes between carriers and the polarization induced by the probe pulse. Received 29 May 2002 / Received in final form 23 September 2002 Published online 19 December 2002 RID="a" ID="a"e-mail: manzke@physik3.uni-rostock.de