Propagation of waves and chaos in transmission line with strongly anharmonic dangling resonator

Delayed differential equation of motion with multiple lags is derived for an anharmonic stub resonator coupled to a monomode transmission line. Transmission and reflection coefficients are found analytically in the harmonic approximation. Nonlinear response of the system is analysed by an electric circuit obeying the same equations of motion. Enhanced second harmonic generation is found at the frequencies, which in the harmonic approximation correspond to the zeros of transmission. An aperiodic (chaotic) response is found mainly in the frequency range close to the resonance of the dangling resonator. Zeros of transmission and total transmissions are shown to be lifted by the anharmonicity nearly in the same frequency region. Higher harmonics are preferentially transmitted at the zero transmission points in the presence of anharmonicity. Received 14 March 2002 / Received in final form 25 November 2002 Published online 14 March 2003     

Phasons, sliding modes and friction

Aperiodic crystals may have additional low frequency modes related to the possibility to describe them in a higher-dimensional space. Dynamics associated with these degrees of freedom is called phasonic, but there are very different phenomena of this type. A discussion is given of the use of the term. The relation between phason modes, the crystal structure, and the modulation and sliding modes is discussed. Finally a relation with frictionless motion is studied. Received 4 April 2002 / Received in final form 22 July 2002 Published online 17 September 2002     

Current and shot noise in two capacitively coupled single electron transistors with an atomic sized spacer

The currents and their fluctuations in two capacitively coupled single electron transistors are determined in the limit of sequential tunnelling. Our considerations are restricted to the case when the islands (dots) of the transistors are atomic-sized, which means each of them has only one single electronic level available for the tunnelling processes. The Coulomb interactions of accumulated charges on the both single electron transistors lead to the effect of the negative differential resistance. An enhancement of the current shot-noise was also found. Spectral decomposition analysis indicated the two main contributions to the shot-noise: low- and high-frequency fluctuations. It was found that the low frequency fluctuations (polarization noise) are responsible for a strong enhancement of the current noise. Received 9 October 2001 / Received in final form 8 March 2002 Published online 9 July 2002     

Stimulated Raman spectroscopic study on intermolecular vibrations of size-selected benzonitrile clusters

Low frequency intermolecular vibrations of benzonitrile-(H₂O)_{n = 1 - 3}, -(CH₃OH)_{n = 1 - 3}, and -(CHCl₃)_{n = 1 - 3} clusters were observed by stimulated Raman - UV double resonance spectroscopy combined with fluorescence detection. The Raman active vibrations, which appear in the region from 5 to 50 cm^-1, exhibit characteristic frequency shifts depending on the cluster structure and on the cluster size. In benzonitrile-(H₂O)_{n = 1 - 3} and -(CH₃OH)_{n = 1 - 3}, the lowest frequency band showed a lower frequency shift with an increase of the number of solvent molecules. On the other hand, that of benzonitrile-(CHCl₃)_{n = 1 - 3} showed a shift to the higher frequency side. Their characteristic shifts are discussed based on the structure of the clusters. Received 28 April 2002 / Received in final form 30 May 2002 Published online 13 September 2002     

Scattering of a sound wave by a vibrating surface

We report an experimental study of the scattering of a sound wave of frequency f by a surface vibrating at frequency F. Both the Doppler shift at the vibrating surface and acoustic nonlinearities in the bulk of the fluid, generate the frequencies f±nF (n integer) in the spectrum of the scattered wave. We show that these two contributions can be separated because they scale differently with respect to the vibration frequency and to the distance between the vibrating scatterer and the detector. We determine the parameter ranges in which one or the other mechanism dominates and present quantitative studies of these two regimes. Received 2 December 2002 / Received in final form 27 March 2003 Published online 4 June 2003 RID="a" ID="a"e-mail: fauve@physique.ens.fr RID="b" ID="b"UMR 8550     

Electromagnetically induced transparency in asymmetric double quantum wells

We show how to compute nonlinear optical absorption spectra of an Asymmetric Double Quantum Well (ADQW) in the region of intersubband electronic transitions. The method uses the microscopic calculation of the dephasing due to electron-electron and electron-phonon scattering rates and the macroscopic real density matrix approach to compute the electromagnetic fields and susceptibilities. The polarization dephasing and the corrections to the Rabi frequencies due to the electron-electron interaction are also taken into account. For a proper choice of the QW widths and of the driving fields we obtain electromagnetically induced transparency. This transparency has a very narrow linewidth when a single driving field is applied resonant to the transition between the second and the third subband. In the case of two resonant driving fields or of a driving field resonant between the first and third subband we obtain a large transparency enhancement over the entire absorption spectrum. Results are given for GaAs/GaAlAs QWs and experiments are proposed. Received 21 June 2001 and Received in final form 21 January 2002     

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     

Measurement of isotope shifts,fine and hyperfine structure splittings of the lithium D lines

The lithium D lines were studied using a diode laser that was frequency modulated by an electro-optic modulator, to excite an atomic beam. The transmission of part of the laser beam through an etalon was monitored to correct for the nonlinearity of the laser scan. The results for the ^6,7Li 2 S _1/2 and 2 P _1/2 hyperfine splittings agree very well with the best existing data while those for the D1 isotope shift and ^6,7Li fine structure splittings disagree significantly from data obtained by a previous laser atomic beam experiment. Our result for the D1 isotope shift is very close to the latest value computed using Hylleraas variational theory. Received 8 April 2002 / Received in final form 26 June 2002 Published online 21 January 2003 RID="a" ID="a"e-mail: wvw@yorku.ca     

Quasi-periodic and periodic solutions for dynamical systems related to Korteweg-de Vries equation

We consider quasi-periodic and periodic (cnoidal) wave solutions of a set of n-component dynamical systems related to Korteweg-de Vries equation. Quasi-periodic wave solutions for these systems are expressed in terms of Novikov polynomials. Periodic solutions in terms of Hermite polynomials and generalized Hermite polynomials for dynamical systems related to Korteweg-de Vries equation are found. Received 15 October 2001 / Received in final form 6 March 2002 Published online 2 October 2002 RID="a" ID="a"e-mail: nakostov@ie.bas.bg     

Phase diagrams of Ising films with competing interactions

The axial next-nearest-neighbour Ising (ANNNI) model of finite thickness is studied. Using mean-field theory, Monte Carlo simulations, and low-temperature analyses, phase diagrams are determined, with a distinct phase diagram for each film thickness. The robustness of the phase diagrams against varying the couplings in the surface layers is analysed. Received 19 March 2002 and Received in final form 2 April 2002 Published online 6 June 2002     

Renormalization by continuous unitary transformations: one-dimensional spinless fermions

A renormalization scheme for interacting fermionic systems is presented where the renormalization is carried out in terms of the fermionic degrees of freedom. The scheme is based on continuous unitary transformations of the Hamiltonian which stays hermitian throughout the renormalization flow, whereby any frequency dependence is avoided. The approach is illustrated in detail for a model of spinless fermions with nearest neighbour repulsion in one dimension. Even though the fermionic degrees of freedom do not provide an easy starting point in one dimension favorable results are obtained which agree well with the exact findings based on Bethe ansatz. Received 21 August 2002 / Received in final form 29 October 2002 Published online 31 December 2002     

Laser-induced fluorescence study of the influence of N <Emphasis Type="Bold">2</Emphasis> and CH <Emphasis Type="Bold">4</Emphasis> on the <Emphasis Type="Bold">114</Emphasis>Cd intercombination line

Using a laser-induced fluorescence method a detailed analysis of profiles of the ¹¹⁴Cd 326.1 nm line perturbed by N₂ and CH₄ was performed which revealed deviations from the ordinary Voigt profile. These deviations are shown to be consistent with fits of experimental profiles to an asymmetric Voigt profile. Coefficients of the pressure broadening, shift and collision-time asymmetry are determined and compared with those calculated for van der Waals interaction potential. Received 29 November 2001 / Received in final form 12 July 2002 Published online 4 February 2003     

Is MFM really useful?

The ill-posed linear inverse problems, characterised by Fredholm integral equations of the first kind, are encountered in many areas of science and technology. This type of problems present some loss of information under the inversion process. The loss of information often makes the inversion process very difficult. Magnetic force microscopy (MFM) is a technique where problems related to loss of information occur. Work is presented here to understand what can be measured by the magnetic force microscope. A simple model is constructed, where the magnetic tip is approximated by a point dipole. Given the force F() acting on the dipole tip, we attempt to determine the magnetization distributlon in a thin ferromagnetic film, M(). This calculation should be interesting due to the rapidiy growing interest in magnetic thin films and magnetic multilayers. Received 3 December 2001 and Received in final form 11 March 2002     

Radial distribution function of rod-like polyelectrolytes

We study the effect of electrostatic interactions on the distribution function of the end-to-end distance of a single polyelectrolyte chain in the rod-like limit. The extent to which the radial distribution function of a polyelectrolyte is reproduced by that of a wormlike chain with an adjusted effective persistence length is investigated. Strong evidence is found for a universal scaling formula connecting the effective persistence length of a polyelectrolyte with the strength of the electrostatic interaction and the Debye screening length. Received 4 March 2002 and Received in final form 1 July 2002 RID="a" ID="a"e-mail: jrudnick@physics.ucla.edu     

Self-averaging in complex brain neuron signals

Nonlinear statistical properties of Ventral Tegmental Area (VTA) of limbic brain are studied in vivo. VTA plays key role in generation of pleasure and in development of psychological drug addiction. It is shown that spiking time-series of the VTA dopaminergic neurons exhibit long-range correlations with self-averaging behavior. This specific VTA phenomenon has no relation to VTA rewarding function. Last result reveals complex role of VTA in limbic brain. Received 17 April 2002 / Received in final form 30 September 2002 Published online 31 December 2002     

Covariant electroweak nucleon form factors in a chiral constituent-quark model

Results for the proton and neutron electric and magnetic form factors as well as the nucleon axial and induced pseudoscalar form factors are presented for the chiral constituent-quark model based on Goldstone-boson exchange dynamics. The calculations are performed in a covariant framework using the point-form approach to relativistic quantum mechanics. The direct predictions of the model yield a remarkably consistent picture of the electroweak nucleon structure. Received: 28 February 2002 / Accepted: 14 March 2002     

Computational leakage: Grover's algorithm with imperfections

We study the effects of dissipation or leakage on the time evolution of Grover's algorithm for a quantum computer. We introduce an effective two-level model with dissipation and randomness (imperfections), which is based upon the idea that ideal Grover's algorithm operates in a 2-dimensional Hilbert space. The simulation results of this model and Grover's algorithm with imperfections are compared, and it is found that they are in good agreement for appropriately tuned parameters. It turns out that the main features of Grover's algorithm with imperfections can be understood in terms of two basic mechanisms, namely, a diffusion of probability density into the full Hilbert space and a stochastic rotation within the original 2-dimensional Hilbert space. Received 12 August 2002 / Received in final form 14 October 2002 Published online 4 February 2003     

Improved sensitivity in the search for a parity-violating energy difference in the vibrational spectrum of the enantiomers of CHFClBr

The theoretical prediction that enantiomers of chiral molecules have different spectra because of parity violation associated with neutral currents in the weak interaction has been experimentally looked for. Last searches of a frequency difference in the vibrational spectrum of the enantiomers of CHFClBr obtained with our infrared saturation spectrometer is presented. The frequencies of a saturation resonance of separated enantiomers of CHFClBr have been compared at a 5×10^-14 level. A residual pressure shift probably induced by uncontrolled impurities of the samples has been observed and found to limit our experimental sensitivity. Finally no parity violating frequency difference is observed within the present sensitivity of 2.5×10^-13. A new experimental scheme is proposed which should let the parity violation effect observable. Received 22 January 2002 Published online 19 July 2002     

Line shape analysis of two-colour photoassociation spectra on the example of the Cs ground state

Two-photon photoassociation spectra in a Λ-type excitation scheme are analysed under the systematically varied experimental conditions of frequency detunings and laser intensities. Line shape fits are presented as well as the investigation of intensity and detuning dependent line shifts. From both we determine the attained spectroscopic precision, that is corrected for a systematic line shift due to the thermal distribution of atoms in the trap. An energy correction for this effect is given. Information about the feasibility of generating translationally cold molecules in a well defined rotational and vibrational level by the photoassociation process is derived from the analysis. Received 21 May 2002 Published online 15 October 2002 RID="a" ID="a"Current address e-mail: christian.lisdat@ptb.de RID="b" ID="b"e-mail: pierre.pillet@lac.u-psud.fr     

Relativistic electron beams detection in a dense plasma focus

Fast electron beams into a hollow anode of a small plasma focus machine (2 kJ, 4 μF) were measured. The diagnostic method designed for this purpose is founded in a small Rogowski coil introduced into a cavity performed in the anode. By means of this, electron beam pulses of about 10 ns width generated in the plasma focus are detected. Simultaneously, hard X-ray signals obtained from a scintillator-photomultiplier system are registered. The electron beam energy was measured through the time-of-flight of the electrons between probe and anode top. The beams are found to be relativistic and its energy is into the range of hard X-rays energy. An analysis of signal intensities and relative delays for three hundred shots are here presented. Received 28 February 2002 / Received in final form 7 May 2002 Published online 24 September 2002