Nonlinear dynamics on catalytic surfaces: The contribution of surface science

Rate oscillations and chemical wave patterns on catalytic surfaces have been intensely studied in the past two decades. Starting with rate oscillations as an exotic phenomenon and with only a few speculative ideas available about the mechanistic cause today a very high level of detailed mechanistic understanding has been reached and very sophisticated experiments are performed in this area. The development in this field over the past 25 years is reviewed briefly highlighting the contribution of the “single crystal approach” to the progress which has been achieved.     

Observation of latent coherent effects in randomized systems

Coherent interference effects of the following three types are experimentally discovered in disordered (randomized) systems: (i) Josephson behavior of the HTSC polycrystal BaKBiO in the phase-separated state; (ii) oscillations of bismuth film resistance, which are periodic in “direct” magnetic field; and (iii) mesoscopic oscillations of the resistance in the course of film growth. In the first case, the method for detecting the “latent” nonstationary Josephson effect is substantiated by the frequency modulation method for microwave radiation, while in the other two cases, simple models are proposed to explain the nature of coherent oscillations of the resistance. The analogy between the observed oscillations and the Josephson effect in randomized systems is discussed.     

Nuclear quadrupole resonance in the gamma-resonance spectra of soft matter

It is shown that the harmonic librations (oscillations) of the principal axis of the electric field gradient tensor in “cages” of liquids, glasses, ferroliquids, and other “soft” systems qualitatively change the shape of the Mössbauer spectra of the quadrupole hyperfine structure. In addition to an effective decrease in the quadrupole coupling constant in the fast-libration limit, nuclear quadrupole resonance is predicted, which must be manifested in the Mössbauer spectra at the libration frequency that is approximately equal to the quadrupole splitting of spectral lines. By analogy with nuclear magnetic resonance, simple analytical expressions are derived, which describe resonance Mössbauer spectra in terms of the effective quadrupole coupling constant and the resonance splitting constant for the main lines. The observed features of the formation of quadrupole hyperfine structure spectra can be manifested in the Mössbauer spectra of soft matter and must be taken into account in analysis of experimental data.     

两个级联型三能级原子受激辐射的非线性性质

本文研究了两个级联型三能级原子同单模腔场的非线性相互作用.研究表明: 在激发场场强达到一定阈值以后, 两个原子的合作辐射效应变成同步辐射, 即多原子系统在一定阈值条件下可以有组织成相当于一个大原子的系统, 而产生同步有序辐射. 同时, 由于这种同步辐射效应, 两原子系统的受激辐射的二阶相干度相对于单原子系统的要大, 即聚束效应强而反聚束效应弱. 另外, 两原子系统由于多光子过程的加强而有更深的压缩效应, 此时要求的激发场场强也比单原子系统的要强. 关键词：     

Nonlinear dynamics of breathing current filaments inn-GaAs andp-Ge

A novel model is presented for spatio-temporal pattern formation in semiconductors. It leads to self-generated nonlinear current oscillations due to “breathing” current filaments in the regime of impurity impact ionization. The four qualitatively different regimes which have been observed in Ge with increasing current are consistently explained as: a stationary nonconducting state; bulkdominated oscillations; breathing filaments; stable filaments. The physical origin of the breathing oscillations is impact ionization coupled with transverse diffusion and longitudinal dielectric relaxation. A method is developed to derive simple nonlinear dynamic equations for the filament radius and the position of the peak transverse electric field by a nonlinear mode expansion.     

Refractive index of two-level gas in quantized field of counterpropagating waves

An expression for the refractive index of a gas of two-level atoms in the quantized single-mode field of counterpropagating waves is calculated. It is shown that in the limit of large numbers of photons the result reproduces the quasiclassical result in only the case of standing wave where intensities of both waves are equal. Explanation of this “strange” situation where the abilities of quantum field theory turn to be more restricted than those of classical theory is given.     

Kink dynamics in the highly discrete sine-Gordon system

We study kink dynamics in a very discrete sine-Gordon system where the kink width is of the order of the lattice spacing. Numerical simulations exhibit new properties of kinks in this case: they lose the memory of their initial velocity and propagate preferentially at well-defined velocities which correspond to quasi-steady states, while a kink moving at other velocities suffers relatively high rates of radiation of small amplitude oscillations. When a small external driving force is applied to the system, the same velocities appear as plateus in the strongly nonlinear mobility of the kink. The energy radiated by the kink is calculated for a simple model that preserves the discrete character of the system, and the preferential velocities for the kink are obtained to good accuracy. Similar results may be expected to be valid for other discrete systems manifesting topological solitons. The numerical simulations reveal also new stable “multiple-kink” excitations which can propagate almost freely in extremely discrete systems where “ordinary” simple kinks are pinned to the lattice by discreteness. The stability of the “multiple-kinks” is discussed.     

Vortex dynamics of counterpropagting laser beams in photorefractive materials

We study vortex patterns of counterpropagating laser beams in a photorefractive crystal, with or without the background photonic lattice. The vortices are effectively planar and have two “flavors” because there are two opposite directions of beam propagation. In a certain parameter range, the vortices form stable equilibrium configurations which we study using the methods of statistical field theory and generalize the Berezinsky–Kosterlitz–Thouless transition of the XY model to the “two-flavor” case. In the nonequilibrium regime, the patterns exhibit an Andronov–Hopf bifurcation which may lead to oscillations (limit cycle), chaos or decay to zero intensity due to radiation losses. We show how to identify various pathways toward instability from intensity patterns, i.e. from experiment.     

Linear photoelectron diffraction: application of a rapid approximation for surface structural studies

The linear superposition approximation proposed by Wander, Pendry and Van Hove for efficient low-energy electron diffraction calculations (“linear LEED”) is applied to photoelectron diffraction (“linear PD”). As with linear LEED, linear PD works very well for calculating the effect of displaced atoms. However, due to strong forward scattering at higher energies, linear PD requires that atoms do not move into or out of alignment. This limitation can be removed by suitable simple adjustments to the basic approximation, promising to make the method effective for structural searches of complex surfaces.     

Optical multistability and self oscillations in three level systems

The steady state behaviour of two cavity modes of the electromagnetic field interacting with a three level atomic medium is studied. This system may display optical tri- and quadra-stability. The results of Kitano et al. appear as a limit of our solutions in the dispersive and unsaturated regime. With the inclusion of saturation in the dispersive limit the asymmetric steady state may become unstable and give rise to self oscillations, period doubling and a new form of “optical turbulence”.     

Semi-transparent hadrons from multi-channel absorption effects

We analyze the absorption structure of diffractive dissociation discussing simultaneously the elastic and inelastic processes. This approach is motivated by their close interdependence and mutual influence. We show that the results differ significantly from the standard picture of elastic scattering. In particular, protons are shown to have very rich internal structure coupling both to “black” and “transparent” diffractive scattering eigenstates. Proton matter distribution may well be very different from that suggested by the analysis of Chou and Yang. Finally, the indicated asymptotic behaviour is that of a “grey” instead of a “black” disc limit.     

Quarks in a constant self-dual Euclidean background field: (II). Influence on the stability of the background field

The fermionic determinant is expanded in powers of the oscillations around a semiclassical background gluon field. In the quadratic approximation, with a translation invariant (anti)self-dual background SU(2) gluon field, the changes of the zero eigenvalues are investigated in a perturbative approximation. Subtracting the field-idependent contributions, the eigenvalue of the “color-longitudinal” zero mode is unchanged while those of the “color-transverse” zero modes get positive shifts, suggesting a further stabilization of the gluonic oscillations.     

Enhanced superradiance effect in a system of interacting two-level atoms and crossover from coherent to many-atom multiphoton relaxation regime

We study effects of direct interatomic interaction on cooperative processes in atom-photon dynamics. Using a model of two-level atoms with Ising-type interaction as an example, it is demonstrated that interparticle interaction can promote cooperative radiative relaxation. For small number of atoms this results in inhibition of incoherent spontaneous decay leading to the regime of collective pulse relaxation. Above superradiance threshold increase in delay time and enhancement of superradiance is occurred. In the case of strong interaction (as compared to excitation energy of an atom) transition to the regime of multiphoton relaxation occurs, which we discuss using a simple model of two atoms in a high-Q single mode cavity. It is shown that such transition is accompanied by Rabi oscillations involving many-atom multiphoton states. Dephasing effect of dipole-dipole interaction and solitonic mechanism of relaxation are discussed as well.     

Nonlocality of a free atomic wave packet

A simple model allows us to study the nonclassical behavior of slowly moving atoms interacting with a quantized field. Atom and field become entangled and their joint state can be identified as a mesoscopic “Schrödinger cat”. By introducing appropriate observables for atom and field and by analyzing correlations between them based on a Bell-type inequality we can show the corresponding nonclassical behavior.     

Grain boundary behavior in metallic solid solutions as deduced from diffusion and segregation experiments

Grain boundary diffusion and segregation experiments have been carried out in the same metallic solid solutions by means of radio-isotopes and Auger techniques. It was shown that the mass transport parameters could only be understood by assuming the formation of “2D phases” in “segregated grain boundaries” where the main bonds between atoms were identical to those which limit the bulk solid solubility of the solutes.     

Oscillations of the impedance of thin tungsten plates in a magnetic field

The surface impedance derivative with respect to the magnetic field of thin (skin depth comparable with thickness) tungsten plates is investigated experimentally and theoretically in circular polarizations of radio-frequency irradiation $\text{(? = 5 MHz)}$. The magnetic field is directed along the normal to sample surface-face (001). It is shown, that the impedance oscillations in both polarizations are due to the holes, lying on the bend of Fermi surface octahedron. The series of oscillations in “?” polarization is completely due to Gantmakher-Kaner (GK) effect [1]. The impedance oscillations in “+” polarization are caused by both GK effect and excitation of doppleron [2].     

Charge distribution in heavy-ion reactions

Marked oscillations are seen in the differential cross section of charge distributions in high-energy heavy-ion reactions with massive projectiles. It is suggested that this can be explained by a simple quantum mechanical potential model over an “enlarged” Hilbert space.     

Transverse relaxation of cesium vapour in a “strong” resonance radio frequency field

The fast adiabatic passage method was used to conduct measurements of the transverse relaxation times within hyperfine states of the ground state of cesium. The results of the experiment confirm the relations presented by Bouchiat for “weak” fields in spite of the fact that the field used, H₀ = 0.40 Oe is not a “weak” field. This apparent controversy is easily removed when one considers that in the presence of a rf field, atoms “see” an effective field which turns out to be a “weak” field.     

Effect of the lattice alignment on Bloch oscillations of a Bose-Einstein condensate in a square optical lattice

We consider a Bose-Einstein condensate of ultracold atoms loaded into a square optical lattice and subject to a static force. For vanishing atom-atom interactions the atoms perform periodic Bloch oscillations for arbitrary direction of the force. We study stability of these oscillations for non-vanishing interactions, which is shown to depend on an alignment of the force vector with respect to the lattice crystallographic axes. If the force is aligned along any of the axes, the mean field approach can be used to identify the stability conditions. On the contrary, for a misaligned force one has to employ the microscopic approach, which predicts periodic modulation of Bloch oscillations in the limit of a large forcing.