External Periodic Field Research Articles

Nonlinear Diffusion of the Magnetic Field in Weakly Ionized Plasmas

Enhanced nonlinear penetration of the external periodic magnetic field into a weakly ionized plasma is investigated. The penetration is enhanced by the convection of the magnetic field due to the Lorentz force. The nonlinearity leads to the wavelike propagation of the magnetic field or to the nonlinear diffusion similar to the diffusion in porous medium depending on plasma collisionality. It is shown that the periodic magnetic field experiences much slower decay inside the plasma compared to that of the standard skin effect.

Attenuation factors of de Haas–van Alphen oscillations in the vortex state of layered superconductors

We consider analytically within the Bogoliubov--de Gennes and Gor'kov approaches the magnetic oscillations due to the Landau quantization [de Haas--van Alphen (dHvA) effect] in the vortex-lattice (VL) state of layered superconductors. We found that the period of the dHvA oscillations does not change when the magnetic field H decreases below the upper critical field ${H}_{{c}_{2}},$ whereas amplitudes of the dHvA oscillations are damped by the attenuation factors. These factors appear due to (a) smearing of the Landau levels by impurities and disorder of the VL, (b) broadening of the Landau levels into dispersive bands by periodic VL, periodic external magnetic field, and periodic layered structure. In case (a) the attenuation factor is a Dinglelike exponent, $R(\ensuremath{\Delta},\ensuremath{\tau}{)=R}_{0}(\ensuremath{\tau}{)R}_{s}(\ensuremath{\Delta}{)R}_{0s}(\ensuremath{\Delta},\ensuremath{\tau}),$ where ${R}_{0}(\ensuremath{\tau})$ is the standard Dingle factor and ${R}_{s}(\ensuremath{\Delta})$ was calculated previously by Maki and Stephen. An extra damping is due to the interference term, ${R}_{0s}(\ensuremath{\Delta},\ensuremath{\tau}) =\mathrm{exp}(\ensuremath{-}\ensuremath{\pi}/\ensuremath{\Omega}{\ensuremath{\tau}}_{\mathrm{int}}),$ whose dependence on the magnetic field H is determined by the cyclotron frequency, \ensuremath{\Omega}, and ${\ensuremath{\tau}}_{\mathrm{int}}^{\ensuremath{-}1}\ensuremath{\sim}{\ensuremath{\Delta}}^{2}{/v}_{f}{l}_{0}H{(v}_{f}$ is the Fermi velocity, ${l}_{0}{=v}_{f}\ensuremath{\tau}$ is the mean free path). In case (b) attenuation factors differ from the simple Dingle exponent and corresponding damping of dHvA oscillations basically less than in case (a), especially for fields well below ${H}_{{c}_{2}}.$ In particular, the attenuation factor due to the layered structure is determined by the one-dimensional density of states $g(\ensuremath{\varepsilon}),$ related to the electron transport across the layers. This factor is a periodic function in $1/H$ with frequencies depending on locations of the van Hove singularities in $g(\ensuremath{\varepsilon})$ and the ones caused by the stacking faults. Competition between different attenuation mechanisms results in nonmonotonous decrease of the dHvA amplitudes and makes it possible to give a qualitative explanation of recent experiments on borocarbide ${\mathrm{YNi}}_{2}{\mathrm{B}}_{2}\mathrm{C}$ where the dHvA oscillations have been observed down to surprisingly low fields about ${0.2H}_{{c}_{2}}$ [T. Terashima et al. Phys. Rev. B 56, 5120 (1997)].

Response of a quantum system to a time-dependent external field and dynamical symmetry of the system

The response of a quantum system to a time-dependent periodic external field is investigated in connection with the dynamical symmetry breaking and level dynamics of the adiabatic states of the system. The main results are as follows. (A) When the periodic external field preserves the dynamical symmetry of the system, its response is like that of elastic matter. (B) When the periodic external field breaks the dynamical symmetry, several cases may occur: (a) in the adiabatic limit, the system still responds elastically; (b) if the initial state is an eigenstate of the evolution operator U(T) for one period T of the external field, the system evolves in time cyclically and responds quasi-elastically; (c) if the initial state is not an eigenstate of the evolution operator U(T), the system evolves in time non-cyclically and responds non-elastically. The detailed non-elastic behaviour depends on the statistical nature of the adiabatic eigenstates of the system. If the adiabatic spectrum is chaotic, the non-elastic response is expected to be strongly dissipative. The avoided level crossings of the adiabatic eigenstates play a crucial role in both producing chaoticity of the adiabatic levels and causing dissipation of the non-elastic response. The non-elastic role played by the adiabatic progressive phase is also addressed. Computer experiments are performed for the su(2) dynamical model to illustrate the above general results.

ELECTROMAGNETIC DETECTION OF AXIONS IN A WAVE GUIDE

The conversion of photons into axions in a periodic external electromagnetic field, i.e. the TEm0 mode, is considered in details by using Feynman methods. The differential cross-sections are given. It is shown that the lowest mode gives the main contribution to the considered process.

Accurate method for determining tilt bias angles in thin films of nematic liquid crystals

We have developed a new method for measuring tilt bias angles in spatially uniform and nonuniform thin films of nematic liquid crystals. The method employs modulation ellipsometry, based on the use of an exponentially decaying light wave to probe the boundary layer. Oscillations of the director of the liquid crystal, which are induced by the flexoelectric torque, are excited with an external periodic field. A periodic variation of the ellipticity of the light wave reflected from the interface is detected at both the first and second harmonics of the exciting electric field. When these two Fourier components of the electrooptic response are known, it is possible to calculate both the tilt bias angle θ0 of the director and the dynamic deviation δ0 of the tilt bias angle. The angles θ0 and δ0 measured by this method on the surface of an electrode (ITO) and on the surface of a ferroelectric film (a copolymer of vinylidene fluoride and trifluoroethylene), oriented in a corona discharge, were equal to θ 0=5.1°, δθ=0.5° and θ0=89°, δθ=0.06°, respectively.

Master equation for a quantum system driven by a strong periodic field in the quasienergy representation

The evolution of a quantum system weakly coupled with a thermal reservoir and influenced by an external periodic field is formulated in the quasienergy representation where the strong external periodic field disappears and the original model is transformed to a time-dependent system weakly coupled with thermal reservoir. Based on this time-dependent subdynamics, we derive a master equation of the reduced density operator for the driven quantum system. This equation is valid in the weak-coupling limit. Our method can be useful for obtaining the master equation of any system coupled with a thermal reservoir and driven by strong external periodic fields.

Splitting of the Low Landau Levels into a Set of Positive Lebesgue Measure under Small Periodic Perturbations

We study the spectral properties of a two-dimensional Schrodinger operator with a uniform magnetic field and a small external periodic field: $$$$ where $$$$ and \(\), \(\) are small parameters. Representing \(\) as the direct integral of one-dimensional quasi-periodic difference operators with long-range potential and employing recent results of E.I.Dinaburg about Anderson localization for such operators (we assume \(\) to be typical irrational) we construct the full set of generalised eigenfunctions for the low Landau bands. We also show that the Lebesgue measure of the low bands is positive and proportional in the main order to \(\).

Entrainment in nerve by a ferroelectric model (II): Quasi-periodic oscillation and the phase locking

A nonlinear state equation for membrane excitation can be simplified by Leuchtag's ferroelectric model which is applied to a chemical network theory. A dissipative structure of such a membrane is described by an equilibrium space, η 3 + aη + b = 0, giving a cusp catastrophe, and the membrane is self-organized in the resting state under the condition, a < 0( T < T c), where η corresponds to the membrane potential, and a and b imply dipole—dipole and dipole—ion interactions of channel proteins embedded in the membrane, respectively. As well known, a specific characteristic of nonlinear electrical phenomena in the membrane is a limit cycle arising through the entrainment by periodical stimuli or chaos. A phase transition between the equilibrium and the non-equilibrium states (a dissipative structure without the resting state) is described by a parameter giving the difference from thermal equilibrium. In this dynamic system, quasi-periodic oscillations which arise in periodic external fields and the phase locking, that is, entrainment, caused by changing I 0 at ω ≠ ω n (ω n — the natural frequency of the membrane) are studied with parameters introduced into Zeeman's formulas of ȧ and ḃ.

Combined influence of random and regular external fields on long-range electron transfer

The dissipative dynamics of a two-level system (TLS) is studied for the case of the simultaneous modulation of the energy bias by a regular external field and by nonequilibrium dichotomic fluctuations. To describe the noise-averaged dynamics driven by the external periodic field, a set of coupled generalized master equations is derived. Quantum fluctuations of the thermal bath are taken into account within the noninteracting blip approximation, whereas the dichotomic fluctuations and the external field are treated in an exact manner. The case of nonadiabatic continuous-wave (cw) driving is considered in detail for an asymmetric TLS strongly coupled to the thermal bath. The general approach is applied to long-range electron transfer in proteins. According to the presence of dynamic disorder, the coarse-grained electron transfer dynamics becomes nonexponential. The gated regime and the inversion effect of the transfer in the strongly biased TLS with a dichotomic fluctuating energy bias are demonstrated. Additionally, it is shown that a strong cw field can switch the electron transfer dynamics between the gated (nonexponential) regime and the nonadiabatic (single-exponential) regime.

Discrete-time picture for multiphoton microwave spectroscopy

The time evolution of atomic and molecular systems driven by periodic external fields is reformulated to combine Floquet's theorem with time-dependent representations of the atomic degrees of freedom. This approach increases the flexibility of Floquet calculations of multiphoton processes in strong radiation fields, particularly at low frequencies, by incorporating adiabatic states into the basis. The depopulation of Rydberg states of He and Na in strong microwave fields illustrates the utility of the method. In particular, a study of the depopulation of the 11s state of Na in an oscillatory field reveals a strong correspondence between dc-field Stark maps and quasienergy spectra and predicts a resonance feature associated with Landau-Zener transitions between dc Stark levels.

Control of long-range electron transfer in dynamically disordered molecular systems by an external periodic field

The influence of a strong periodic field on the long-range electron transfer is studied theoretically within the driven spin-boson model extended by a dichotomically fluctuating tunneling coupling. Applying the noninteracting blip approximation, a set of coupled kinetic equations is derived. It describes the time-development of the electronic population difference between the donor and acceptor states averaged with respect to the stochastic process, the quantum fluctuations of the bath and over the fast oscillating field. The strength of the periodic field is taken into account in a nonperturbative manner. A detailed analysis is carried out for the case of a strong coupling of the transferred electron to a specific reaction coordinate. Analytical expressions for the effective transfer rate are obtained and their numerical analysis is presented. For the case of adiabatically controlled (gated) transfer the existence of a transfer regime is demonstrated where the strong external field does not influence the effective transfer rate, however, it can completely revert the direction of the transfer. Finally, it is shown that the periodic field can induce transitions between the quasi-adiabatic (gated) and the nonadiabatic regime of electron transfer.

Resonant subharmonic absorption and second-harmonic generation by a fluctuating nonlinear oscillator.

The effect of fluctuations on the nonlinear response of an underdamped oscillator to an external periodic field at a subharmonic frequency has been investigated theoretically, numerically, and with an analog electronic circuit model. The system studied has often been analyzed in nonlinear optics in the context of two-photon absorption and second-harmonic generation. We consider its nonlinear spectroscopy. Its resonant nonlinear response is described over a broad range of the fluctuation intensities. It is shown that the fluctuation intensity can be used to tune the oscillator so as to maximize the nonlinear response. The dependence of the absorption cross section on the fluctuation intensity displays a clearly resolved maximum. If the eigenfrequency of the oscillator is a nonmonotonic function of its energy, the signal at the second harmonic displays a resonant peak at one of two different frequencies, depending on the noise intensity.

Transform-limited coherent synchrotron radiation wavepackets in a chirped pulse free-electron laser

A novel source of transform-limited pulses of coherent electromagnetic radiation relying on the synchrotron radiation process in a fast wave guiding structure is investigated theoretically. An ultrashort electron bunch transversally accelerated by a periodic external field is considered. At grazing, where the bunch and group velocities are matched, the duration of the resulting ultrawideband chirped pulse is governed by group velocity dispersion instead of slippage. Because of the intimate connection between the rate of chirping and the bandwidth, the corresponding pulse duration is shown to be very close to the Fourier transform limit. In addition, the propagation of such chirped pulses through a guiding structure with negative group velocity dispersion is investigated both theoretically and computationally. The spectral and temporal characteristics of the chirped and compressed pulses are derived analytically. Detailed computer calculations complement this theoretical analysis.

Control of the dynamics of a dissipative two-level system by a strong periodic field

The incoherent dynamics of a two-level system (TLS) coupled to a thermal bath and driven by a strong external periodic field is studied. Starting with the master equation for a dissipative TLS in an external field, we derive analytical expressions for the effective rate constant and for the apparent energy bias of the TLS in a fast oscillating periodic field. The expressions obtained include the field in a non-perturbative manner and they are used to study the influence of a strong periodic driving field on long-range electron transfer reactions in condensed media. It is shown that, for some cases, the steady-state populations of the donor and acceptor levels and therefore the direction of electron transfer can be inverted by a strong periodic field.

Field dependent resonance frequency of hysteresis loops in a few monolayer thick Co/Cu(001) films

Dynamic responses of magnetic hysteresis loops in a few monolayer (ML) thick Co/Cu(001) films were studied using surface magneto-optic Kerr effect (SMOKE). For a fixed external field strength H0, the hysteresis loop area increases as a function of frequency with a power law and reaches a maximum at a resonance frequency Ω0. This Ω0 depends on the external periodic field strength as well as the thickness and roughness of the films. The thickness and roughness parameters were measured quantitatively using high-resolution low-energy electron diffraction. For a fixed film thickness, the Ω0 in the low field region is highly dependent on H0, which is consistent with the prediction from the mean field model. For two Co films with an equivalent thickness but different degrees of film roughness, the resonance frequency Ω0 is lower for the rougher films in all the field strengths studied. For a fixed field strength, the value of Ω0 decreases as Co film roughness increases in a few ML regime. The roughness dependency in Ω0 indicates that the slowing down in the magnetization reversal process is due to the increased film roughness.

Scaling and dynamics of low-frequency hysteresis loops in ultrathin Co films on a Cu(001) surface.

The hysteresis loops of epitaxially grown ultrathin Co films on a Cu(001) surface with magnetic anisotropy were measured in situ at room temperature under a periodic external field by the surface magneto-optical Kerr-effect technique. A dynamic phase transition occurs at high frequencies. At very low frequencies, \ensuremath{\Omega}, a constant hysteresis loop area exists. We also observed power-law scaling of the loop area, A\ensuremath{\sim}${\mathit{H}}_{0}^{\mathrm{\ensuremath{\alpha}}}$${\mathrm{\ensuremath{\Omega}}}^{\mathrm{\ensuremath{\beta}}}$, for ${\mathit{H}}_{0}$&gt;40 Oe and \ensuremath{\Omega}/2\ensuremath{\pi}90 Hz, with exponents \ensuremath{\alpha} and \ensuremath{\beta} each about 2/3. The observations are consistent with a mean-field Ising model.

Stochastic resonance in a mean-field model of cooperative behavior

We study the long-time response of a stochastic system formed by very many interacting subsystems coupled by a mean-field interaction and subject to a time periodic external field. In the absence of a driving field; the system shows an order-disorder phase transition and its time evolution is well described by a Fokker-Planck equation which is nonlinear in the probability density. We carry out an analysis of the dynamics in the case of a weak driving field by means of a perturbation analysis (linear response theory). The response of the system is then given in terms of a generalized susceptibility. Its evaluation shows that the phenomenon of stochastic resonance, typical of driven bistable systems, is greatly enhanced by the dynamical feedback induced by mean-field coupling.

Non-Periodic Current Oscillations in the Gunn-Effect Device with the Impact-Ionization Effect

A simulation model of the Gunn-effect device is considered. Using the finite difference method, spatio-temporal evolution of the system in the presence of the impact-ionization effect in the device is computed for n -GaAs with the recombination rate and the bias voltage being taken as the control parameters. We thereby show the motion of the Gunn-effect device exhibits non-periodic behavior due to its own autonomous nonlinearity even if it is not driven by an external periodic field. The domain motion is perturbed by the carrier generation due to the impact ionization, and it becomes non-periodic for specially chosen model parameters. It also exhibits the interpulse incoherent current oscillations similar to the ones observed experimentally. Some remarks are given on the mechanism giving rise to the nonperiodicity on the basis of spatio-temporal evolution of the high-field domain.

Behaviour of hole and electron dominated photorefractive CdTe: V crystals under external continuous or periodic electric field

The photorefractive properties of two CdTe: V crystals are compared in the infrared range. For both crystals, an increase of the electron-hole competition factor (from electrons to holes) is measured when the operating wavelength increases. The values of the wavelength where the sign of the dominating carriers changes are different. In the high wavelength range, high TWM gains are obtained by applying a square-shaped electric field at an optimum frequency. This frequency dependence can be explained by considering the effect of a second deep level. In the low wavelength range, a resonant intensity-temperature effect, as in InP:Fe, is demonstrated for the first time in this material. The difference between the two crystals is assumed to be particularly sensitive to the compensation - or not - of the cadmium losses during the crystal growth.

Waveform analysis of the voltage from a pick-up coil with a granular superconducting core: Critical state behavior

We have observed the waveform of the voltage induced in a pick-up coil surrounding a granular superconducting sample in a periodic external magnetic field. The voltage waveform depends strongly on the amplitude of the external field, and its symmetry is broken by the presence of a static dc field. The results can be interpreted as the response of a superconductor in the critical state. A critical state model calculation is given to confirm this interpretation.