Dynamics of a pair of coupled nonlinear oscillators

A pair of coupled classical oscillators with a general potential and general form of coupling is investigated. For general potentials, the single-frequency solution is shown to be stable for small excitations. For special potentials, such system remains stable for an arbitrary excitation. In both cases, the stability does not depend on the form of coupling. Transition to the instability regime follows from the way how nonlinear potential entrains the energy transfer between the oscillators. Relation between the existence of multi-frequency quasi-periodic or periodic solutions and the instability of single-frequency ones is discussed.     

Dynamics of a coupled pair of two-level tunnelling systems

An exact solution for the dynamics of a coupled pair of symmetric two-level-systems is given by calculating the resolvent of the Liouvillian and the statistical operator of the problem. At low temperatures interference effects between the two systems turn out to be of major importance. Depending on the value and the sign of the interaction parameter the susceptibility of the pair increases or decreases compared to the situation of isolated systems. For high temperatures the interference contributions disappear.     

Propagation of a pair of vortices through a tilted lens

The propagation of a pair of vortices nested in a Gaussian beam through a tilted lens is studied. It is shown that after passing through the tilted lens, the relation between the transverse position of vortices and the tilt coefficient is linear in the propagation for isopolar vortex pair and vortex dipole, and in the three-dimensional (3D) case the vortex trajectories are sometimes like U or X shapes. With increasing the orientation angle of the vortex pair, the trajectories of vortices are circles for the both cases. The overlap of vortices may take place for the isopolar vortex pair, while the annihilation and revival of vortices occur for the vortex dipole in the propagation.     

Magnetization reversal in submicron disks: exchange biased vortices

Submicron, circular, ferromagnetic-antiferromagnetic dots exhibit different magnetization reversal mechanisms depending on the direction of the magnetic applied field. Shifted, constricted hysteresis loops, typical for vortex formation, are observed for fields along the exchange bias direction. However, for fields applied close to perpendicular to the exchange bias direction, magnetization reversal occurs via coherent rotation. Magnetic force microscopy imaging together with micromagnetic simulations are used to further clarify the different magnetic switching behaviors.     

Dynamics of magnetic vortices

The canonical conservation laws of linear and angular momentum in the ferromagnetic continuum have been known to be plagued by certain ambiguities which are resolved in this paper by constructing conservation laws as suitable moments of a topological density. The resulting canonical structure is then shown to be analogous to that encountered in the familiar Hall effect and explains the unusual features of the dynamics of magnetic vortices without resorting to a detailed solution of the underlying nonlinear equations. Thus, in the absence of external magnetic fields, a magnetic vortex is shown to be spontaneously pinned around a fixed guiding center. The guiding center would drift in a direction perpendicular to an applied magnetic field gradient, provided that dissipation can be neglected, with a Hall velocity that is calculated explicitly in terms of the initial configuration of the vortex. In the presence of dissipation, the vortex undergoes skew deflection at an angle δ ≠ 90° with respect to the applied field gradient. The angle δ is related to the winding number of the vortex according to the well-known golden rule of bubble dynamics.     

Dynamics of kinematic vortices in a mesoscopic superconducting loop

Using the time-dependent Ginzburg–Landau formalism, we study the dynamic properties of a submicron superconducting loop in applied current and in presence of a perpendicular magnetic field. The resistive state of the sample is caused by the motion of kinematic vortex–antivortex pairs. Vortices and antivortices move in opposite directions to each other, perpendicularly to the applied drive, and the periodic creation and annihilation of such pairs results in periodic oscillations of the voltage across the sample. The dynamics of these kinematic pairs is strongly influenced by the applied magnetic field, which for high fields leads to the flow of just vortices. Kinematic vortices can be temporarily pinned inside the loop with observable trace in the voltage vs. time characteristics.     

Coherent vortices in strongly coupled liquids

Strongly coupled liquids are ubiquitous in both nature and laboratory plasma experiments. They are unique in the sense that their average potential energy per particle dominates over the average kinetic energy. Using "first principles" molecular dynamics (MD) simulations, we report for the first time the emergence of isolated coherent tripolar vortices from the evolution of axisymmetric flows in a prototype two-dimensional (2D) strongly coupled liquid, namely, the Yukawa liquid. Linear growth rates directly obtained from MD simulations are compared with a generalized hydrodynamic model. Our MD simulations reveal that the tripolar vortices persist over several turn over times and hence may be observed in strongly coupled liquids such as complex plasma, liquid metals and astrophysical systems such as white dwarfs and giant planetary interiors, thereby making the phenomenon universal.     

Electron vortices in photoionization by a pair of elliptically polarized attosecond pulses

The photoionization by two elliptically polarized, time delayed attosecond pulses is investigated to display a momentum distribution having the helical vortex or ring structures. The results are obtained by the strong field approximation method and analyzed by the pulse decomposition. The ellipticities and time delay of the two attosecond pulses are found to determine the rotational symmetry and the number of vortex arms. For observing these vortex patterns, the energy bandwidth and temporal duration of the attosecond pulses are ideal.     

Far-field properties of nonparaxial Gaussian beams with a pair of vortices

The analytical far-field expressions for the TE and TM terms and energy flux distributions of nonparaxial Gaussian beams with a pair of vortices are derived by using vector angular spectrum representation and stationary phase method. The far-field properties including phase singularities and energy flux distributions of the TE and TM terms and whole beam are studied in detail. It is shown that there exist a saddle point and phase singularities that depend on the off-axis distance, waist width, and propagation distance. By suitably varying the off-axis distance, the motion and variation of topological charge of phase singularities may take place. The results are interpreted and compared with the previous work.     

Dynamics of a vortex pair in radial flow

The problem of vortex pair motion in two-dimensional radial flow is solved. Under certain conditions for flow parameters, the vortex pair can reverse its motion within a bounded region. The vortex-pair translational velocity decreases or increases after passing through the source/sink region, depending on whether the flow is diverging or converging, respectively. The rotational motion of a corotating vortex pair in a quiescent environment transforms into motion along a logarithmic spiral in radial flow. The problem may have applications in astrophysics and geophysics.     

Dynamics of quantum vortices in two-dimensional superconductors

The dynamics of rigid vortex translations in two-dimensional arrays of Josephson junctions is shown to be equivalent to the motion of a mass, proportional to the junction capacitance, in a periodic pinning potential. The quantum tunneling of the vortex through the potential barriers is predicted of importance in the existing Nb-arrays at very low temperatures. Above the vortex unbinding temperature there is a plasma resonance of the free vortices leading to an anomaly in the vortex frequency dependent dielectric constant, which could be observed via a radio frequency impedance measurement.     

Exchange bias in nearly perpendicularly coupled ferromagnetic/ferromagnetic system

Exchange bias phenomena appear not only in ferromagnetic/antiferromagnetic systems but also in ferromagnetic/ferromagnetic systems in which two layers are nearly perpendicularly coupled. We investigated the origin of the symmetry-breaking mechanism and the relationship between the exchange bias and the system's energy parameters. We compared the results of computational Monte Carlo simulations with those of theoretical model calculation. We found that the exchange bias exhibited nonlinear behaviors, including sign reversal and singularities. These complicated behaviors were caused by two distinct magnetization processes depending on the interlayer coupling strength. The exchange bias reached a maximum at the transition between the two magnetization processes.     

Dynamics of a quantum phase transition in a ferromagnetic Bose-Einstein condensate

We discuss dynamics of a slow quantum phase transition in a spin-1 Bose-Einstein condensate. We analytically determine the scaling properties of the system magnetization and verify them with numerical simulations in a one dimensional model.     

Pinning-induced formation of vortex clusters and giant vortices in mesoscopic superconducting disks

Merged, or giant, multiquanta vortices (GVs) are known to appear in very small superconductors near the superconducting transition due to strong confinement of magnetic flux. Here we present evidence for a new, pinning-related, mechanism for vortex merger. Using Bitter decoration to visualize vortices in small Nb disks with varying degrees of disorder, we show that confinement in combination with strong disorder causes individual vortices to merge into clusters or even GVs well below Tc and Hc2, in contrast to well-defined shells of individual vortices found in the absence of pinning.     

Magnetic vortices in small ferromagnetic particles with the strong dipolar interaction

The ground state of cylindrical magnetic samples of different sizes at nonzero applied magnetic field is studied theoretically taking into account the exchange and dipole-dipole interactions at an arbitrary ratio of coupling constants. In addition to the weakly inhomogeneous and standard vortex states well known for the case of the weak dipole-dipole interaction, the vortex states with the complicated structure of the vortex core have been found. The state diagram for these particles has been constructed and analyzed in terms of scaling consideration.     

Quasi-particle excitations around a pair of half-quantum vortices in p- wave superconductors

Triplet superconductors such as Sr₂RuO₄ and Na_xCoO₂⋅yH₂O are now found to be p-wave (p_x ± ip_y) or f-wave ((p_x ± ip_y) cos cp_z) superconductors. It was phenomenologically suggested that in these p-wave or f-wave superconductors, a pair of half-quantum vortices (HQVs) becomes stable. Using the Bogoliubov-de Gennes equation, previously we have analyzed quasi-particle excitations around an HQV at one end of a d-soliton for simplicity. In next study, we will investigate the stability of the pair of HQV’s, which are connected by the d-soliton. For this purpose, we have developed a new numerical method to solve the Bogoliubov-de Gennes equation for two vortices state, using Mathieu functions.     

Tight focusing properties of linearly polarized Gaussian beam with a pair of vortices

The properties of a pair of vortices embedded in a Gaussian beam focused by a high numerical-aperture are studied on the basis of vector Debye integral. The vortices move and rotate in the vicinity of the focal plane for a pair of vortices with equal topological charges. For incident beam with a pair of vortices with opposite topological charges, the vortices move toward each other, annihilate and revive in the vicinity of focal plane.     

Dynamics of a pair of spherical gravitating shells

The dynamical N body problem for a system of mass points interacting solely through gravitational forces is not integrable. The difficulties which arise in constructing accurate numerical codes for simulating the motion over long time scales are legend. Thus, in order to test their theories, astronomers and astrophysicists resort to simpler, one-dimensional models which avoid the problems of binary formation, escape, and the singularity of the inverse square force law. To date, the most frequently employed "test" model consists of a system of parallel mass sheets moving perpendicular to their surface. While this system avoids all of the above problems, the time scale for reaching equilibrium is extremely long and probably arises from the system's weak ergodic properties, which become manifest even in the three sheet system. Here we consider a different one-dimensional gravitating system consisting of nonrotating concentric mass shells. For the case of two shells we investigate the structure of the phase space by studying the stability of periodic trajectories. By employing an event driven algorithm, we are able to directly investigate the influence of the singularity without having to resort to regularization of the force. Although stable structures are present at every energy, we find that the ergodic properties of this system are more robust than its planar counterpart. (c) 1997 American Institute of Physics.     

Nonlinear nonstationary processes in a pair of coupled gyro-backward-wave oscillators

The nonlinear dynamics of a pair of unidirectionally coupled gyro-backward-wave oscillators is studied numerically. When the control parameters vary, both developed chaotic oscillations and steady single-frequency oscillations may arise in this pair. The ranges of parameters within which the pair of gyro-oscillators exhibits developed chaotic oscillations are found. Physical processes complicating chaotic processes in the active medium are considered.