Excitation and control of large amplitude standing magnetization waves

A robust approach to excitation and control of large amplitude standing magnetization waves in an easy axis ferromagnetic by starting from a ground state and passage through resonances with chirped frequency microwave or spin torque drives is proposed. The formation of these waves involves two stages, where in the first stage, a spatially uniform, precessing magnetization is created via passage through a resonance followed by a self-phase-locking (autoresonance) with a constant amplitude drive. In the second stage, the passage trough an additional resonance with a spatial modulation of the driving amplitude yields transformation of the uniform solution into a doubly phase-locked standing wave, whose amplitude is controlled by the variation of the driving frequency. The stability of this excitation process is analyzed both numerically and via Whitham's averaged variational principle

Autoresonant excitation of Bose-Einstein condensates

Controlling the state of a Bose-Einstein condensate driven by a chirped frequency perturbation in a one-dimensional anharmonic trapping potential is discussed. By identifying four characteristic time scales in this chirped-driven problem, three dimensionless parameters $P_{1,2,3}$ are defined describing the driving strength, the anharmonicity of the trapping potential, and the strength of the particles interaction, respectively. As the driving frequency passes the linear resonance in the problem, and depending on the location in the $P_{1,2,3}$ parameter space, the system may exhibit two very different evolutions, i.e. the quantum energy ladder climbing (LC) and the classical autoresonance (AR). These regimes are analysed both in theory and simulations with the emphasis on the effect of the interaction parameter $P_{3}$. In particular, the transition thresholds on the driving parameter $P_{1}$ and their width in $P_{1}$ in both the AR and LC regimes are discussed. Different driving protocols are also illustrated, showing efficient control of excitation and de-excitation of the condensate

Resonant control of solitons

It is shown that the effect of "scattering on resonance" can be used to control envelope solitons in the driven nonlinear Schrödinger equation. The control occurs by the frequency modulated driving with multiple crossing of the resonant frequency of the soliton. Crown Copyright © 2013 Published by Elsevier B.V. All rights reserved

Narrow autoresonant magnetization structures in finite-length ferromagnetic nanoparticles

The autoresonant approach to excitation and control of large-amplitude uniformly precessing magnetization structures in finite-length easy axis ferromagnetic nanoparticles is suggested and analyzed within the Landau-Lifshitz-Gilbert model. These structures are excited by using a spatially uniform, oscillating, chirped frequency magnetic field, while the localization is imposed via boundary conditions. The excitation requires the amplitude of the driving oscillations to exceed a threshold. The dissipation effect on the threshold is also discussed. The autoresonant driving effectively compensates the effect of dissipation but lowers the maximum amplitude of the excited structures. Fully nonlinear localized autoresonant solutions are illustrated in simulations and described via an analog of a quasiparticle in an effective potential. The precession frequency of these solutions is continuously locked to that of the drive, while the spatial magnetization profile approaches the soliton limit when the length of the nanoparticle and the amplitude of the excited solution increase. © 2019 American Physical Society

Standing autoresonant plasma waves

The formation and control of strongly nonlinear standing plasma waves (SPWs) from a trivial equilibrium by a chirped frequency drive are discussed. If the drive amplitude exceeds a threshold, after passage through the linear resonance in this system, the excited wave preserves the phase locking with the drive, yielding a controlled growth of the wave amplitude. We illustrate these autoresonant waves via Vlasov-Poisson simulations, showing the formation of sharply peaked excitations with local electron density maxima significantly exceeding the unperturbed plasma density. The Whitham averaged variational approach applied to a simplified water bag model yields the weakly nonlinear evolution of the autoresonant SPWs and the autoresonance threshold. If the chirped driving frequency approaches some constant level, the driven SPW saturates at a target amplitude, avoiding the kinetic wave breaking. © The Author(s), 2020. Published by Cambridge University Press.This work was supported by the US-Israel Binational Science Foundation grant no. 6079 and the Russian state program AAAA-A18- 118020190095-4. The authors are also grateful to J. S. Wurtele, P. Michel and G. Marcus for helpful comments and suggestions

Quantum versus classical phase-locking transition in a driven-chirped oscillator

Classical and quantum-mechanical phase locking transition in a nonlinear oscillator driven by a chirped frequency perturbation is discussed. Different limits are analyzed in terms of the dimensionless parameters $/\sqrt{2m\hbar \omega_{0}\alpha}$ and $P_{2}=(3\hbar \beta)/(4m\sqrt{\alpha})$ ($\epsilon,$ $\alpha,$ $\beta$ and $\omega_{0}$ being the driving amplitude, the frequency chirp rate, the nonlinearity parameter and the linear frequency of the oscillator). It is shown that for $P_{2}\ll P_{1}+1$, the passage through the linear resonance for $P_{1}$ above a threshold yields classical autoresonance (AR) in the system, even when starting in a quantum ground state. In contrast, for $$, the transition involves quantum-mechanical energy ladder climbing (LC). The threshold for the phase-locking transition and its width in $P_{1}$ in both AR and LC limits are calculated. The theoretical results are tested by solving the Schrodinger equation in the energy basis and illustrated via the Wigner function in phase space

Parametric autoresonant excitation of the nonlinear Schrödinger equation

Parametric excitation of autoresonant solutions of the nonlinear Schrodinger (NLS) equation by a chirped frequency traveling wave is discussed. Fully nonlinear theory of the process is developed based on Whitham's averaged variational principle and its predictions verified in numerical simulations. The weakly nonlinear limit of the theory is used to find the threshold on the amplitude of the driving wave for entering the autoresonant regime. It is shown that above the threshold, a flat (spatially independent) NLS solution can be fully converted into a traveling wave. A simplified, few spatial harmonics expansion approach is also developed for studying this nonlinear mode conversion process, allowing interpretation as autoresonant interaction within triads of spatial harmonics. © 2016 American Physical Society

Autoresonant excitation of dark solitons

Continuouslyphase-locked (autoresonant) dark solitons of the defocusing nonlinear Schrodinger equation are excited and controlled by driving the system by a slowly chirped wavelike perturbation. The theory of these excitations is developed using Whitham's averaged variational principle and compared with numerical simulations. The problem of the threshold for transition to autoresonance in the driven system is studied in detail, focusing on the regime when the weakly nonlinear frequency shift in the problem differs from the typical quadratic dependence on the wave amplitude. The numerical simulations in this regime show a deviation of the autoresonance threshold on the driving amplitude from the usual 3/4 power dependence on the driving frequency chirp rate. The theory of this effect is suggested. © 2015 American Physical Society

Anomalous autoresonance threshold for chirped-driven Korteweg-de-Vries waves

Large amplitude traveling waves of the Korteweg-de-Vries (KdV) equation can be excited and controlled by a chirped frequency driving perturbation. The process involves capturing the wave into autoresonance (a continuous nonlinear synchronization) with the drive by passage through the linear resonance in the problem. The transition to autoresonance has a sharp threshold on the driving amplitude. In all previously studied autoresonant problems the threshold was found via a weakly nonlinear theory and scaled as α3/4,α being the driving frequency chirp rate. It is shown that this scaling is violated in a long wavelength KdV limit because of the increased role of the nonlinearity in the problem. A fully nonlinear theory describing the phenomenon and applicable to all wavelengths is developed. © 2015 American Physical Society