Chirped-frequency excitation of gravitationally bound ultracold neutrons

Manfredi, Giovanni; Morandi, Omar; Frièdland, L.; Jenke, Tobias; Abele, H.

doi:10.1103/physrevd.95.025016

Cited by 18 publications

(18 citation statements)

References 32 publications

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“…In particular, in the case  ′′ ( 0 ; , ) > 0, there are two modes corresponding to the simple roots. In the opposite case,  ′′ ( 0 ; , ) < 0, there are two additional modes corresponding to 0 and associated with the particular solutions having asymptotics (6). One of these additional modes with 1 = − is stable on the asymptotically long time interval.…”

Section: Resultsmentioning

confidence: 99%

“…• If  ′ ( ; , ) = 0 and  ′′ ( ; , ) < 0, then system (1) has two different solutions * ( ), * ( ) with asymptotic expansion in the form (6).…”

Section: The Roots Of Multiplicitymentioning

confidence: 99%

“…1,2 The autoresonance was first suggested in the problems associated with the acceleration of relativistic particles in the middle of the twentieth century, and nowadays it is considered as a universal phenomenon that plays the important role in a wide range of physical systems. [3][4][5][6][7] The study of relevant mathematical models leads to new and interesting problems in the field of nonlinear dynamics. [8][9][10][11] Mathematical models associated with the autoresonance have been actively studied recently.…”

Section: Introductionmentioning

confidence: 99%

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Bifurcations of autoresonant modes in oscillating systems with combined excitation

Sultanov

2019

Stud Appl Math

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A mathematical model describing the capture of nonlinear systems into the autoresonance by a combined parametric and external periodic slowly varying perturbation is considered. The autoresonance phenomenon is associated with solutions having an unboundedly growing amplitude and a limited phase mismatch. The paper investigates the behavior of such solutions when the parameters of the excitation take bifurcation values. In particular, the stability of different autoresonant modes is analyzed and the asymptotic approximations of autoresonant solutions on asymptotically long time intervals are proposed by a modified averaging method with using the constructed Lyapunov functions. K E Y W O R D Sautoresonance, asymptotics, bifurcation, nonlinear equations, stability Stud Appl Math. 2020;144:213-241.wileyonlinelibrary.com/journal/sapm

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Section: Resultsmentioning

confidence: 99%

“…• If  ′ ( ; , ) = 0 and  ′′ ( ; , ) < 0, then system (1) has two different solutions * ( ), * ( ) with asymptotic expansion in the form (6).…”

Section: The Roots Of Multiplicitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bifurcations of autoresonant modes in oscillating systems with combined excitation

Sultanov

2019

Stud Appl Math

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“…Note that the influence of small oscillatory perturbations on dynamical systems is well-studied problem [16][17][18][19][20]. In particular, chirped-frequency perturbations with a small parameter are effectively used to control the dynamics of nonlinear systems [21][22][23][24][25]. However, in this paper the presence of a small parameter is not assumed.…”

Section: Introductionmentioning

confidence: 99%

Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation

Sultanov¹

2021

Preprint

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The influence of oscillatory perturbations on autonomous strongly nonlinear systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time, and their frequency increases according to a power law. The long-term behaviour of perturbed trajectories is discussed. It is shown that, depending on the structure and the parameters of perturbations, there are at least two different asymptotic regimes: a phase locking and a phase drifting. In the case of phase locking, resonant solutions with an unlimitedly growing energy occur. The stability and asymptotics at infinity of such solutions are investigated. The proposed analysis is based on a combination of the averaging technique and the method of Lyapunov functions.

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“…LC is the quantum counterpart of the classical AR and it is a series of successive two-level Landau-Zener (LZ) transitions, where only two adjacent energy levels of the driven oscillator are coupled at any given time. Compared with AR, the discrete nature of LC is visible only when spectra of the systems is discrete enough, therefore, it is studied only in quantum systems including anharmonic oscillators [13][14][15], Rydberg atom [16] and bouncing neutrons [17]. Interestingly, it is demonstrated that classical systems, for example, Langmuir waves in bounded plasma, also can exhibit LC much like a quamtum system [18,19].…”

Section: Introductionmentioning

confidence: 99%

Ladder climbing and autoresonant acceleration of the spherical plasma density wave

et al. 2019

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Ladder climbing (LC) and autoresonance (AR) of the spherical plasma density wave are studied for the first time. The governing equation of the perturbed spherical density wave in the energy level space based on a hydrodynamic model of the electron plasma is presented, and it is demonstrated that the quantum LC and classical AR transition can be achieved in the spherical plasma. The asymptotic thresholds of the LC and AR transition of the spherical plasma wave are obtained analytically and confirmed numerically. We find that the spherical wave energy is concentrated to the sphere center as the density wave climbs to the higher level, the spherical plasma behaves obvious compression character, and the perturbed density of the sphere center even can be amplified to 100 times larger of the initial perturbed density. Compared to the one-dimensional case, the energy spectrum of the spherical plasma wave shifts upward, and the energy level spacing of the spherical plasma wave is broadened. These result in the facts that the spherical plasma needs the larger driving strength to achieve the LC and AR, while the total perturbed density of the spherical plasma always is larger than that of the one-dimensional case.

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Chirped-frequency excitation of gravitationally bound ultracold neutrons

Cited by 18 publications

References 32 publications

Bifurcations of autoresonant modes in oscillating systems with combined excitation

Bifurcations of autoresonant modes in oscillating systems with combined excitation

Resonances in asymptotically autonomous systems with a decaying chirped-frequency excitation

Ladder climbing and autoresonant acceleration of the spherical plasma density wave

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