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Driven transitions between megastable quantized orbits.

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Title: Driven transitions between megastable quantized orbits.
Authors: López, Álvaro G.1 (AUTHOR) alvaro.lopez@urjc.es, Valani, Rahil N.2 (AUTHOR)
Source: Chaos, Solitons & Fractals. Sep2025, Vol. 198, pN.PAG-N.PAG. 1p.
Subjects: Energy levels (Quantum mechanics), Orbits (Astronomy), Dynamical systems, Atomic transitions, Phase space, Limit cycles
Abstract: We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, i.e. megastability. In the low-memory regime, the equation reduces to a self-excited nonlinear oscillator and we use averaging methods to analytically show quasilinear increasing amplitude of the megastable spectrum of quantized quasicircular orbits. We further assign a mechanical energy to each orbit using the Lyapunov energy function and obtain a quadratically increasing energy spectrum and (almost) constant frequency spectrum. We demonstrate transitions between different quantized orbits, i.e. different energy levels, by subjecting the system to an external finite-time harmonic driving. In the absence of external driving force, the oscillator asymptotes towards one of the megastable quantized orbits having a fixed average energy. For a large driving amplitude with frequency close to the limit cycle frequency, resonance drives transitions to higher energy levels. Alternatively, for large driving amplitude with frequency slightly detuned from limit-cycle frequency, beating effects can lead to transitions to lower energy levels. Such driven transitions between quantized orbits form a classical analog of quantum jumps. For excitations to higher energy levels, we show amplitude locking where nearby values of driving amplitudes result in the same response amplitude, i.e. the same final higher energy level. We rationalize this effect based on the basins of different limit cycles in phase space. From a practical viewpoint, our work might find applications in physical and engineering system where controlled transitions between several limit cycles of a multistable dynamical system is desired. • A self-excited oscillator with state-dependent time delay is considered. • We find a countably infinite number of nested limit cycles (megastability). • Transitions between quantized orbits are driven by periodic external pulses. • The amplitude response of the resonance curves is studied as a function of parameters. • Jumps driven with different amplitude can "lock", ending in the same energy level. [ABSTRACT FROM AUTHOR]
Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: Driven transitions between megastable quantized orbits.
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  Data: We consider a nonlinear oscillator with state-dependent time-delay that displays a countably infinite number of nested limit cycle attractors, i.e. megastability. In the low-memory regime, the equation reduces to a self-excited nonlinear oscillator and we use averaging methods to analytically show quasilinear increasing amplitude of the megastable spectrum of quantized quasicircular orbits. We further assign a mechanical energy to each orbit using the Lyapunov energy function and obtain a quadratically increasing energy spectrum and (almost) constant frequency spectrum. We demonstrate transitions between different quantized orbits, i.e. different energy levels, by subjecting the system to an external finite-time harmonic driving. In the absence of external driving force, the oscillator asymptotes towards one of the megastable quantized orbits having a fixed average energy. For a large driving amplitude with frequency close to the limit cycle frequency, resonance drives transitions to higher energy levels. Alternatively, for large driving amplitude with frequency slightly detuned from limit-cycle frequency, beating effects can lead to transitions to lower energy levels. Such driven transitions between quantized orbits form a classical analog of quantum jumps. For excitations to higher energy levels, we show amplitude locking where nearby values of driving amplitudes result in the same response amplitude, i.e. the same final higher energy level. We rationalize this effect based on the basins of different limit cycles in phase space. From a practical viewpoint, our work might find applications in physical and engineering system where controlled transitions between several limit cycles of a multistable dynamical system is desired. • A self-excited oscillator with state-dependent time delay is considered. • We find a countably infinite number of nested limit cycles (megastability). • Transitions between quantized orbits are driven by periodic external pulses. • The amplitude response of the resonance curves is studied as a function of parameters. • Jumps driven with different amplitude can "lock", ending in the same energy level. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Chaos, Solitons & Fractals is the property of Pergamon Press - An Imprint of Elsevier Science and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1016/j.chaos.2025.116549
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      – Code: eng
        Text: English
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      – SubjectFull: Energy levels (Quantum mechanics)
        Type: general
      – SubjectFull: Orbits (Astronomy)
        Type: general
      – SubjectFull: Dynamical systems
        Type: general
      – SubjectFull: Atomic transitions
        Type: general
      – SubjectFull: Phase space
        Type: general
      – SubjectFull: Limit cycles
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      – TitleFull: Driven transitions between megastable quantized orbits.
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            NameFull: López, Álvaro G.
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            NameFull: Valani, Rahil N.
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            – D: 01
              M: 09
              Text: Sep2025
              Type: published
              Y: 2025
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