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Peter Schmelcher1

  • 1Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany and Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.

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Summary
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This study investigates a driven power-law oscillator with periodically changing shape, revealing unbounded motion with exponential energy growth. The dynamics show alternating energy gain, loss, and conservation phases due to confinement geometry shifts.

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Area of Science:

  • Nonlinear Dynamics
  • Complex Systems Physics
  • Chaos Theory

Background:

  • Driven nonlinear oscillators are fundamental in physics, exhibiting complex behaviors.
  • Power-law potentials and time-varying confinement introduce rich dynamical phenomena.
  • Understanding energy dynamics in such systems is crucial for predicting system evolution.

Purpose of the Study:

  • To explore the nonlinear dynamics of a driven power-law oscillator with time-periodic shape variations.
  • To investigate the emergence of unbounded motion and exponential energy growth.
  • To analyze the transition between regular, chaotic, bounded, and unbounded motions.

Main Methods:

  • Computational study of the driven power-law oscillator's phase space.
  • Analysis of motion phases exhibiting energy gain, loss, and conservation.
  • Investigation of phase space structure changes with varying frequency and amplitude.
  • Derivation of an effective potential in the high-frequency regime.

Main Results:

  • The system exhibits both bounded (regular and chaotic) and unbounded motions with exponential energy growth.
  • Alternating phases of energy gain, loss, and conservation are observed within a single driving period.
  • A crossover from a single- to a two-component phase space is demonstrated with parameter variation.
  • An effective potential is derived for the high-frequency dynamics.

Conclusions:

  • The driven power-law oscillator with time-varying confinement displays complex dynamics, including unbounded motion.
  • The interplay of confinement geometry and driving parameters dictates the energy evolution and phase space structure.
  • The findings provide insights into energy transfer mechanisms in periodically driven nonlinear systems.