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Area of Science:

  • Quantum mechanics
  • Classical mechanics
  • Mathematical physics

Background:

  • Quantum scars link quantum probability density to classical periodic orbits.
  • Anisotropic harmonic oscillators exhibit Lissajous orbits in classical mechanics.

Purpose of the Study:

  • To demonstrate quantum Lissajous scars in perturbed two-dimensional anisotropic harmonic oscillators.
  • To investigate the connection between scar geometry and harmonic confinement anisotropy.
  • To explore the survival of scars under potential perturbations.

Main Methods:

  • Analysis of eigenstates of a perturbed two-dimensional anisotropic harmonic oscillator.
  • Comparison with classical Lissajous orbits.
  • Investigation of the role of quantum degeneracies and perturbation localization.

Main Results:

  • Eigenstates of the perturbed anisotropic harmonic oscillator exhibit strong quantum Lissajous scars.
  • Scar occurrence and geometry depend on harmonic confinement anisotropy.
  • Quantum Lissajous scars persist under small potential perturbations, unlike classical orbits.

Conclusions:

  • Quantum Lissajous scarring is a robust phenomenon in perturbed anisotropic harmonic oscillators.
  • The scarring arises from quantum near-degeneracies and localized perturbations.
  • Experimental observation schemes for perturbation-induced scarring are discussed.