Quantum Lissajous Scars

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.