Quantum chaos in a harmonic waveguide with scatterers

An effective method of numerical solution, based on properties of high-rank separable perturbations, is developed for an atom in a harmonic waveguide with either periodic boundary conditions or hard-wall box in the axial direction, perturbed by zero-range scatterers along the waveguide axis [1]. The energy-degeneracy of the unperturbed system can be lifted by an axial vector potential which also lifts T-invariance. The energy spectra properties — near-neighbor distribution and spectral rigidity, as well as the inverse participation ratio (IPR) and fluctuation variance of observable expectation values, are calculated for 10⁶ eigenstates. The chaoticity measures of the model increase with the number of scatterers and their strengths.

The system properties are insensitive to scatterer positions unless the Hamiltonian acquires an additional symmetry, e.g., periodicity [2]. Calculations for different numbers of scatterers and their strengths confirm the prediction [1] that IPR decreases with the number of scatterers. The decrease is inversely proportional for strong scatterers and slower for weak ones. Transition between the T-invariant and T-noninvariant systems and dependencies on the state energy are explored as well. The predictions should be testable experimentally with cold atoms.

1. V. A. Yurovsky, Phys. Rev. Lett. 130, 020404 (2023).

2. V. A. Yurovsky, arxiv/2301.06065.