Origins and selection criteria of quantum scarring

Ascertain the precise physical mechanisms responsible for quantum scarring in chaotic billiard systems and develop criteria that determine which eigenstates exhibit scarring and to what extent, resolving whether such scars reflect integrable or nearly integrable structures.

Background

The paper presents extensive numerical evidence of both scars and superscars in bean-shaped and peanut-shaped billiards, highlighting non-ergodic localisation of eigenfunctions along unstable periodic orbits or symmetry-induced structures. These observations stress a subtle quantum–classical correspondence within mixed-curvature chaotic boundaries.

The authors note limitations of existing scar theory and explicitly state that the precise origins of quantum scarring and the selection of scarred states are not yet fully understood. Clarifying these mechanisms and predictive criteria remains an open problem.