Level statistics and quantum scars in a few-body quantum model

Studies in recent years have brought new understandings of integrability, many-body quantum scars, and spectral properties in quantum many-body systems. While integrability and quantum scars for single-particle systems have been studied decades ago, their connection with their many-body counterparts is less clear. We study a 1D interacting quantum model of few particles which is closely related to the quantum billiard model, aimed at interpolating the spectral properties and quantum scars between single-particle and many-body systems. We report the scaling behavior of the level spacing statistics with respect to system size and number of particles and give an understanding of such spectral behaviors in terms of approximate quantum scar states.