Classification of ergodicity-breaking mechanisms in chaotic spinor condensates

We find two classes of ergodicity-breaking many-body quantum eigenstates that support robust oscillatory dynamics in an otherwise chaotic spinor condensate. The first class consists of towers of low-entropy "regular" states separated from the chaotic band of states, violating Eigenstate Thermalization Hypothesis (ETH) and associated with stable periodic orbits in the limit of large atom number. The origin of these athermal states can be traced back to an integrable effective Hamiltonian. The second class consists of eigenstates that, while embedded in the chaotic band and satisfying the first criterion of ETH, are not fully ergodic, because they are scarred by unstable periodic orbits with positive Lyapunov exponents in the classical limit. Scarring affects a significant fraction of eigenstates, to an extent that we quantify with a "scarness" figure of merit. Our theory could be experimentally verified in trapped spin-1 Bose-Einstein condensates by preparing Fock and coherent states, and measuring the population of the hyperfine levels and the state fidelity.