Open-system analogy of Berry conjecture

Abstract: Berry conjecture is central to understanding quantum chaos in isolated systems and foundational for the eigenstate thermalization hypothesis. Here we establish an open-system analogy of the Berry conjecture, connecting quantum steady states to classical dissipative attractors in the semiclassical limit. We demonstrate that the Wigner distribution of quantum steady states delocalizes over classical chaotic attractors in the semiclassical limit. We validate this correspondence using a Floquet Kerr oscillator. In the chaotic phase, the quasi-steady state is dominated by the chaotic delocalization instead of the quantum fluctuations, resulting in entropy divergence in the semiclassical limit. This entropy divergence provides a robust chaos signature beyond non-Hermitian random matrix approaches. We further identify dissipative phase transitions via Liouvillian gap closures, revealing a discrete time crystal phase and its breakdown into chaos at strong driving. Our framework thus establishes a universal paradigm for quantum chaos in open systems.