The ergodicity landscape of quantum theories

Wen Wei Ho, Đorđe Radičević
2018 International Journal of Modern Physics A  
This paper is a physicist's review of the major conceptual issues concerning the problem of spectral universality in quantum systems. Here we present a unified, graph-based view of all archetypical models of such universality (billiards, particles in random media, interacting spin or fermion systems). We find phenomenological relations between the onset of ergodicity (Gaussian-random delocalization of eigenstates) and the structure of the appropriate graphs, and we construct a heuristic picture
more » ... of summing trajectories on graphs that describes why a generic interacting system should be ergodic. We also provide an operator-based discussion of quantum chaos and propose criteria to distinguish bases that can usefully diagnose ergodicity. The result of this analysis is a rough but systematic outline of how ergodicity changes across the space of all theories with a given Hilbert space dimension. As a special case, we study the SYK model and report on the transition from maximal to partial ergodicity as the disorder strength is decreased.
doi:10.1142/s0217751x18300041 fatcat:7722hqun2fb6vhbxnajxuuvjny