Fading ergodicity

We uncover a novel ergodic regime dubbed fading ergodicity – this is a regime in which a quantum system is still ergodic, however, it also acts as a precursor of the ergodictiy breaking phase transition. In other words, »fading« ergodicity is a synonym of the »fading« colors of the leafs that are just about to fall off the tree. We conjecture this regime to be a generic property of quantum systems approaching the ergodicity breaking phase transition, and therefore, one cannnot make a system nonergodic without first making the ergodicity to fade.