We demonstrate that a weakly disordered metal with short-range interactions exhibits a transition in the quantum chaotic dynamics when changing the temperature or the interaction strength. For weak interactions, the system displays exponential growth of the out-of-time-ordered correlator (OTOC) of the current operator. The Lyapunov exponent of this growth is temperature-independent in the limit of vanishing interaction. With increasing the temperature or the interaction strength, the system undergoes a transition to a non-chaotic behaviour, for which the exponential growth of the OTOC is absent. We conjecture that the transition manifests itself in the quasiparticle energy-level statistics and also discuss ways of its explicit observation in cold-atom setups.

1 aSyzranov, S., V.1 aGorshkov, A., V.1 aGalitski, V., M. uhttps://arxiv.org/abs/1709.0929601571nas a2200133 4500008004100000245005700041210005400098260001500152520117000167100002101337700002501358700001701383856003701400 2017 eng d00aOut-of-time-order correlators in finite open systems0 aOutoftimeorder correlators in finite open systems c2017/04/273 aWe study out-of-time order correlators (OTOCs) of the form hAˆ(t)Bˆ(0)Cˆ(t)Dˆ(0)i for a quantum system weakly coupled to a dissipative environment. Such an open system may serve as a model of, e.g., a small region in a disordered interacting medium coupled to the rest of this medium considered as an environment. We demonstrate that for a system with discrete energy levels the OTOC saturates exponentially ∝ Paie −t/τi + const to a constant value at t → ∞, in contrast with quantum-chaotic systems which exhibit exponential growth of OTOCs. Focussing on the case of a two-level system, we calculate microscopically the decay times τi and the value of the saturation constant. Because some OTOCs are immune to dephasing processes and some are not, such correlators may decay on two sets of parametrically different time scales related to inelastic transitions between the system levels and to pure dephasing processes, respectively. In the case of a classical environment, the evolution of the OTOC can be mapped onto the evolution of the density matrix of two systems coupled to the same dissipative environment.

1 aSyzranov, S., V.1 aGorshkov, Alexey, V.1 aGalitski, V. uhttps://arxiv.org/abs/1704.08442