Syzranov S V, Gorshkov A V, Galitski V M
Physics Department, University of California, Santa Cruz, CA 95064, USA.
Joint Quantum Institute, NIST/University of Maryland, College Park, MD 20742, USA.
Ann Phys (N Y). 2019;405. doi: 10.1016/j.aop.2019.03.008.
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.
我们证明，具有短程相互作用的弱无序金属在改变温度或相互作用强度时，量子混沌动力学中会出现转变。对于弱相互作用，系统表现出电流算符的时间反演序关联函数（OTOC）的指数增长。在相互作用消失的极限情况下，这种增长的李雅普诺夫指数与温度无关。随着温度或相互作用强度的增加，系统会转变为非混沌行为，此时OTOC不存在指数增长。我们推测，这种转变在准粒子能级统计中表现出来，并讨论了在冷原子装置中对其进行明确观测的方法。
