  Two properties are needed for a classical system to be chaotic: exponential
stretching and mixing. Recently, out-of-time order correlators were proposed as
a measure of chaos in a wide range of physical systems. While most of the
attention has previously been devoted to the short time stretching aspect of
chaos, characterized by the Lyapunov exponent, we show for quantum maps that
the out-of-time correlator approaches its stationary value exponentially with a
rate determined by the Ruelle-Pollicot resonances. This property constitutes
clear evidence of the dual role of the underlying classical chaos dictating the
behavior of the correlator at different timescales.
