Chaotic dynamics of complex trajectory and its quantum signature

We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with PT symmetry.For the quantum dynamics,both the mean momentum and mean square of momentum exhibit the staircase growth with time when the system parameter is in the neighborhood of the PT symmetry breaking point.If the system parameter is much larger than the PT symmetry breaking point,the accelerator mode results in the directed spreading of the wavepackets as well as the ballistic diffusion in momentum space.For the classical dynamics,the non-Hermitian kicking potential leads to the exponentially-fast increase of classical complex trajectories.As a consequence,the imaginary part of the trajectories exponentially diffuses with time,while the real part exhibits the normal diffusion.Our analytical prediction of the exponential diffusion of imaginary momentum and its breakdown time is in good agreement with numerical results.The quantum signature of the chaotic diffusion of the complex trajectories is reflected by the dynamics of the out-of-timeorder correlators(OTOC).In the semiclassical regime,the rate of the exponential increase of the OTOC is equal to that of the exponential diffusion of the complex trajectories.

General Formalism for Setting Up Unitary Transform Operators from Classical Transforms via IWOP Technique

We present a general formalism for setting up unitary transform operators from classical transforms via the technique of integration within an ordered product of operators, their normally ordered form can be obtained too.