Classical breathers and quantum coherent states in discrete NLS systems

Highlights: • Study evolution of coherent states in quantized discrete NLS system. • Derive expression for distance between quantum and classical trajectories of breather SU(N) coherent states. • Show robustness under perturbation for stable breathers. • Quantify recurrence times to small distance between quantum and classical trajectories. -- Abstract: We present a comparison of quantum and "semiclassical" trajectories of coherent states that correspond to classical breather solutions of finite discrete nonlinear Schrödinger (DNLS) lattices. The main goal is to explain earlier numerical observations of recurrent return to the vicinity of initial coherent states corresponding to stable breathers that are also spatially localized. This effect can be considered as a quantum manifestation of classical spatial localization. We show that these phenomena are encoded in a simple expression for the distance between the quantum and semiclassical states that involves the basic frequencies of the classical and quantum systems, as well as the breather amplitude and quantum spectral decomposition of the system. A corollary is that recurrence phenomena are robust under perturbation of the initial conditions for stable breathers.