Perturbation-free prediction of resonance-assisted tunneling in mixed regular-chaotic systems.

Complex-path prediction of resonance-assisted tunneling in mixed systems.

We present a semiclassical prediction of regular-to-chaotic tunneling in systems with a mixed phase space, including the effect of a nonlinear resonance chain. We identify complex paths for direct and resonance-assisted tunneling in the phase space of an integrable approximation with one nonlinear resonance chain. We evaluate the resonance-assisted contribution analytically and give a predictio...

Resonance-assisted tunneling in mixed regular-chaotic systems

Regular-to-chaotic tunneling rates using a fictitious integrable system.

We derive a formula predicting dynamical tunneling rates from regular states to the chaotic sea in systems with a mixed phase space. Our approach is based on the introduction of a fictitious integrable system that resembles the regular dynamics within the island. For the standard map and other kicked systems we find agreement with numerical results for all regular states in a regime where reson...

Experimental Observation of Resonance-Assisted Tunneling.

We present the first experimental observation of resonance-assisted tunneling, a wave phenomenon, where regular-to-chaotic tunneling is strongly enhanced by the presence of a classical nonlinear resonance chain. For this we use a microwave cavity made of oxygen free copper with the shape of a desymmetrized cosine billiard designed with a large nonlinear resonance chain in the regular region. It...

Dynamical tunneling in systems with a mixed phase space

Typical dynamical systems have a mixed phase space, in which regions of chaotic motion coexist with regions of regular motion. While classically they are dynamically separated, quantum mechanically, these regions are connected by the fundamental process of tunneling. In this talk we review how to predict dynamical tunneling rates in systems with a mixed phase space by the fictitious integrable ...