Related papers: Regular-to-Chaotic Tunneling Rates: From the Quant…

For generic Hamiltonian systems we derive predictions for dynamical tunneling from regular to chaotic phase-space regions. In contrast to previous approaches, we account for the resonance-assisted enhancement of regular-to-chaotic tunneling…

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…

In generic Hamiltonian systems tori of regular motion are dynamically separated from regions of chaotic motion in phase space. Quantum mechanically these phase-space regions are coupled by dynamical tunneling. We introduce a semiclassical…

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…

We show that the pattern of tunnelling rates can display a vivid and regular pattern when the classical dynamics is of mixed chaotic/regular type. We consider the situation in which the dominant tunnelling route connects to a stable…

We review the fictitious integrable system approach which predicts dynamical tunneling rates from regular states to the chaotic region in systems with a mixed phase space. It is based on the introduction of a fictitious integrable system…

In systems with a mixed phase space, where regular and chaotic motion coexists, regular states are coupled to the chaotic region by dynamical tunneling. We give an overview on the determination of direct regular-to-chaotic tunneling rates…

We investigate the tunneling process between two symmetric stable islands of a forced pendulum Hamiltonian in the weak chaos regime. We show that when the tunneling doublet is quantized over a classical non-linear resonance the tunneling…

We present evidence that nonlinear resonances govern the tunneling process between symmetry-related islands of regular motion in mixed regular-chaotic systems.In a similar way as for near-integrable tunneling, such resonances induce…

We discuss the statistics of tunnelling rates in the presence of chaotic classical dynamics. This applies to resonance widths in chaotic metastable wells and to tunnelling splittings in chaotic symmetric double wells. The theory is based on…

Dynamical tunnelling between symmetry-related stable modes is studied in the periodically driven pendulum. We present strong evidence that the tunnelling process is governed by nonlinear resonances that manifest within the regular…

This work establishes a firm relationship between classical nonlinear resonances and the phenomenon of dynamical tunneling. It is shown that the classical phase space with its hierarchy of resonance islands completely characterizes…

We present a comprehensive theory of resonance-assisted tunneling in quantum systems that exhibit a mixed regular-chaotic classical phase space structure. After general considerations, we specifically focus on quantum systems with one…

The interplay between classical chaos and quantum tunneling is examined in driven nonlinear systems, with emphasis on how semi classical phase space structures influence purely quantum transport phenomena. We show that, in the presence of…

We study the interplay between coherent transport by tunneling and diffusive transport through classically chaotic phase-space regions, as it is reflected in the Floquet spectrum of the periodically driven quartic double well. The tunnel…

We consider the problem of a semiclassical description of quantum chaotic transport, when a tunnel barrier is present in one of the leads. Using a semiclassical approach formulated in terms of a matrix model, we obtain transport moments as…

We present evidence that tunneling processes in near-integrable systems are enhanced due to the manifestation of nonlinear resonances and their respective island chains in phase space. A semiclassical description of this…

In generic Hamiltonian systems that are neither completely integrable nor fully chaotic, phase space consists of a mixture of regular and chaotic components. In classical dynamics, transitions between different invariant sets in phase space…

We develop the semiclassical method of complex trajectories in application to chaotic dynamical tunneling. First, we suggest a systematic numerical technique for obtaining complex tunneling trajectories by the gradual deformation of the…

We develop a quantitative semiclassical theory for the resosnant tunneling through a quantum well in a tilted magnetic field. It is shown, that in the leading semiclassical approximation the tunneling current depends only on periodic orbits…