Related papers: Homoclinic Structure Controls Chaotic Tunnelling
Recent experimental and theoretical studies on the magnetization dynamics driven by an electric current have uncovered a number of unprecedented rich dynamic phenomena. We predict an intrinsic chaotic dynamics that has not been previously…
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 study the driven tunneling of a one-dimensional charged particle confined to a rectangular double-well. The numerical simulation of the Schr\"odinger equation based on the Cranck-Nicholson finite-difference scheme, shows that the…
We consider dynamical tunneling between two symmetry-related regular islands that are separated in phase space by a chaotic sea. Such tunneling processes are dominantly governed by nonlinear resonances, which induce a coupling mechanism…
Traditionally quantum tunneling in a static SQUID is studied on the basis of a classical trajectory in imaginary time under a two-dimensional potential barrier. The trajectory connects a potential well and an outer region crossing their…
Special subsets of orbits in chaotic systems, e.g. periodic orbits, heteroclinic orbits, closed orbits, can be considered as skeletons or scaffolds upon which the full dynamics of the system is built. In particular, as demonstrated in…
Over the preceeding twenty years, the role of underlying classical dynamics in quantum mechanical tunneling has received considerable attention. A number of new tunneling phenomena have been uncovered that have been directly linked to the…
We developed a powerful computational approach to elaborate on onset mechanisms of deterministic chaos due to complex homoclinic bifurcations in diverse systems. Its core is the reduction of phase space dynamics to symbolic binary…
An iterface structure between turbulence and laminar flow is investigated in two-dimensional channel flow. This spatially localized structure not only sustains itself, but also converts laminar state into turbulence actively. In other…
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…
According to a recent theory \cite{Li14}, when the Reynolds number is large, fully developed turbulence is caused by short term unpredictability (rough dependence upon initial data); when the Reynolds number is moderate, often transient…
Quantum tunneling between two potential wells in a magnetic field can be strongly increased when the potential barrier varies in the direction perpendicular to the line connecting the two wells and remains constant along this line. An…
A chaos control algorithm is developed to actively stabilize unstable periodic orbits of higher-dimensional systems. The method assumes knowledge of the model equations and a small number of experimentally accessible parameters. General…
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…
Systems of $N$ identical globally coupled phase oscillators can demonstrate a multitude of complex behaviours. Such systems can have chaotic dynamics for $N>4$ when a coupling function is biharmonic. The case $N = 4$ does not possess…
We report on the first direct observation of coherent control of single particle tunneling in a strongly driven double well potential. In our setup atoms propagate in a periodic arrangement of double wells allowing the full control of the…
There is a long tradition of studying chaotic trajectories in systems whose integrability is broken by means of an external perturbation. Here we explore a different route to chaos, in the dynamics of extended bodies, which arises due to…
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 study quantum-mechanical tunneling in mixed dynamical systems between symmetry-related phase space tori separated by a chaotic layer. Considering e.g. the annular billiard we decompose tunneling-related energy splittings and shifts into…
A semiclassical theory is developed and compared to experiments on the tunneling resonance spectrum for a quantum well in magnetic field tilted with respect to the tunneling direction. As the tilt angle is increased from zero the classical…