相关论文: Resonance-assisted tunneling in near-integrable sy…

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…

Resonance-assisted tunneling is investigated within the framework of one-dimensional integrable systems. We present a systematic recipe, based on Hamiltonian normal forms, to construct one-dimensional integrable models that exhibit…

The life times of optical modes in whispering-gallery cavities crucially depend on the underlying classical ray dynamics and may be spoiled by the presence of classical nonlinear resonances due to resonance--assisted tunneling. Here we…

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…

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…

We study dynamical tunneling in a near-integrable Hamiltonian with three degrees of freedom. The model Hamiltonian does not have any discrete symmetry. Despite this lack of symmetry we show that the mixing of near-degenerate quantum states…

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…

A tight binding representation of the kicked Harper model is used to obtain an integrable semiclassical Hamiltonian consisting of degenerate "quantized" orbits. New orbits appear when renormalized Harper parameters cross integer multiples…

Quantum integrable systems and their classical counterparts are considered. We show that the symplectic structure and invariant tori of the classical system can be deformed by a quantization parameter $\hbar$ to produce a new (classical)…

Dissipative systems play a very important role in several physical models, most notably in Celestial Mechanics, where the dissipation drives the motion of natural and artificial satellites, leading them to migration of orbits, resonant…

We investigate the existence of whiskered tori in some dissipative systems, called \sl conformally symplectic \rm systems, having the property that they transform the symplectic form into a multiple of itself. We consider a family $f_\mu$…

We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry action. We analyze how the invariant tori…

The classical and quantum mechanics of isolated, nonlinear resonances in integrable systems with N>=2 degrees of freedom is discussed in terms of geometry in the space of action variables. Energy surfaces and frequencies are calculated and…

Rotators interacting with a pendulum via small, velocity independent, potentials are considered. If the interaction potential does not depend on the pendulum position then the pendulum and the rotators are decoupled and we study the…

We compute the dispersion laws of chaotic periodic systems using the semiclassical periodic orbit theory to approximate the trace of the powers of the evolution operator. Aside from the usual real trajectories, we also include complex…

We apply the theory of Resonance Assisted Tunneling (RAT) to a many-body quantum kicked system with a well-defined semiclassical limit. Using a quantum resonant condition, we identify eigenstates associated with classical resonances and…

Quasi-periodic motions on invariant tori of an integrable system of dimension smaller than half the phase space dimension may continue to exists after small perturbations. The parametric equations of the invariant tori can often be computed…

Classical KAM theory guarantees the existence of a positive measure set of invariant tori for sufficiently smooth non-degenerate near-integrable systems. When seen as a function of the frequency this invariant collection of tori is called…

This work explores the possibility of controlling the dissociation of a monochromatically driven one-dimensional Morse oscillator by recreating barriers, in the form of invariant tori with irrational winding ratios, at specific locations in…

In the framework of KAM theory, the persistence of invariant tori in quasi-integrable systems is proved by assuming a non-resonance condition on the frequencies, such as the standard Diophantine condition or the milder Bryuno condition. In…