Diffusion in smooth Hamiltonian systems

Smooth Hamiltonian Systems with Soft Impacts

In a Hamiltonian system with impacts (or “billiard with potential”), a point particle moves about the interior of a bounded domain according to a background potential and undergoes elastic collisions at the boundaries. When the background potential is identically zero, this is the hard-wall billiard model. Previous results on smooth billiard models (where the hard-wall boundary is replaced by a...

Geometric Integrators for Piecewise Smooth Hamiltonian Systems

Abstract. In this paper, we consider C1,1 Hamiltonian systems. We prove the existence of a first derivative of the flow with respect to initial values and show that it satisfies the symplecticity condition almost everywhere in the phase-space. In a second step, we present a geometric integrator for such systems (called the SDH method) based on B-splines interpolation and a splitting method intr...

Basins of attraction in piecewise smooth Hamiltonian systems.

Piecewise smooth Hamiltonian systems arise in physical and engineering applications. For such a system typically an infinite number of quasi-periodic "attractors" coexist. (Here we use the term "attractors" to indicate invariant sets to which typically initial conditions approach, as a result of the piecewise smoothness of the underlying system. These "attractors" are therefore characteristical...

Intrinsic decoherence dynamics in smooth Hamiltonian systems: Quantum-classical correspondence

A direct classical analog of the quantum dynamics of intrinsic decoherence in Hamiltonian systems, characterized by the time dependence of the linear entropy of the reduced density operator, is introduced. The similarities and differences between the classical and quantum decoherence dynamics of an initial quantum state are exposed using both analytical and computational results. In particular,...

Arnold diffusion in perturbations of analytic integrable Hamiltonian systems