相关论文: Fast Arnold Diffusion in three time scale systems

In this paper, we prove that the net of transition chain is $\delta$-dense for nearly integrable positive definite Hamiltonian systems with 3 degrees of freedom in the cusp-residual generic sense in $C^r$-topology, $r\ge 6$. The main…

In this paper, we design an algorithm to accelerate the diffusion process on the $SO(3)$ manifold. The inherently sequential nature of diffusion models necessitates substantial time for denoising perturbed data. To overcome this limitation,…

We consider coupled slow-fast stochastic processes, where the averaged slow motion is given by a two-dimensional Hamiltonian system with multiple critical points. On a proper time scale, the evolution of the first integral converges to a…

We revisit the problem of diffusion in a driven system consisting of an inertial Brownian particle moving in a symmetric periodic potential and subjected to a symmetric time-periodic force. We reveal parameter domains in which diffusion is…

In this paper, we study the chaotic motion of a massive particle moving in a perturbed Schwarzschild or Kerr background. We discover three novel orbits that do not exist in the unperturbed cases. First, we find zoom-whirl orbits moving…

We consider a drift-diffusion process with a time-independent and divergence-free random drift that is of white-noise character. We are interested in the critical case of two space dimensions, where one has to impose a small-scale cut-off…

We prove that for any non-trivial perturbation depending on any two independent harmonics of a pendulum and a rotor there is global instability. The proof is based on the geometrical method and relies on the concrete computation of several…

The analytical techniques of the Nekhoroshev theorem are used to provide estimates on the coefficient of Arnold diffusion along a particular resonance in the Hamiltonian model of Froeschl\'{e} et al. (2000). A resonant normal form is…

We employ the recently developed multi-time scale averaging method to study the large time behavior of slowly changing (in time) Hamiltonians. We treat some known cases in a new way, such as the Zener problem, and we give another proof of…

We develop a geometric mechanism to prove the existence of orbits that drift along a prescribed sequence of cylinders, under some general conditions on the dynamics. This mechanism can be used to prove the existence of Arnold diffusion for…

The relation between relaxation and diffusion is investigated in a Hamiltonian system of globally coupled rotators. Diffusion is anomalous if and only if the system is going towards equilibrium. The anomaly in diffusion is not anomalous…

There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…

In this paper, we consider a fast and second-order implicit difference method for approximation of a class of time-space fractional variable coefficients advection-diffusion equation. To begin with, we construct an implicit difference…

We describe diffractive deeply inelastic scattering in terms of diffractive parton distributions. We investigate these distributions in a hamiltonian formulation that emphasizes the spacetime picture of diffraction scattering. For hadronic…

Long ago appeared a discussion in quantum mechanics of the problem of opening a completely absorbing shutter on which were impinging a stream of particles of definite velocity. The solution of the problem was obtained in a form entirely…

The 2-step staggered (also called leap-frog) time discretisation of linear 2nd-order Hamiltonian systems (typically linear elastodynamics in a stress-velocity form) is extended for a 3-step staggered discretisation applicable for systems…

We investigate the existence of Arnold diffusion-type orbits for systems obtained by iterating in any order the time-one maps of a family of Tonelli Hamiltonians. Such systems are known as 'polysystems' or 'iterated function systems'. When…

We consider the limiting behavior of fluctuations of small noise diffusions with multiple scales around their homogenized deterministic limit. We allow full dependence of the coefficients on the slow and fast motion. These processes arise…

We study the fingerprint of the Arnol'd diffusion in a quantum system of two coupled nonlinear oscillators with a two-frequency external force. In the classical description, this peculiar diffusion is due to the onset of a weak chaos in a…

The diffusion of a particle in a crowded environment typically proceeds through three regimes: for very short times the particle diffuses freely until it collides with an obstacle for the first time, while for very long times diffusion the…