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A particle driven by deterministic chaos and moving in a spatially extended environment can exhibit normal diffusion, with its mean square displacement growing proportional to the time. Here we consider the dependence of the diffusion…
Diffusion is a central phenomenon in almost all fields of natural science revealing microscopic processes from the observation of macroscopic dynamics. Here, we consider the paradigmatic system of a single atom diffusing in a periodic…
For a given a normally hyperbolic invariant manifold, whose stable and unstable manifolds intersect transversally, we consider several tools and techniques to detect trajectories with prescribed itineraries: the scattering map, the…
A Hamiltonian reduction approach is defined, studied, and finally used to derive asymptotic models of internal wave propagation in density stratified fluids in two-dimensional domains. Beginning with the general Hamiltonian formalism of…
Aggregation-diffusion equations are foundational tools for modelling biological aggregations. Their principal use is to link the collective movement mechanisms of organisms to their emergent space use patterns in a concrete mathematical…
We develop a non-perturbative numerical method to study tunneling of a single electron through an Aharonov-Bohm ring where several strongly interacting electrons are bound. Inelastic processes and spin-flip scattering are taken into…
To describe the energy transport in the seismic coda, we introduce a system of radiative transfer equations for coupled surface and body waves in a scalar approximation. Our model is based on the Helmholtz equation in a half-space geometry…
In this paper, we exactly solve, within the grand canonical ensemble, a minimal spin model with the hybrid phase transition. We call the model "diffusion-based" because its hamiltonian can be recovered from a simple dynamic procedure, which…
The escape mechanism of orbits in a star cluster rotating around its parent galaxy in a circular orbit is investigated. A three degrees of freedom model is used for describing the dynamical properties of the Hamiltonian system. The…
We demonstrate and analyze anomalous diffusion properties of point-like particles in a two-dimensional system with circular scatterers arranged in a square lattice and governed by smooth potentials, referred to as the square soft Lorentz…
This paper extends the Lorentz-Abraham model of an electron (i.e. the equations of motion for a small spherical shell of charge, which is rigid in its proper frame) to treat a small spherically symmetric charge distribution, allowing for…
We prove an existence result for nonlinear diffusion equations in the presence of a nonlocal density-dependent drift which is not necessarily potential. The proof is constructive and based on the Helmholtz decomposition of the drift and a…
We prove, under suitable non-resonance and non-degeneracy ``twist'' conditions, a Birkhoff-Lewis type result showing the existence of infinitely many periodic solutions, with larger and larger minimal period, accumulating onto elliptic…
We investigate both the quantum and classical dynamics of a non-Hermitian system via a kicked rotor model with $\mathcal{PT}$ symmetry. For the quantum dynamics, both the mean momentum and mean square of momentum exhibits the staircase…
The Aharonov--Bohm effect is considered as a scattering event with nonrelativistic charged particles of the wavelength which is less than the transverse size of an impenetrable magnetic vortex. The quasiclassical WKB method is shown to be…
Spectral properties of super-Eddington accretion flows are investigated by means of a parallel line-of-sight calculation. The subjacent model, taken from two-dimensional radiation hydrodynamic simulations by Ohsuga et al. (2005), consists…
The discovery in [G. Pinzari. PhD thesis. Univ. Roma Tre. 2009], [L. Chierchia and G. Pinzari, Invent. Math. 2011] of the Birkhoff normal form for the planetary many--body problem opened new insights and hopes for the comprehension of the…
Self-force methods can be applied in calculations of the scatter angle in two-body hyperbolic encounters, working order by order in the mass ratio (assumed small) but with no recourse to a weak-field approximation. This, in turn, can inform…
Collisions of atoms and molecules with metal surfaces create electronic excitations in the metal, leading to nonadiabatic energy dissipation, inelastic scattering, and sticking. Mixed quantum-classical molecular dynamics simulation methods,…
We study chaotic many-body quantum dynamics in a minimal model with spatial structure and local interactions. It has a time-independent Hamiltonian, in contrast to quantum circuits and Brownian models, and is simple at the single-site…