相关论文: Refraction Periodic Trajectories in Central Mass G…
The aim of this work is to continue the analysis, started in arXiv:2105.02108, of the dynamics of a point-mass particle $P$ moving in a galaxy with an harmonic biaxial core, in whose center sits a Keplerian attractive center (e.g. a Black…
An extension of the Gutzwiller trace formula is given that includes diffraction effects due to hard wall scatterers or other singularities. The new trace formula involves periodic orbits which have arcs on the surface of singularity and…
We prove the presence of topological chaos at high internal energies for a new class of mechanical refraction billiards coming from Celestial Mechanics. Given a smooth closed domain $D\in\mathbb{R}^2$, a central mass generates a Keplerian…
Artificial gauge fields enable extending the control over dynamics of uncharged particles, by engineering the potential landscape such that the particles behave as if effective external fields are acting on them. Recent years have witnessed…
We investigate the dynamics in a galactic potential with two reflection symmetries. The phase-space structure of the real system is approximated with a resonant detuned normal form constructed with the method based on the Lie transform.…
We consider waves travelling in two different mediums each endowed with a different constant speed of propagation. At the interface between the two mediums, the refraction of the rays of the optic geometry is described by the…
This paper investigates the global structures of periodic orbits that appear in Rayleigh-B\'enard convection, which is modeled by a two-dimensional perturbed Hamiltonian model, by focusing upon resonance, symmetry and bifurcation of the…
We consider the time dependent Maxwell system in the sense of distributions in the context of temporal interfaces. Just as with spatial interfaces, electromagnetic waves at temporal interfaces scatter and create a transmitted and reflected…
We study dynamics and bifurcations of two-dimensional reversible maps having non-transversal heteroclinic cycles containing symmetric saddle periodic points. We consider one-parameter families of reversible maps unfolding generally the…
We study the dynamics of two bodies moving on elliptic Keplerian orbits around a fixed center of attraction and interacting only by means of elastic or inelastic collisions. We show that there exists a bounded invariant region: for suitable…
The attractors of a dynamical system govern its typical long-term behaviour. The presence of many attractors is significant as it means the behaviour is heavily dependent on the initial conditions. To understand how large numbers of…
Non-Hermitian systems give rise to distinct topological phenomena, yet their manifestations at temporal interfaces characterized by abrupt changes in system parameters remain largely unex plored. Upon an abrupt alteration of the Hamiltonian…
We study the scattering resonances between two confocal hyperbolae and show that the spectrum is dominated by the effect of a single periodic orbit. There are two distinct cases depending on whether the orbit is geometric or diffractive. A…
A cornerstone equation of optics, Snell's law, relates the angles of incidence and refraction for light passing through an interface between two media. It is built on two fundamental constrains: the conservation of tangential momentum and…
We derive the reflection and refraction laws for an electron spin incident from a quasi-two-dimensional medium with no spin-orbit interaction on another with both Rashba and Dresselhaus spin-orbit interaction using only energy conservation.…
Fermat's principle is fully generalized to the case where a smooth interface separates two cone structures -- Lorentz-Finsler lightcones -- representing wave propagation in a potentially inhomogeneous, anisotropic, time-dependent and…
Large and abrupt variations in the electromagnetic properties of materials lead to dramatic effects: even a single step-like change in the refractive index induces striking phenomena, such as time-refraction and time-reflection. When the…
We study a class of elliptic billiards with a Keplerian potential inside, considering two cases: a reflective one, where the particle reflects elastically on the boundary, and a refractive one, where the particle can cross the billiard's…
Refraction, traditionally viewed as a geometric event occurring at material interfaces, is now being re-examined through the lens of coherence. Recent studies in optics and photonics, including coherence tomography, Moire interference, and…
When an electromagnetic wave is obliquely incident on the interface between two homogeneous media with different refractive indices, the requirement of phase continuity across the interface generally leads to a shift in the trajectory of…