arXiv subjects

Marcello Seri

Publications and source records attributed to Marcello Seri.

23 records · Page 2Linked to original sources

arXiv2015

Accumulation of complex eigenvalues of an indefinite Sturm--Liouville operator with a shifted Coulomb potential

For a particular family of long-range potentials $V$, we prove that the eigenvalues of the indefinite Sturm--Liouville operator $A = \mathrm{sign}(x)(-Δ+ V(x))$ accumulate to zero asymptotically along specific curves in the complex plane. Additionally, we relate the asymptotics of complex eigenvalues to the two-term asymptotics of the eigenvalues of associated self-adjoint operators.

math.SP↗

arXiv2015

Spectral analysis and the Aharonov-Bohm~effect on certain almost-Riemannian manifolds

We study spectral properties of the Laplace-Beltrami operator on two relevant almost-Riemannian manifolds, namely the Grushin structures on the cylinder and on the sphere. This operator contains first order diverging terms caused by the divergence of the volume. We get explicit descriptions of the spectrum and the eigenfunctions. In particular in both cases we get a Weyl's law with leading term $E\log E$. We then study the drastic effect of Aharonov-Bohm magnetic potentials on the spectral properties. Other generalised Riemannian structures including conic and anti-conic type manifolds are also studied. In this case, the Aharonov-Bohm magnetic potential may affect the self-adjointness of the Laplace-Beltrami operator

math.SP↗

arXiv2014

The Problem of Two Fixed Centers: Bifurcation Diagram for Positive Energies

We give a comprehensive analysis of the Euler-Jacobi problem of motion in the field of two fixed centers with arbitrary relative strength and for positive values of the energy. These systems represent nontrivial examples of integrable dynamics and are analysed from the point of view of the energy-momentum mapping from the phase space to the space of the integration constants. In this setting we describe the structure of the scattering trajectories in phase space and derive an explicit description of the bifurcation diagram, i.e. the set of critical value of the energy-momentum map.

math-ph↗

arXiv2011

Recurrence and higher ergodic properties for quenched random Lorentz tubes in dimension bigger than two

We consider the billiard dynamics in a non-compact set of R^d that is constructed as a bi-infinite chain of translated copies of the same d-dimensional polytope. A random configuration of semi-dispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global realization of the scatterers, is called `quenched random Lorentz tube'. Under some fairly general conditions, we prove that every system in the ensemble is hyperbolic and almost every system is recurrent, ergodic, and enjoys some higher chaotic properties.

math.DS↗

arXiv2010

Recurrence for quenched random Lorentz tubes

We consider the billiard dynamics in a strip-like set that is tessellated by countably many translated copies of the same polygon. A random configuration of semidispersing scatterers is placed in each copy. The ensemble of dynamical systems thus defined, one for each global choice of scatterers, is called `quenched random Lorentz tube'. We prove that, under general conditions, almost every system in the ensemble is recurrent.

math.DS↗