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Matias Moreno

Publications and source records attributed to Matias Moreno.

6 recordsLinked to original sources
arXiv2024

On absence of embedded eigenvalues and stability of BGK waves

We consider space-periodic and inhomogeneous steady states of the one-dimensional electrostatic Vlasov-Poisson system, known as the Bernstein-Greene-Kruskal (BGK) waves. We prove that there exists a large class of fixed background ion densities and spatial periods, so that the corresponding linearised operator around the associated BGK-equilibria has no embedded eigenvalues inside the essential spectrum. As a consequence we conclude a nonquantitative version of Landau damping around a subclass of such equilibria with monotone dependence on particle energy. The BGK equilibria under investigation feature trapped electrons which lead to presence of both elliptic and hyperbolic critical points in the characteristic phase-space diagram. They also feature a small parameter, which roughly speaking governs the size of the trapped zone - also referred to as electron hole. Our argument uses action-angle variables and a careful analysis of the associated period function. To exclude embedded eigenvalues we develop an energy-based approach which deals with resonant interactions between the energy (action)-space and the angle frequencies; their singular structure and summability properties are the key technical challenge. Our approach is robust and applicable to other spectral problems featuring elliptic and hyperbolic critical points.

math.AP↗
arXiv2023

Existence and stability of steady states solutions of Flat Vlasov-Poisson system with a central mass density

We study a Newtonian model which allows us to describe some extremely flat objects in galactic dynamics. This model is described by a partial differential equation system called Vlasov-Poisson, whose solutions describe the temporal evolution of a collisionless particle system in the phase space, subject to a self interacting gravitational potential. We treat the Flat VlasovPoisson system with an external gravitational potential induced by a fixed mass density. The aim of this article is the study of the existence, regularity, and stability of steady states solutions of the Flat Vlasov-Poisson system in this case. We solved a variational problem to find minimizers for the Casimir-Energy functional in a suitable set of functions. The minimization problem is solved through a reduction of the original optimization problem with a scheme used in [FR06], but instead of a concentration-compactness argument, we use a symmetrization argument to construct a spherically symmetric solution for the reduced problem. It was proven that this minimizer induces a solution for the original minimization problem. The regularity of the gravitational potential was also obtained, implying that the solutions are steady states of the Flat Vlasov-Poisson system. The minimization problem also works as a key to give us a similar non-linear stability result.

math.AP↗
arXiv2009

Perturbative quantum analysis and classical limit of the electron scattering by a solenoidal magnetic field

A well known example in quantum electrodynamics (QED) shows that Coulomb scattering of unpolarized electrons, calculated to lowest order in perturbation theory, yields a results that exactly coincides (in the non-relativistic limit) with the Rutherford formula. We examine an analogous example, the classical and perturbative quantum scattering of an electron by a magnetic field confined in an infinite solenoid of finite radius. The results obtained for the classical and the quantum differential cross sections display marked differences. While this may not be a complete surprise, one should expect to recover the classical expression by applying the classical limit to the quantum result. This turn not to be the case. Surprisingly enough, it is shown that the classical result can not be recuperated even if higher order corrections are included. To recover the classic correspondence of the quantum scattering problem a suitable non-perturbative methodology should be applied.

quant-ph↗
arXiv2004

Quantum versus classical scattering of Dirac particles by a solenoidal magnetic field and the correspondence principle

We present a detailed analysis of the scattering of charged particles by the magnetic field of a long solenoid of constant magnetic flux and finite radius. We study the relativistic and non-relativistic quantum and classical scenarios. The classical limit of the perturbative quantum expressions, understood as the Planck's limit (making $\hbar$ going to zero) is analyzed and compared with the classical result. The classical cross section shows a general non-symmetric behavior with respect to the scattering angle in contradistinction to the quantum calculations performed so far. The various regimes analyzed show that the quantum cross sections do not satisfy the correspondence principle: they do not reduce to the classical result in any considered limit, an argument in favor of the interpretation of the process as a purely quantum phenomenon. We conclude that in order to restore the classical correspondence of the phenomenon, a complete non-perturbative quantum calculation for a finite solenoid radius is required.

quant-ph↗
arXiv2002

Quantum effects in the scattering by the magnetic field of a solenoid

We present a relativistic quantum calculation at first order in perturbation theory of the differential cross section for a Dirac particle scattered by the magnetic field of a solenoid. The resulting cross section is symmetric in the scattering angle as those obtained by Aharonov and Bohm (AB) in the string limit and by Landau and Lifshitz (LL) for the non relativistic case. We show that taking pr_0 sin(theta/2) << 1 in our expression of the differential cross section it reduces to that one reported by AB, and if additionally we assume theta << 1 our result becomes the one obtained by LL. However, these limits are explicitly singular in hbar as opposed to our initial result. We analyse the singular behavior in hbar and show that the perturbative Planck limit (hbar -> 0) is consistent, contrarily to those of the AB and LL expressions.

physics.class-ph↗