arXiv subjects

Jonathan Ben-Artzi

Publications and source records attributed to Jonathan Ben-Artzi.

24 records · Page 2Linked to original sources

arXiv2016

Approximations of strongly continuous families of unbounded self-adjoint operators

The problem of approximating the discrete spectra of families of self-adjoint operators that are merely strongly continuous is addressed. It is well-known that the spectrum need not vary continuously (as a set) under strong perturbations. However, it is shown that under an additional compactness assumption the spectrum does vary continuously, and a family of symmetric finite-dimensional approximations is constructed. An important feature of these approximations is that they are valid for the entire family uniformly. An application of this result to the study of plasma instabilities is illustrated.

math.SP↗

arXiv2015

Instabilities of the relativistic Vlasov-Maxwell system on unbounded domains

The relativistic Vlasov-Maxwell system describes the evolution of a collisionless plasma. The problem of linear instability of this system is considered in two physical settings: the so-called "one and one-half" dimensional case, and the three dimensional case with cylindrical symmetry. Sufficient conditions for instability are obtained in terms of the spectral properties of certain Schrödinger operators that act on the spatial variable alone (and not in full phase space). An important aspect of these conditions is that they do not require any boundedness assumptions on the domains, nor do they require monotonicity of the equilibrium.

math.AP↗

arXiv2014

Instabilities in kinetic theory and their relationship to the ergodic theorem

A method for obtaining simple criteria for instabilities in kinetic theory is described and outlined, specifically for the relativistic Vlasov-Maxwell system. An important ingredient of the method is an analysis of a parametrized set of averaging operators along trajectories. This leads to a connection with similar problems in ergodic theory. In particular the rate of convergence in the ergodic theorem is a common feature which is studied.

math.AP↗

arXiv2013

On the spectrum of shear flows and uniform ergodic theorems

The spectra of parallel flows (that is, flows governed by first-order differential operators parallel to one direction) are investigated, on both $L^2$ spaces and weighted-$L^2$ spaces. As a consequence, an example of a flow admitting a purely singular continuous spectrum is provided. For flows admitting more regular spectra the density of states is analyzed, and spaces on which it is uniformly bounded are identified. As an application, an ergodic theorem with uniform convergence is proved.

math.SP↗

arXiv2011

Instability of Nonsymmetric Nonmonotone Equilibria of the Vlasov-Maxwell System

We consider the 1/2-dimensional relativistic Vlasov-Maxwell system that describes the time-evolution of a plasma. We find a relatively simple criterion for spectral instability of a wide class of equilibria. This class includes non-homogeneous equilibria that need not satisfy any additional symmetry properties (as was the case in previous results), nor should they be monotone in the particle energy. The criterion is given in terms of the spectral properties of two Schrödinger operators that arise naturally from Maxwell's equations. The spectral analysis of these operators is quite delicate, and some general functional analytic tools are developed to treat them. These tools can be applied to similar systems in higher dimensions, as long as their domain is finite or periodic.

math.AP↗

arXiv2011

Instability of Nonmonotone Magnetic Equilibria of the Relativistic Vlasov-Maxwell System

We consider the question of linear instability of an equilibrium of the Relativistic Vlasov-Maxwell (RVM) System that has a strong magnetic field. Standard instability results deal with systems where there are fewer particles with higher energies. In this paper we extend those results to the class of equilibria for which the number of particles does not depend monotonically on the energy. Without the standard sign assumptions, the analysis becomes significantly more involved.

math-ph↗