Explanipedia

Arbitrary Polynomial Decay Rates of Neutral, Collisionless Plasmas Open

Grace Mattingly, Stephen Pankavich, Jonathan Ben-Artzi · 2025

A multispecies, collisionless plasma is modeled by the Vlasov-Poisson system. Assuming the plasma is neutral and the electric field decays with sufficient rapidity as $t \to\infty$, we show that solutions can be constructed with arbitraril…

Arbitrary Polynomial Decay Rates of Neutral, Collisionless Plasmas Open

Jonathan Ben-Artzi, Grace Mattingly, Stephen Pankavich · 2025

Modified Scattering of Solutions to the Relativistic Vlasov-Maxwell System Inside the Light Cone Open

Stephen Pankavich, Jonathan Ben-Artzi · 2023

We consider the relativistic Vlasov-Maxwell system in three dimensions and study the limiting asymptotic behavior as $t \to \infty$ of solutions launched by small, compactly supported initial data. In particular, we prove that such solutio…

Asymptotic growth and decay of two-dimensional symmetric plasmas Open

Jonathan Ben-Artzi, Baptiste Morisse, Stephen Pankavich · 2023

We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that…

A uniform ergodic theorem for degenerate flows on the annulus Open

Jonathan Ben-Artzi, Baptise Morisse · 2023

Motivated by the well-known phase-space portrait of the nonlinear pendulum, the purpose of this paper is to obtain convergence rates in the ergodic theorem for flows in the plane that have arbitrarily slow trajectories. Considering bounded…

Computing scattering resonances Open

Jonathan Ben‐Artzi, Marco Marletta, Frank Rösler · 2022

The question of whether it is possible to compute scattering resonances of Schrödinger operators – independently of the particular potential – is addressed. A positive answer is given, with the potential merely required to be \mathcal{C}^1…

On the complexity of the inverse Sturm-Liouville problem Open

Jonathan Ben-Artzi, Marco Marletta, Frank Rösler · 2022

This paper explores the complexity associated with solving the inverse Sturm-Liouville problem with Robin boundary conditions: given a sequence of eigenvalues and a sequence of norming constants, how many limits does a universal algorithm …

Universal algorithms for computing spectra of periodic operators Open

Jonathan Ben‐Artzi, Marco Marletta, Frank Rösler · 2022

Schrödinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely, u…

Asymptotic Growth and Decay of Two-Dimensional Symmetric Plasmas Open

Jonathan Ben‐Artzi, Baptiste Morisse, Stephen Pankavich · 2022

We study the large time behavior of classical solutions to the two-dimensional Vlasov-Poisson (VP) and relativistic Vlasov-Poisson (RVP) systems launched by radially-symmetric initial data with compact support. In particular, we prove that…

Global Strichartz estimates for the Dirac equation on symmetric spaces Open

Jonathan Ben‐Artzi, Federico Cacciafesta, Anne-Sophie de Suzzoni, Junyong Zhang · 2022

In this paper, we study global-in-time, weighted Strichartz estimates for the Dirac equation on warped product spaces in dimension $n\geq 3$ . In particular, we prove estimates for the dynamics restricted to eigenspaces of the Dirac operat…

A toy model for the relativistic Vlasov-Maxwell system Open

Jonathan Ben‐Artzi, Stephen Pankavich, Junyong Zhang · 2022

The global-in-time existence of classical solutions to the relativistic Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after nearly four decades of mathematical research. In this note, a simplified "toy model" is pre…

A toy model for the relativistic Vlasov-Maxwell system Open

Jonathan Ben-Artzi, Stephen Pankavich, Junyong Zhang · 2021

The global-in-time existence of classical solutions to the relativistic Vlasov-Maxwell (RVM) system in three space dimensions remains elusive after nearly four decades of mathematical research. In this note, a simplified ``toy model'' is p…

Computing the Sound of the Sea in a Seashell Open

Jonathan Ben‐Artzi, Marco Marletta, Frank Rösler · 2021

Universal algorithms for computing spectra of periodic operators Open

Jonathan Ben‐Artzi, Marco Marletta, Frank Rösler · 2021

Schrödinger operators with periodic (possibly complex-valued) potentials and discrete periodic operators (possibly with complex-valued entries) are considered, and in both cases the computational spectral problem is investigated: namely, u…

Strichartz estimates for the Klein-Gordon equation in a conical singular space Open

A-S de Suzzoni, Jonathan Ben-Artzi, Federico Cacciafesta, Jiaxing Zhang · 2020

Consider a conical singular space $X=C(Y)=(0,\infty)_r\times Y$ with the metric $g=\mathrm{d}r^2+r^2h$, where the cross section $Y$ is a compact $(n-1)$-dimensional closed Riemannian manifold $(Y,h)$. We study the Klein-Gordon equations wi…

Computing Scattering Resonances Open

Jonathan Ben‐Artzi, Marco Marletta, Frank Rösler · 2020

The question of whether it is possible to compute scattering resonances of Schrödinger operators - independently of the particular potential - is addressed. A positive answer is given, and it is shown that the only information required to …

Uniform convergence in von Neumann’s ergodic theorem in the absence of a spectral gap Open

Jonathan Ben‐Artzi, Baptiste Morisse · 2020

Von Neumann’s original proof of the ergodic theorem is revisited. A uniform convergence rate is established under the assumption that one can control the density of the spectrum of the underlying self-adjoint operator when restricted to su…

A uniform ergodic theorem for degenerate flows on the annulus Open

Jonathan Ben-Artzi, Baptiste Morisse · 2019

Motivated by the well-known phase-space portrait of the nonlinear pendulum, the purpose of this paper is to obtain convergence rates in the ergodic theorem for flows in the plane that have arbitrarily slow trajectories. Considering bounded…

Uniform convergence in von Neumann's ergodic theorem in the absence of a\n spectral gap Open

Jonathan Ben-Artzi, Baptiste Morisse · 2019

Von Neumann's original proof of the ergodic theorem is revisited. A uniform\nconvergence rate is established under the assumption that one can control the\ndensity of the spectrum of the underlying self-adjoint operator when restricted\nto…

Concentrating solutions of the relativistic Vlasov–Maxwell system Open

Jonathan Ben‐Artzi, Simone Calogero, Stephen Pankavich · 2019

We study smooth, global-in-time solutions of the relativistic Vlasov-Maxwell system that possess arbitrarily large charge densities and electric fields. In particular, we construct spherically symmetric solutions that describe a thin shell…

Weak Poincaré inequalities in the absence of spectral gaps Open

Jonathan Ben‐Artzi, Amit Einav · 2018

For generators of Markov semigroups which lack a spectral gap, it is shown how bounds on the density of states near zero lead to a so-called "weak Poincaré inequality" (WPI), originally introduced by Liggett [Ann. Probab., 1991]. Applicati…

Weak Poincar\'e and Nash-type inequalities via density of states estimates Open

Jonathan Ben-Artzi, Amit Einav · 2018

Arbitrarily Large Solutions of the Vlasov--Poisson System Open

Jonathan Ben‐Artzi, Simone Calogero, Stephen Pankavich · 2018

We study smooth, global-in-time solutions of the Vlasov-Poisson system in the plasma physical case that possess arbitrarily large charge densities and electric fields. In particular, we construct two classes of solutions with this property…

Approximations of Strongly Continuous Families of Unbounded Self-Adjoint Operators Open

Jonathan Ben-Artzi, Thomas Holding · 2016

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. …

Can everything be computed? - On the Solvability Complexity Index and Towers of Algorithms. Open

Jonathan Ben-Artzi, Anders C. Hansen, Olavi Nevanlinna, Markus Seidel · 2015

This paper addresses and establishes some of the fundamental barriers in the theory of computation and finally settles the long standing computational spectral problem. Due to the barriers presented in this paper, there are many problems, …

Computing Spectra -- On the Solvability Complexity Index Hierarchy and Towers of Algorithms Open

Jonathan Ben-Artzi, Matthew J. Colbrook, Anders C. Hansen, Olavi Nevanlinna, Markus Seidel · 2015

This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra $\mathrm{…

On the Solvability Complexity Index Hierarchy and Towers of Algorithms Open

Jonathan Ben-Artzi, Matthew J. Colbrook, Anders C. Hansen, Olavi Nevanlinna, M. Seidel · 2015

This paper establishes some of the fundamental barriers in the theory of computations and finally settles the long-standing computational spectral problem. That is to determine the existence of algorithms that can compute spectra $\mathrm{…

Instabilities of the relativistic Vlasov-Maxwell system on unbounded\n domains Open

Jonathan Ben-Artzi, Thomas Holding · 2015

The relativistic Vlasov-Maxwell system describes the evolution of a\ncollisionless plasma. The problem of linear instability of this system is\nconsidered in two physical settings: the so-called "one and one-half"\ndimensional case, and th…

Instabilities of the relativistic Vlasov-Maxwell system on unbounded domains Open

Jonathan Ben-Artzi, Thomas Holding · 2015

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 t…

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