Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 0805.0520

The Radial Wave Operator in Similarity Coordinates

Roland Donninger
View original source ↗Read source document ↗Export metadata ↓

Abstract

We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyse linear stability of the fundamental self--similar solution of the wave equation with a focusing power nonlinearity.

Explore related subjects

math-phmath.MP

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Roland Donninger. 2010-02-24. The Radial Wave Operator in Similarity Coordinates. https://doi.org/10.1063/1.3299302

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

A modified Fermi Golden Rule at threshold for 3D magnetic Schrödinger operators

In this paper we consider three-dimensional Schrödinger operators with a simple threshold eigenvalue. We show, under certain assumptions, that when a small magnetic field is introduced, this eigenvalue turns into a resonance in the time-dependent sense. We find the leading term in the asymptotic expansion of the imaginary part of the resonance and discuss the principal differences with respect to resonances induced by weak electric fields obtained previously in the literature.

math-ph↗
arXiv2026

Instantaneous Sobolev Regularization for Dissipative Bosonic Dynamics

We investigate quantum Markov semigroups on bosonic Fock space and identify a broad class of infinite-dimensional dissipative evolutions that exhibit instantaneous Sobolev regularization. Motivated by stability problems in quantum computation, we show that for certain Lindblad operators that are polynomials of creation and annihilation operators, the resulting dynamics immediately transform any initial state into one with finite expectation in all powers of the number operator. A key application is in the bosonic cat code, where we obtain explicit estimates in the trace norm for the speed of convergence. These estimates sharpen existing perturbative bounds at both short and long times, offering new analytic tools for assessing stability and error suppression in bosonic quantum information processing. For example, we improve the strong exponential convergence of the (shifted) $2$-photon dissipation to its asymptotic channel to the uniform topology. For multi-mode systems, a generation theorem in concentrated single-sandwich norms supplies the domain properties required for the regularization argument.

math-ph↗
arXiv2026

Imaging through rough interfaces: The shower curtain effect

The quality of an image observed through a scattering layer, such as a shower curtain, depends strongly on the relative position of the scattering layer between the object and the observer. This well-known phenomenon is commonly referred to as the shower curtain effect. When the scattering layer is placed close to the observer, the image is strongly degraded, whereas if it is located close to the object, the object may still be observed with relatively high resolution. Previous analyses of the shower curtain effect have primarily modeled the scattering layer as a section of a random medium. In this work, we present a new analysis in which the scattering layer is modeled instead as a rough interface, a description that arises naturally in many physical configurations. Within this framework, we derive explicit characterizations of both the image resolution and the signal-to-noise ratio, and determine how these quantities depend on the statistical properties of the rough interface and on its relative location between the object and the observer.

math-ph↗