arXiv subjects

M. Goldberg

Publications and source records attributed to M. Goldberg.

3 recordsLinked to original sources

arXiv2005

A counterexample to dispersive estimates for Schrödinger operators in higher dimensions

In dimension $n>3$ we show the existence of a compactly supported potential in the differentiability class $C^α$, $α< \frac{n-3}2$, for which the solutions to the linear Schrödinger equation in $\R^n$, $$ -i\partial_t u = - Δu + Vu, \quad u(0)=f, $$ do not obey the usual $L^1\to L^{\infty}$ dispersive estimate. This contrasts with known results in dimensions $n \leq 3$, where a pointwise decay condition on $V$ is generally sufficient to imply dispersive bounds.

math.AP↗

arXiv2004

Detectors for Time-of-Flight Fast-Neutron Radiography: 1. Neutron Counting Gas Detector

One of our two methods for fast-neutron imaging with spectrometric capability is presented here. It is a neutron-counting technique based on a hydrogenous neutron converter coupled to Gaseous Electron Multipliers (GEM). The principles of the detection techniques and the optimization of the converter, electron amplification and the readout are described. Evaluation of the properties are derived from a experiment in a pulsed neutron beam of spectral distribution between 2 and 10 MeV

physics.ins-det↗

arXiv2004

Dispersive estimates for Schrodinger operators in dimensions one and three

We prove L^1 --> L^\infty estimates for linear Schroedinger equations in dimensions one and three. The potentials are only required to satisfy some mild decay assumptions. No regularity on the potentials is assumed.

math.AP↗