Multiple solutions for singularly perturbed nonlinear magnetic Schrödinger equations

In this paper we consider singularly perturbed nonlinear Schrödinger equations with electromagnetic potentials and involving continuous nonlinearities with subcritical, critical or supercritical growth. By means of suitable variational techniques, truncation arguments and Lusternik–Schnirelman theory, we relate the number of nontrivial complex-valued solutions with the topology of the set where the electric potential attains its minimum value.

The Darwin-Breit Interaction vs. the Aharonov-Bohm Potentials

The paper shows that the Darwin-Breit form of electromagnetic interaction disproves the Aharonov-Bohm assertion about the fundamental meaning of the electromagnetic potentials in quantum theory. A specific analysis of the Aharonov-Bohm electric and magnetic effects substantiates this result.

Ultrafast electron diffraction from nanophotonic waveforms via dynamical Aharonov-Bohm phases

Electron interferometry via phase-contrast microscopy, holography, or picodiffraction can provide a direct visualization of the static electric and magnetic fields inside or around a material at subatomic precision, but understanding the electromagnetic origin of light-matter interaction requires time resolution as well. Here, we demonstrate that pump-probe electron diffraction with all-optically compressed electron pulses can capture dynamic electromagnetic potentials in a nanophotonic material with sub-light-cycle time resolution via centrosymmetry-violating Bragg spot dynamics. The origin of this effect is a sizable quantum mechanical phase shift that the electron de Broglie wave obtains from the oscillating electromagnetic potentials within less than 1 fs. Coherent electron imaging and scattering can therefore reveal the electromagnetic foundations of light-matter interaction on the level of the cycles of light.