65 citations · 439 across the 44 of their papers we have counts for
47 papers
On Analyticity of Solitons for the Periodic Dispersion-Managed Nonlinear Schrödinger Equation
Sebastian Herr, Dirk Hundertmark, Jeremy L. Marzuola +1
We explore the regularity of energy maximizers for the Lagrangian of a periodic dispersion managed fiber optic at fixed intensity, on a torus of length and with vanishing avera…
On the Excess Charge Problem of Atoms
Dirk Hundertmark, Nikolaos Pattakos, Marvin Raimund Schulz
This paper establishes new bounds on the maximum number of electrons that an atom with nuclear charge can bind. Specifically, we show that \begin{equation*} N_c(Z) <…
Why a System of Three Bosons on Separate Lines Can Not Exhibit the Confinement Induced Efimov Effect
Dirk Hundertmark, Marvin R. Schulz, Semjon Vugalter
We study a system of three bosons interacting with short-range potentials which can move along three different lines. Two of these lines are parallel to each other within one plane…
Quantum Systems at The Brink
Dirk Hundertmark, Michal Jex, Markus Lange
We present a method to calculate the asymptotic behavior of eigenfunctions of Schrödinger operators that also works at the threshold of the essential spectrum. It can be viewed as…
Out-of-equilibrium optomechanical resonance self-excitation
P. Milde, M. Langenhorst, H. Hölscher +4
The fundamental sensitivity limit of atomic force microscopy is strongly correlated to the thermal noise of the cantilever oscillation. A method to suppress this unwanted noise is…
Quantum Systems at the Brink: Existence of Bound States, Critical Potentials and Dimensionality
Dirk Hundertmark, Michal Jex, Markus Lange
One of the crucial properties of a quantum system is the existence of bound states. While the existence of eigenvalues below zero, i.e., below the essential spectrum, is well under…