Related papers: On the Smooth Feshbach-Schur Map
We give an overview of recent experiments on an ultracold Fermi-Bose quantum gas where the interspecies interaction can be tuned via magnetic Feshbach resonances. We first describe the various steps that have led to the observation of…
We review the geometric theory of \emp{smooth systems of smooth maps}, of \emp{smooth systems of smooth sections} of a smooth double fibred manifold and of \emp{smooth systems of smooth connections} of a smooth fibred manifold. Moreover,…
$\alpha$-Dirac-harmonic maps are variations of Dirac-harmonic maps, analogous to $\alpha$-harmonic maps that were introduced by Sacks-Uhlenbeck to attack the existence problem for harmonic maps from surfaces. For $\alpha >1$, the latter are…
As a higher dimensional version of the theory of Morse functions, there have been various studies of smooth manifolds using generic smooth maps. As fundamental results, in these studies, they have found that inverse images of such maps…
In our previous work, we have constructed explicit smooth real algebraic functions which may have both compact and non-compact preimages on smooth real algebraic manifolds. This paper presents its variant. Our result is new in obtaining…
Quasi branch and bound is a recently introduced generalization of branch and bound, where lower bounds are replaced by a relaxed notion of quasi-lower bounds, required to be lower bounds only for sub-cubes containing a minimizer. This paper…
We show that the photon self-energy in quantum electrodynamics on noncommutative $\mathbb{R}^4$ is renormalizable to all orders (both in $\theta$ and $\hbar$) when using the Seiberg-Witten map. This is due to the enormous freedom in the…
Completely positive maps are useful in modeling the discrete evolution of quantum systems. Spectral properties of operators associated with such maps are relevant for determining the asymptotic dynamics of quantum systems subjected to…
We extend the Feynman-Kac formula for Schr\"odinger type operators on vector bundles over noncompact Riemannian manifolds to possibly very singular potentials that appear in hydrogen like quantum mechanical problems and that need not be…
Dosi and, quite recently, the author showed that, on the character space of a nilpotent Lie algebra, there exists a sheaf of Fr\'echet--Arens--Michael algebras (of noncommutative holomorphic functions in the complex case and of…
$\mathcal C^2$-partial smoothness of functions has been an important subject of research in optimization, on both theoretical and algorithmic aspects, since it was first introduced by Lewis in 2002. Our work aims at providing a fresh…
The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this model, we review basic notions, results and…
The paper deal with the noncommutative Fr\'echet ${}^*$-algebra $\mathcal{L}(s',s)$ of the so-called smooth operators, i.e. linear and continuous operators acting from the space $s'$ of slowly increasing sequences to the Fr\'echet space $s$…
We generalize the Uhlenbeck-Segal theory for harmonic maps into compact semi-simple Lie groups to general Lie groups equipped with torsion free bi-invariant connection.
We use spherical cap harmonic (SCH) basis functions to analyse and reconstruct the morphology of scanned genus-0 rough surface patches with open edges. We first develop a novel one-to-one conformal mapping algorithm with minimal area…
We characterize Feshbach resonances in all isotopologues of the $\mathrm{Li}{-}\mathrm{Li}$ system with improved interaction potentials. Starting from spectroscopically accurate Morse/long-range (MLR) potential-energy curves for the singlet…
We recall and partially improve four versions of smooth, non-abelian gerbes: Cech cocycles, classifying maps, bundle gerbes, and principal 2-bundles. We prove that all these four versions are equivalent, and so establish new relations…
A general invariant manifold theorem is needed to study the topological classes of smooth dynamical systems. These classes are often invariant under renormalization. The classical invariant manifold theorem cannot be applied, because the…
Magnetic Feshbach resonances are an invaluable tool for controlling ultracold atoms and molecules. They can be used to tune atomic interactions and have been used extensively to explore few- and many-body phenomena. They can also be used…
This paper numerically computes the topological and smooth invariants of Eschenburg spaces with small fourth cohomology group, following Kruggel's determination of the Kreck-Stolz invariants of Eschenburg spaces that satisfy condition C.…