Departamento de Matemáticas

Jul 30, 2024 | link.aps.org | Departamento de Matemáticas

Entanglement is a resource under local operations assisted by classical communication (LOCC). Given a set of states S, if there is one state in S that can be transformed by LOCC into all other states in S, then this state is maximally entangled in S. It is a well-known result that the d-dimensional Bell state is the maximally entangled state in the set of all bipartite states of local dimension d.

Jul 10, 2024 | onlinelibrary.wiley.com | Arnaud Bodin |Laboratoire Paul Painlevé |Departamento de Matemáticas |Patrick Popescu-Pampu

1 INTRODUCTION In this paper, by a singularity we mean a germ of real or complex analytic function with an isolated critical point. By a Morse function on a compact manifold with boundary, we mean a smooth function having only non-degenerate critical points, all of them interior to the manifold, and pairwise distinct critical values. A powerful method for analyzing a singularity is to deform it in a suitable way and relate it to the various resulting simpler singularities.

Apr 29, 2024 | link.springer.com | Departamento de Matemáticas

AbstractWe examine the relations between different capacities in the setting of a metric measure space. First, we prove a comparability result for the Riesz \((\beta ,p)\)-capacity and the relative Hajłasz \((\beta ,p)\)-capacity, for \(1<p<\infty \) and \(0<\beta \le 1\), under a suitable kernel estimate related to the Riesz potential. Then we show that in geodesic spaces the corresponding capacity density conditions are equivalent even without assuming the kernel estimate.

Mar 11, 2024 | pubs.aip.org | Departamento de Matemáticas |Universidad de Jaén

George Polya noted that: “Mathematical problems are often inspired by nature, or rather by our interpretation of nature, the physical sciences.

Feb 5, 2024 | link.springer.com | Laboratoire Jacques-Louis Lions |Departamento de Matemáticas

AbstractWe recall some recent results concerning the Initial Value Problem of 1d-cubic non-linear Schrödinger equation (NLS) and other related systems as the Schrödinger Map. For the latter we prove the existence of a cascade of energy. Finally, some new examples of the Talbot effect at the critical level of regularity are given.