Optimisation of the first principle code Octopus for massive parallel architectures: application to light harvesting complexes

150 p.

Giant diamagnetism of gold nanorods

The presence of giant diamagnetism in Au nanorods, NRs, is shown to be a possible consequence of field induced currents in the surface electrons. The distance, Delta , between quantum surface energy levels has been calculated as a function of the NRs radius. Note that those electrons occupying states for which Delta > k(B)T are steadily orbiting with constant orbital moment. The diamagnetic response induced when a field is turned on remains constant during the time the field is acting. As the NRs radius increases, Delta decreases and accordingly the electron fraction available to generate constant currents decreases, consequently the surface diamagnetic susceptibility decreases towards its bulk value. The surface electronic motion induced by the axial applied field on electrons confined into a cylindrical surface accounts with extremely good quantitative agreement for the giant diamagnetism recently measured and reported.

A quantitative witness for Greenberger-Horne-Zeilinger entanglement

Along with the vast progress in experimental quantum technologies there is an increasing demand for the quantification of entanglement between three or more quantum systems. Theory still does not provide adequate tools for this purpose. The objective is, besides the quest for exact results, to develop operational methods that allow for efficient entanglement quantification. Here we put forward an analytical approach that serves both these goals. We provide a simple procedure to quantify Greenberger-Horne-Zeilinger-type multipartite entanglement in arbitrary three-qubit states. For two qubits this method is equivalent to Wootters' seminal result for the concurrence. It establishes a close link between entanglement quantification and entanglement detection by witnesses, and can be generalised both to higher dimensions and to more than three parties.

Distribution theory and fundamental solutions of differential operators

The objective of this dissertation is to study the theory of distributions and some of its applications. Certain concepts which we would include in the theory of distributions nowadays have been widely used in several fields of mathematics and physics. It was Dirac who first introduced the delta function as we know it, in an attempt to keep a convenient notation in his works in quantum mechanics. Their work contributed to open a new path in mathematics, as new objects, similar to functions but not of their same nature, were being used systematically. Distributions are believed to have been first formally introduced by the Soviet mathematician Sergei Sobolev and by Laurent Schwartz. The aim of this project is to show how distribution theory can be used to obtain what we call fundamental solutions of partial differential equations.