Existence, uniqueness and approximation for stochastic Schrodinger equation: the Poisson case

In quantum physics, recent investigations deal with the so-called "quantum trajectory" theory. Heuristic rules are usually used to give rise to "stochastic Schrodinger equations" which are stochastic differential equations of non-usual type describing the physical models. These equations pose tedious problems in terms of mathematical justification: notion of solution, existence, uniqueness, justification... In this article, we concentrate on a particular case: the Poisson case. Random measure theory is used in order to give rigorous sense to such equations. We prove existence and uniqueness of a solution for the associated stochastic equation. Furthermore, the stochastic model is physically justified by proving that the solution can be obtained as a limit of a concrete discrete time physical model.Comment: 35 page

Top Quark Modelling and Tuning at CMS

Recent measurements dedicated to improving the understanding of modelling top quark pair (${\text{t}\overline{\text{t}}}$) production at the LHC are summarised. These measurements, performed with proton-proton collision data collected by the CMS detector at $\sqrt{s}=$ 13 TeV, probe the underlying event in ${\text{t}\overline{\text{t}}}$ events, and use the abundance of jets in ${\text{t}\overline{\text{t}}}$ events to study the substructure of jets. A new set of tunes for PYTHIA 8, and their performance with ${\text{t}\overline{\text{t}}}$ data, are also discussed.Comment: Proceedings for the 11th International Workshop on Top Quark Physics (TOP2018