Physical processes leading to surface inhomogeneities: the case of rotation

In this lecture I discuss the bulk surface heterogeneity of rotating stars, namely gravity darkening. I especially detail the derivation of the omega-model of Espinosa Lara & Rieutord (2011), which gives the gravity darkening in early-type stars. I also discuss the problem of deriving gravity darkening in stars owning a convective envelope and in those that are members of a binary system.Comment: 23 pages, 11 figure, Lecture given to the school on the cartography of the Sun and the stars (May 2014 in Besan\c{c}on), to appear in LNP, Neiner and Rozelot edts V2: typos correcte

Solution to the Landau-Zener problem via Susskind-Glogower operators

We show that, by means of a right-unitary transformation, the fully quantized Landau-Zener Hamiltonian in the weak-coupling regime may be solved by using known solutions from the standard Landau-Zener problem. In the strong-coupling regime, where the rotating wave approximation is not valid, we show that the quantized Landau-Zener Hamiltonian may be diagonalized in the atomic basis by means of a unitary transformation; hence allowing numerical solutions for the few photons regime via truncation.Comment: 6 pages, 5 figure

Propagation and perfect transmission in three-waveguide axially varying couplers

We study a class of three-waveguide axially varying structures whose dynamics are described by the su(3) algebra. Their analytic propagator can be found based on the corresponding Lie group generators. In particular, we show that the field propagator corresponding to three-waveguide structures that have arbitrarily varying coupling coefficients and identical refractive indices is associated with the orbital angular momentum algebra. The conditions necessary to achieve perfect transmission from the first to the last waveguide element are obtained and particular cases are elucidated analytically.Comment: 5 pages, 4 figure