Semiclassical measures for the Schrödinger equation on the torus

First the wave packet method for approximating solutions of the Schrödinger equation (see for example [7] and [17], or [3] for a generalized notion of wave packet) that we will

In the first part of this thesis we completed the dynamical study – previously undertook in [45] – of Wigner measure propagation for solutions of the Schrödinger equation with

We extend the results of [11] about the large time behaviour of the solution (dispersion faster than usual with an additional logarithmic factor, convergence of the rescaled modulus

For any sequence of initial data microlocalized on the unit cotangent bundle, we look at the quantum evolution (below the Ehrenfest time) under small pertur- bations of the

Schr¨ odinger equation, semiclassical limit, numerical simulation, uniformly accurate, Madelung transform, splitting schemes.. 1 Univ Rennes, INRIA, CNRS, IRMAR - UMR 6625,

In our case, invariance of the semiclassical measure under the geodesic flow is a consequence of the Egorov property (1): to prove that subadditivity almost holds (in the sense of

In fact, the equation for b t (x) has turned to be a linear Schr¨ odinger equation with an harmonic potential (and all constants appearing in the potential terms are finite thanks

In this paper, we establish (1) the classical limit of the Hartree equation leading to the Vlasov equation, (2) the classical limit of the N-body linear Schr¨ odinger equation