COOKIES: By using this website you agree that we can place Google Analytics Cookies on your device for performance monitoring. |

University of Cambridge > Talks.cam > Partial Differential Equations seminar > Dynamics, dispersion and control of Schrödinger equations

## Dynamics, dispersion and control of Schrödinger equationsAdd to your list(s) Download to your calendar using vCal - Fabricio Macià, Universidad Politécnica de Madrid
- Monday 23 April 2018, 15:00-16:00
- CMS, MR13.
If you have a question about this talk, please contact Ivan Moyano. We are interested in the dynamics of linear Schrödinger equations: i\partial_t u(t,x)+\Delta_x u(t,x)-V(t,x)u(t,x)=0,\quad (t,x)\in \mathbb{R}\times M, in bounded geometries such as a compact manifold, equipped with a Riemannian metric, or a bounded domain in Euclidean space. More specifically, we would like to understand the structure of those subsets on which high-frequency solutions can concentrate (in the sense of the L2 norm); that is, regions on which the position probability densities |u_n(t,x)|^2 of a normalized sequence of solutions can accumulate. This problem is also related to quantifying dispersion and understanding controllability properties for Schrödinger equations. We give a detailed answer to this question for systems whose underlying classical dynamics (the geodesic flow or the billiard flow) is completely integrable (as flat tori, spheres or the planar disk). Our analysis is based on understanding the structure of Wigner measures associated to sequences of solutions. We accomplish that by analysing the solutions to the corresponding Wigner equations by means of a (second-micro)localization with respect to a partition of phase-space adapted to the classical dynamical system. This talk is based on joint works with Nalini Anantharaman, Clotilde Fermanian-Kammerer, Matthieu Léautaud and Gabriel Rivière. This talk is part of the Partial Differential Equations seminar series. ## This talk is included in these lists:- All CMS events
- All Talks (aka the CURE list)
- CMS Events
- CMS, MR13
- DPMMS Lists
- DPMMS Pure Maths Seminar
- DPMMS info aggregator
- DPMMS lists
- Hanchen DaDaDash
- Interested Talks
- My seminars
- Partial Differential Equations seminar
- School of Physical Sciences
- bld31
Note that ex-directory lists are not shown. |
## Other listsINTP Forum Engineering Department Mechanics and Materials Seminar Romina Vuono## Other talksIn search of amethysts, black gold and yellow gold On determinations of the strong coupling constant from hadronic data Comparative perspectives on social inequalities in life and death: an interdisciplinary conference Cohomology of the moduli space of curves Deficits in axonal transport in ALS and Charcot-Marie-Tooth disease models Mesembs - Actual and Digital |