Mathematical Colloquium Wednesday 11th of April 4.30pm

[Emanuele Tuillier Illingworth]

Dear all,

the next Mathematical Colloquium is Wednesday the *11th of April 4.30 pm 
  room 128*

*Speaker:* Didier Robert, Département de Mathématiques, Laboratoire 
Jean Leray, CNRS-UMR 6629 Université de Nantes,


*Title: *Quantum Ergodicity and Orthonormal Basis of States
Abstract: Our aim in this talk is to give an introduction to a domain of 
Mathematical Physics often named "Quantum Chaos”.
A natural physical definition of this concept is always problematic 
(what means instability in quantum mechanics?).
In mathematics the central problem is to understand the specific 
properties of states of a quantum system when the corresponding classical
system is chaotic; typically Ergodic in L. Boltzman sense [1871].The 
main mathematical result connecting the classical world and the quantum
world is the famous Shnirelman Theorem [1974]. The result was extended 
later in different settings including billiards (P. Gérard-E. Leichtnam 
[1993]).

It was noticed by S. Zelditch [1992] that some classical integrable 
systems may have random quantum states with a chaotic behaviour.
Finally we shall mention a beautiful result by G. Rivière [2013] 
proving a quantum analogous of the general Birkhoff Ergodic Theorem.