## On the relation between classical and quantum dynamics --- a mathematician's perspective |

TYPE | Colloquium |

Speaker: | Professor Elon Lindenstrauss |

Affiliation: | Einstein Institute of Mathematics- The Hebrew Univesity |

Date: | 19.01.2012 |

Time: | 16:30 |

Location: | Lidow Rosen Auditorium (323) |

Abstract: | Classical mechanics and quantum mechanics give very different descriptions of the laws of evolution of a physical system which at high energies should be quite similar. I will discuss one aspect of this in a very simple system: one spineless particle constraint to lie on a closed and bounded manifold with no external force. In this case the quantum unique ergodicity conjecture states that if the classicaldynamics is uniformly hyperbolic ("chaotic" in a strong sense) the steady states of the Schroedinger evolution (which are just the eigenfunctions of the Laplace-Beltrami operator) become equidistributed in the high energy limit. I will present some of the rigorous results in this direction, and focus on the case of arithmetic manifolds which have a subtle but very rich symmetry whichcan be used to aid the analysis. |