graduate

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

TYPEColloquium
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.




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 classical

dynamics 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 which

can be used to aid the analysis.

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