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Quantum cat maps: their symmetries and spectral distributions
Optimization| Speaker: | Dr. Francesco Mezzadri, American Institute of Mathematics |
| Location: | 0 Kerr |
| Start time: | Thu, May 23 2002, 4:10PM |
Description
The quantum cat maps are the Weil represention of a subgroup of
SL(2,Z). They are among the most important models used to study
the quantum mechanical properties of dynamical systems whose
corresponding classical dynamics is hyperbolic.
In this talk the main features of these
systems will be discussed. In particular for each quantum map U(A)
there exists a set of unitary operators that commute with U(N) and
among themselves. Such operators (known as Hecke operators in
analogy with an analogous phenomenon in the theory of modular
surfaces) are responsible for the unusual properties of these
systems, like their spectral degeneracy.
We shall also describe how these maps can be coupled with SU(2)
matrices to study quantum system with spin when the underlying
dynamics is chaotic, for which relatively few models are
available.