Lund, 22nd - 24th January 2004
Quantum Ergodicity - Basic Ideas and Recent Developments
Quantum ergodicity for matrix valued operators
Jens Bolte (Ulm)
We consider semiclassical pseudodifferential operators that are
(Weyl-) quantisations of matrix valued symbols such as, e.g.,
Dirac operators. In this setting to each eigenvalue of the principal
symbol of the Hamiltonian operator there corresponds an almost
invariant subspace of the quantum Hilbert space as well as a
classical dynamical system. The latter consists of a skew product
flow built over the Hamiltonian flow generated by the eigenvalue
of the principal symbol. Suitable invariant semiclassical
observables are identified and an Egorov theorem is proven for
them. Quantum ergodicity is then shown to hold for the projections
of eigenvectors to an almost invariant subspace provided the
corresponding skew product flow is ergodic.
Slides:
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Workshop Home
Last modified: Jan 28 2004
Stefan Keppeler
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