Absolutely continuous spectrum implies ballistic transport for quantum particles in a random potential on tree graphs. (English) Zbl 1278.81090
Summary: We discuss the dynamical implications of the recent proof that for a quantum particle in a random potential on a regular tree graph absolutely continuous (ac) spectrum occurs non-perturbatively through rare fluctuation-enabled resonances. The main result is spelled in the title. {
©2012 American Institute of Physics}
©2012 American Institute of Physics}
MSC:
| 81Q35 | Quantum mechanics on special spaces: manifolds, fractals, graphs, lattices |
| 81Q05 | Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics |
| 81Q10 | Selfadjoint operator theory in quantum theory, including spectral analysis |
| 05C05 | Trees |
| 35B34 | Resonance in context of PDEs |
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