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Applications of Kato's formula to quantum dynamics
Probability| Speaker: | David Damanik, Caltech |
| Location: | 693 Kerr |
| Start time: | Tue, Oct 11 2005, 3:10PM |
Description
The Plancherel Theorem allows one to relate the unitary group
generated by a self-adjoint operator to the resolvent. This explicit
formula, due to Kato, has recently played an important role in the study of
anomalous transport and quantum dynamics associated with singular continuous
spectral measures. We will explain some applications of Kato's formula to
one-dimensional quantum systems that show how transfer matrix bounds give
rise to bounds on transport exponents. As a consequence, we are able to
prove anomalous transport for the Fibonacci Hamiltonian. This is joint work
with Serguei Tcheremchantsev.