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Applications of Kato's formula to quantum dynamics

Mathematical Physics & Probability

Speaker: David Damanik, Caltech
Location: 693 Kerr
Start time: Tue, Oct 11 2005, 3:10PM

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.