06.06.2023, 15 Uhr
Phenomena in High Dimensions
Pierre Youssef (New York University, Abu Dhabi)
David Damanik (Rice University, Houston) und Marko Lindner (Hamburg University of Technology)
2 pm: David Damanik (Rice University, Houston): The Fibonacci Hamiltonian
3 pm: Marko Lindner (Hamburg University of Technology): Finite Sections of the Fibonacci Hamiltonian & Friends
David Damanik (Rice University, Houston): The Fibonacci Hamiltonian
Abstract: This talk gives a gentle introduction to the Fibonacci Hamiltonian, which is the central model in the study of quantum motion in aperiodically ordered environments. After briefly explaining how the discovery of quasicrystals by Dan Shechtman in 1982 led to the formation of a new mathematical discipline, the study of aperiodic order, we will define the Fibonacci Hamiltonian, explain its relevance in this context, and discuss its spectral and quantum dynamical properties.
Marko Lindner (Hamburg University of Technology): Finite Sections of the Fibonacci Hamiltonian & Friends
Abstract: We cut finite matrices out of an infinite matrix A and ask whether we can approximate quantities such as spectrum, singular values, norm and the inverse of A by increasing the size of the finite matrix. As an interim step, the study of one-sided infinite matrices plays a crucial role and we look at the interplay between the one- and two-sided infinite case. We illustrate and extend our results in the case of discrete Schrödinger operators such as the Fibonacci Hamiltonian from the previous talk of D. Damanik.
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