Regina, June 7 - 10, 2019
In the first part of my talk, I will discuss such a model (joint work with A. Zagoskin, ref.1). Our analysis directly involves multiresolution analysis, specifically the Haar basis. While applications of the Fourier transform in studies of spin systems are already classical, a quantum application of the Haar transform is, to our best knowledge, unprecedented. Also intriguing is an unexpected emergence of fractals in this very context. In the time remaining I will discuss some other connections between classical harmonic analysis and modern quantum theory, ref.2, and implications. In particular, I will demonstrate that band gaps can arise in a qubit-array Hamiltonian via a mechanism that does not involve a periodic potential.
1. A. Sowa and A. Zagoskin, An exactly solvable quantum-metamaterial type model, Preprint, available via https://arxiv.org/abs/1902.05324
2. A. Sowa, Encoding spatial data into quantum observables, Preprint, available via http://arxiv.org/abs/1609.01712