|
Index Theory of Chiral Unitaries and Split-Step Quantum Walks
Chris Bourneab a Institute for Liberal Arts and Sciences and Graduate School of Mathematics,
Nagoya University, Furo-cho, Chikusa-ku, Nagoya, 464-8601, Japan
b RIKEN iTHEMS, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
Аннотация:
Building from work by Cedzich et al. and Suzuki et al., we consider topological and index-theoretic properties of chiral unitaries, which are an abstraction of the time evolution of a chiral-symmetric self-adjoint operator. Split-step quantum walks provide a rich class of examples. We use the index of a pair of projections and the Cayley transform to define topological indices for chiral unitaries on both Hilbert spaces and Hilbert $C^*$-modules. In the case of the discrete time evolution of a Hamiltonian-like operator, we relate the index for chiral unitaries to the index of the Hamiltonian. We also prove a double-sided winding number formula for anisotropic split-step quantum walks on Hilbert $C^*$-modules, extending a result by Matsuzawa.
Ключевые слова:
index theory, $K$-theory, quantum walk, operator algebras.
Поступила: 4 декабря 2022 г.; в окончательном варианте 24 июля 2023 г.; опубликована 28 июля 2023 г.
Образец цитирования:
Chris Bourne, “Index Theory of Chiral Unitaries and Split-Step Quantum Walks”, SIGMA, 19 (2023), 053, 39 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1948 https://www.mathnet.ru/rus/sigma/v19/p53
|
Статистика просмотров: |
Страница аннотации: | 49 | PDF полного текста: | 4 | Список литературы: | 7 |
|