Quantum walks in external gauge fields

verfasst von
C. Cedzich, T. Geib, A. H. Werner, R. F. Werner
Abstract

Describing a particle in an external electromagnetic field is a basic task of quantum mechanics. The standard scheme for this is known as "minimal coupling" and consists of replacing the momentum operators in the Hamiltonian by the modified ones with an added vector potential. In lattice systems, it is not so clear how to do this because there is no continuous translation symmetry, and hence, there are no momenta. Moreover, when time is also discrete, as in quantum walk systems, there is no Hamiltonian, but only a unitary step operator. We present a unified framework of gauge theory for such discrete systems, keeping a close analogy to the continuum case. In particular, we show how to implement minimal coupling in a way that automatically guarantees unitary dynamics. The scheme works in any lattice dimension, for any number of internal degrees of freedom, for walks that allow jumps to a finite neighbourhood rather than to nearest neighbours, is naturally gauge invariant, and prepares possible extensions to non-abelian gauge groups.

Organisationseinheit(en)
Fakultät für Mathematik und Physik
Institut für Theoretische Physik
SFB 1227: Designte Quantenzustände der Materie (DQ-mat)
Externe Organisation(en)
Universität zu Köln
Københavns Universitet
Typ
Artikel
Journal
Journal of Mathematical Physics
Band
60
ISSN
0022-2488
Publikationsdatum
01.2019
Publikationsstatus
Veröffentlicht
Peer-reviewed
Ja
ASJC Scopus Sachgebiete
Statistische und nichtlineare Physik, Mathematische Physik
Elektronische Version(en)
https://doi.org/10.48550/arXiv.1808.10850 (Zugang: Offen)
https://doi.org/10.1063/1.5054894 (Zugang: Geschlossen)