Quantum walks in external gauge fields - Kölner UniversitätsPublikationsServer

Cedzich, C., Geib, T., Werner, A. H. and Werner, R. F. (2019). Quantum walks in external gauge fields. J. Math. Phys., 60 (1). MELVILLE: AMER INST PHYSICS. ISSN 1089-7658

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DOI:10.1063/1.5054894

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. Published under license by AIP Publishing.

Item Type:

Journal Article

Creators:

Creators	Email	ORCID	ORCID Put Code
Cedzich, C.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Geib, T.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Werner, A. H.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED
Werner, R. F.	UNSPECIFIED	UNSPECIFIED	UNSPECIFIED