Quantum walks in external gauge fields

Understand

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 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, only a unitary step operator.