title: Invariants of broken discrete symmetries.
abstract: The parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries in one dimension are shown to yield invariant currents that characterize wave propagation. These currents map the wave function from an arbitrary spatial domain to any symmetry-related domain. Our approach addresses any combination of local symmetries, thus applying, in particular, to acoustic, optical, and matter waves. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries.
authors.affiliation: Department of Physics, University of Athens, GR-15771 Athens, Greece.
authors.forename: P A
authors.initials: PA
authors.lastname: Kalozoumis
authors.affiliation: Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
authors.forename: C
authors.initials: C
authors.lastname: Morfonios
authors.affiliation: Department of Physics, University of Athens, GR-15771 Athens, Greece.
authors.forename: F K
authors.initials: FK
authors.lastname: Diakonos
authors.affiliation: Zentrum für Optische Quantentechnologien, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany and Hamburg Centre for Ultrafast Imaging, Universität Hamburg, Luruper Chaussee 149, 22761 Hamburg, Germany.
authors.forename: P
authors.initials: P
authors.lastname: Schmelcher