26 January 2021 Tue 4 pm

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The concept of local symmetries which hold only in spatially limited domains is developed. Decomposing space into domains where different local symmetries hold a novel layer of complexity is derived. This way the parity and Bloch theorems are generalized to the case of broken global symmetry. Local inversion or translation symmetries 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. Nonvanishing values of the invariant currents provide a systematic pathway to the breaking of discrete global symmetries. Some examples of applications and corresponding

experimental verifications in acoustics and optics are provided. A classification of perfectly transmitting resonances in completely locally symmetric scattering setups allows for the design of the scattering behaviour in these non-periodic setups. Local symmetries also allow for the real space design of edge states in aperiodic chains. A generalization to interacting many-body systems is outlined.