Fig. 1: Classification of topological systems and examples of strategies to engineer symmetries and/or break Hermiticity. | Nature Physics

Fig. 1: Classification of topological systems and examples of strategies to engineer symmetries and/or break Hermiticity.

From: Topology and broken Hermiticity

Fig. 1

The classification comprises four quadrants, (1) Hermitian and time-invariant systems; (2) non-Hermitian and time-invariant systems; (3) Hermitian and time-varying systems; and (4) non-Hermitian and time-varying systems. The examples are a non-exhaustive list of possible wave-based platforms: quantum materials, depicted as a tight-binding model; electromagnetic waves, represented by a magnetic field; active mechanics and acoustics, in which momentum and/or energy can be injected by motorized particles or loudspeakers; optomechanical devices, depicted by a laser cavity coupled to mechanical motion; water waves close to a parametric instability, in which waves at a frequencies ω are being pumped by a periodic drive at twice the frequency 2ω; active electronics, depicted by a transistor; cold gases under laser pumping; and superconducting circuits.

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