Non-Hermitian systems exhibit a number of surprising features, many of which are still poorly understood. One example is "spectral flow", which is the evolution of a system's eigenvalue spectrum when its parameters are varied around a closed path. It is widely appreciated that the spectral flow is determined by the manner in which this path encloses the degeneracies known as exceptional points (EPs). However, the general relationship between this path, the EPs, and the resulting spectral flow is less well-known. In this talk I will give a pedagogical introduction to this topic and its relationship to a range of physical systems. I will describe how braids and knots naturally emerge as generic features in eigenvalue spectra, and will present measurements of these features in a cavity optomechanical system.
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