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Basic modelling of transport in 2D wave-mechanical nanodots and billiards with balanced gain and loss mediated by complex potentials

Non-Hermitian quantum mechanics with parity-time (PT) symmetry is presently gaining great interest, especially within the fields of photonics and optics. Here, we give a brief overview of low-dimensional semiconductor nanodevices using the example of a quantum dot with input and output leads, which are mimicked by imaginary potentials for gain and loss, and how wave functions, particle flow, coalescence of levels and associated breaking of PT symmetry may be analysed within such a framework. Special attention is given to the presence of exceptional points and symmetry breaking. Related features for musical string instruments and ‘wolf-notes’ are outlined briefly with suggestions for further experiments.