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arXiv · 1208.2259

Fractal Weyl laws for amplified states in PT-symmetric resonators

Christopher Birchall·Henning Schomerus
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Abstract

We find that in nonhermitian PT-symmetric systems (as realized in resonators with balanced absorption and amplification), a mechanism based on quantum-to-classical correspondence reduces the occurrence of strongly amplified states. The reduction arises from semiclassically emerging hierarchical phase-space structures that are associated with the coupling of the amplifying and absorbing regions (forward and backward-trapped sets and their complements), and amounts to a generalization of the fractal Weyl law, earlier proposed for ballistically open systems. In the context of the recently introduced class of PT-symmetric laser-absorbers, this phenomenon reduces the number of states participating in the mode competition.

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Christopher Birchall, Henning Schomerus. 2012-08-10. Fractal Weyl laws for amplified states in PT-symmetric resonators. https://arxiv.org/abs/1208.2259

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