PT-symmetry in quantum and nonlinear systems | Dr. Andreas Fring

PT-symmetry in quantum and nonlinear systems
Prof. Andreas Fring
City University of London

I will provide a pedagogical introduction to non-Hermitian quantum systems that are PT-symmetric, meaning that they are left invariant under a simultaneous parity transformation (P) and time-reversal (T). I will explain how generalised versions of this antilinear symmetry can be utilised to explain that these type of systems possess real eigenvalue spectra in parts of their parameter spaces and how to set up a consistent quantum mechanical framework for them that enables a unitary time-evolution. I will also discuss time-dependent versions of these systems. In the second part of the talk I will discuss more recent results on how these general ideas can be used in the context of nonlinear classical systems and quantum field theory. For the former I will discuss how new types of integrable systems can be constructed and how to establish that solutions to these systems are stable. For the latter I will discuss in particular how to set up the Higgs mechanism for these systems.

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