Seminarium "Modeling of Complex Systems"

Gain and loss are omnipotent in the physical, chemical and biological systems. Their effects can in a convenient way be modelled by effective non-Hermitian Hamiltonians. Imaginary contributions to the potential introduce source and drain terms for the probability amplitude. A special class of non-Hermitian Hamiltonians are those which possess a parity-time symmetry. In spite of their non-Hermiticity these Hamiltonians allow for real energy eigenvalues, i.e. the existence of stationary states in the presence of balanced gain and loss. This effect has been identified theoretically in a large number of quantum systems. Its existence has also been proved experimentally in coupled optical wave guides. In my talk I will provide concise review of these systems including the aspect of physics of energy conversion in nanostructures. Effects described above have very broad context. The dynamics can be very interesting and worth studying even if the parity-time symmetry is not conserved. The list of systems that belong to this class include whispering gallery modes in the micro-resonators, coupled wave-guides, unidirectional reflectionless metamaterial at optical frequencies, polariton condensates and may, many others. In my talk I consider a nanostructure of two coupled ring waveguides with constant linear gain and nonlinear absorption - the system that can be implemented in various settings including polariton condensates, optical waveguides or atomic Bose-Einstein condensates. It was found that, depending on the parameters, this simple configuration allows for observing several complex nonlinear phenomena, which include spontaneous symmetry breaking, modulational instability leading to generation of stable circular flows with various vorticities, stable inhomogeneous states with interesting structure of currents flowing between rings, as well as dynamical regimes having signatures of chaotic behavior.