Analysis of non-hermitian metamaterials with the methods of mathematical physics

Current experimental advances make it possible to create artificial materials that possess properties unmatched in nature. In particular, it is possible to make experiments with artificial lattices composed from optical fibers where the effective interaction is manifestly non-hermitian. Theoretical description of these settings is remarkably similar to the one of quantum systems. Dynamics of quasi-particles can be described by tight-binding Hamiltonian. There can exist Dirac points in the band structure where physics is effectively described by a low-dimensional Dirac equation.

The student is expected to analyze relevant properties of such systems via construction of solvable models described either by tight-binding Hamiltonian or by Dirac equation. First, the student should become familiar with description of the non-hermitian systems and with the adequate methods for construction of their models, e.g. Darboux transformation. Then the application of these techniques would be in order. Analytical treatment of peculiar scattering and transport properties of the quasi-particles, e.g. asymmetric transmission, presence of exceptional spectral points, are of primary interest.

References:

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