April 2011
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Day April 5, 2011

On eigenvalues of the Schrödinger operator with an even complex-valued polynomial potential

Per Alexandersson

In this paper, we generalize several results of the article “Analytic continuation of eigenvalues of a quartic oscillator” of A. Eremenko and A. Gabrielov. We consider a family of eigenvalue problems for a Schr\”odinger equation with even polynomial potentials of arbitrary degree d with complex coefficients, and k<(d+2)/2 boundary conditions. We show that the spectral determinant in this case consists of two components, containing even and odd eigenvalues respectively.
In the case with k=(d+2)/2 boundary conditions, we show that the corresponding parameter space consists of infinitely many connected components.

Mathematical Physics (math-ph)

Complex photonic graphene: Optical tachyons, strain, and PT-symmetry

Alexander Szameit, Mikael C. Rechtsman, Omri Bahat-Treidel, Mordechai Segev

We apply gain/loss to honeycomb photonic lattices and demonstrate that optical tachyons, a photonic version of particles that travel faster than the speed of light, can be generated by PT-symmetry breaking in this structure. We further show that the PT-symmetry can be restored via strain.

Optics (physics.optics)