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A universal form of complex potentials with spectral singularities
Dmitry A. Zezyulin, Vladimir V. Konotop
We establish necessary and sufficient conditions for complex potentials in the Schrödinger equation to enable spectral singularities (SSs) and show that such potentials have the un…
Rotating patterns in polariton condensates in ring-shaped potentials under bichromatic pump
Yaroslav V. Kartashov, Dmitry A. Zezyulin
We consider a polariton condensate in a microcavity driven by a bichromatic resonant pump formed by two vortical laser beams carrying different topological charges. The system is a…
Sequences of closely spaced resonances and eigenvalues for bipartite complex potentials
D. I. Borisov, D. A. Zezyulin
We consider a Schroedinger operator on the axis with a bipartite potential consisting of two compactly supported complex-valued functions, whose supports are separated by a large d…
Spacing gain and absorption in a simple -symmetric model: spectral singularities and ladders of eigenvalues and resonances
D. I. Borisov, D. A. Zezyulin
We consider a parity-time (-) symmetric waveguide consisting of a localized gain and loss elements separated by a variable distance. The situation is modelled by a Sc…
Stable multi-ring and rotating solitons in two-dimensional spin-orbit coupled Bose-Einstein condensates with a radially-periodic potential
Yaroslav V. Kartashov, Dmitry A. Zezyulin
We consider two-dimensional spin-orbit coupled atomic Bose-Einstein condensate in a radially-periodic potential. The system supports different types of stable self-sustained states…
Spectral singularities of a potential created by two coupled microring resonators
Vladimir V. Konotop, Barry C. Sanders, Dmitry A. Zezyulin
Two microring resonators, one with gain and one with loss, coupled to each other and to a bus waveguide, create an effective non-Hermitian potential for light propagating in the wa…