M. I. Molina
We examine the conditions for the existence of bounded dynamical phases for finite PT-symmetric arrays of split-ring resonators. The dimer (N=2), trimer (N=3) and pentamer (N=5) cases are solved in closed form, while for \(N>5\) results were computed numerically for several gain/loss spatial distributions. It is found that the parameter stability window decreases monotonically with the size of the array.
http://arxiv.org/abs/1301.5291
Pattern Formation and Solitons (nlin.PS); Materials Science (cond-mat.mtrl-sci)
Francisco Correa, Mikhail S. Plyushchay
The origin of spectral singularities in finite-gap singly periodic PT-symmetric quantum systems is investigated. We show that they emerge from a limit of band-edge states in a doubly periodic finite gap system when the imaginary period tends to infinity. In this limit, the energy gaps are contracted and disappear, every pair of band states of the same periodicity at the edges of a gap coalesces and transforms into a singlet state in the continuum. As a result, these spectral singularities turn out to be analogous to those in the non-periodic systems, where they appear as zero-width resonances. The specific degeneration related to the presence of finite number of spectral singularities in periodic quantum systems with compact and non-compact topologies is shown to be coherently reflected by a hidden, bosonized nonlinear supersymmetry.
http://arxiv.org/abs/1208.4448
High Energy Physics – Theory (hep-th); Mathematical Physics (math-ph); Quantum Physics (quant-ph)
Francisco Correa, Mikhail S. Plyushchay
We study a reflectionless PT-symmetric quantum system described by the pair of complexified Scarf II potentials mutually displaced in the half of their pure imaginary period. Analyzing the rich set of intertwining discrete symmetries of the pair, we find an exotic supersymmetric structure based on three matrix differential operators that encode all the properties of the system, including its reflectionless (finite-gap) nature. The structure we revealed particularly sheds new light on the splitting of the discrete states into two families, related to the bound and resonance states in Hermitian Scarf II counterpart systems, on which two different series of irreducible representations of sl(2,C) are realized.
http://arxiv.org/abs/1201.2750
High Energy Physics – Theory (hep-th)