Spectra, eigenstates and transport properties of a $\mathcal{P}\mathcal{T}$-symmetric ring

Abstract

We study, analytically and numerically, a simple $\mathcal{P}\mathcal{T}$-symmetric tight-binding ring with an onsite energy $a$ at the gain and loss sites. We show that if $a\ne 0$, the system generically exhibits an unbroken $\mathcal{P}\mathcal{T}$-symmetric phase. We study the nature of the spectrum in terms of the singularities in the complex parameter space as well as the behavior of the eigenstates at large values of the gain and loss strength. We find that in addition to the usual exceptional points, there are "diabolical points", and inverse exceptional points at which complex eigenvalues reconvert into real eigenvalues. We also study the transport through the system. We calculate the total flux from the source to the drain, and how it splits along the branches of the ring. We find that while usually the density flows from the source to the drain, for certain eigenstates a stationary "backflow" of density from the drain to the source along one of the branches can occur. We also identify two types of singular eigenstates, i.e. states that do not depend on the strength of the gain and loss, and classify them in terms of their transport properties.

References in corpus (7)

• The physics of exceptional points
• A non-Hermitian $PT-$symmetric Bose-Hubbard model: eigenvalue rings from unfolding higher-order exceptional points
• Coupling of eigenvalues of complex matrices at diabolic and exceptional points
• Exceptional points and enhanced sensitivity in PT-symmetric continuous elastic media
• The robust $\mP\mT$-symmetric chain and properties of its Hermitian counterpart
• PT-symmetry breaking and universal chirality in a PT-symmetric ring
• PT-symmetry breaking and maximal chirality in a nonuniform PT-symmetric ring

Cited by in corpus (1)

• On a class of non-Hermitian Hamiltonians with tridiagonal matrix representation