Bounded dynamics of finite PT-symmetric magnetoinductive arrays

TL;DR

This paper investigates the conditions under which finite PT-symmetric magnetoinductive arrays of split-ring resonators exhibit bounded dynamical phases, analyzing small arrays analytically and larger ones numerically, revealing stability window trends.

Contribution

It provides closed-form solutions for small arrays and numerical analysis for larger arrays, advancing understanding of stability in finite PT-symmetric magnetoinductive systems.

Findings

Stability window decreases with array size

Closed-form solutions for N=2,3,5 arrays

Numerical results for larger arrays

Abstract

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.