Fig. 4: Non-reciprocity and amplification in the susceptibility, and convergence of Eq. (23).
From: Topological framework for directional amplification in driven-dissipative cavity arrays
a ν = +1 and b ν = −1. The susceptibility χobc is dominated by the middle sum in (24) and (25): products of the functions In lead to the asymmetry of the scattering matrix with one dominant matrix element indicating non-reciprocity, whereas the amplification is determined by the pre-factor 1/εν(1−N), Eq. (26), and grows exponentially with the number of cavities N. a μ0 = 0.3, μ1 = 0.5, μ−1 = 4 and b μ0 = 0.3, μ1 = 4, μ−1 = 0.5. c Relative error of \(| {({\chi }_{{\rm{obc}}})}_{N,1}| \), Eq. (25), for different points in the topological `phase diagram'. All show exponential convergence with the fastest close to the EP, and a slower rate in the dynamically unstable regime (hatched region) and at the boundary. d Relative error of \(| {({\chi }_{{\rm{obc}}})}_{N,1}| \) in the regime ν = −1. For N = 10 and N = 20 the color scale is cut at 0.1. The case ν = +1 is analogous.
