LAUSR

We study the effects of the position of the passive and active cavities on the spontaneous parity-time- ($\mathcal{PT}$-) symmetry-breaking behavior in a non-Hermitian coupled-cavity-array model. We analyze and discuss the energy eigenvalue spectra and $\mathcal{PT}$ symmetry in the topologically trivial and nontrivial regimes under three different cases in detail; that is, the passive and active cavities are located at, respectively, the two end positions, the second and penultimate positions, and each position in the coupled-cavity array. The odevity of the number of cavities is further considered to check the effects of the non-Hermitian terms applied on the $\mathcal{PT}$-symmetric and -asymmetric systems. We find that the position of the passive and active cavities has remarkable impacts on the spontaneous $\mathcal{PT}$-symmetry-breaking behavior, and in each case the system exhibits distinguishable and novel spontaneous $\mathcal{PT}$-symmetry-breaking characteristics. The effects of the non-Hermitian terms on the $\mathcal{PT}$-symmetric and -asymmetric systems due to the odevity are comparatively different in the first case but qualitatively the same in the second case.