| Gaia: | By studying the eigenvalues and eigenvectors of a non-Markovian anti parity-time (APT) symmetric system, we investigate the possibility of exceptional points (EPs) that may arise within it. Our work is motivated by a recently studied APT-symmetric experimental configuration consisting of a pair of time-delay coupled semiconductor lasers (SCLs). In such a system, a single time-delay represents the memory. The time-delayed coupling makes the system’s effective Hamiltonian infinite-dimensional and leads to novel features in the corresponding eigenvalues and eigenvectors. In particular, we demonstrate analytically and numerically that unlike a typical PT-symmetric dimer with zero time-delay, which has one second-order EP, our time-delayed system has parameter regimes that give rise to either one, two, or zero second-order EPs and one third-order EP, and one can select these regimes though a judicious choice of the time-delay and coupling.
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