This talk    consists of two independent topics: 1. Long-range hopping limit of    1D free-space alternating quantum emitters and 2. Relaxation    dynamics in random k-local Liouvillians.  
 
 Topic 1(arXiv    2305.16059): Recently, structured arrays of quantum emitters have    attracted much attention in the context of quantum optics. In this    work, we study the single excitation sector of alternating atomic    chains in 3D free space at a particular physical parameter, where    the hopping amplitude of emitter excitation is proportional to the    inverse of the distance and equals the lattice dimension. We find    the system shows a macroscopic number of exceptional points, dubbed    exceptional-point phase transition. Also, we numerically find the    system contains an edge state, that can be eliminated via a    continuous deformation, consistent with the illdefinedness of bulk    topological invariant.  
 
 Topic 2(arXiv    2304.09017): The spectrum support of purely dissipative open quantum    many-body systems with local dissipation processes can be    investigated using random matrix theory, revealing a hierarchy of    decay timescales of observables organized by their k-locality. We    investigate how the spectrum evolves when a random 2-local    Hamiltonian is present, and show that the hierarchy of decay    timescales is stable up to second-order perturbation in unitary strength.