Dissipative quantum dynamics in static networks with different topologies

Abstract We investigate the dissipative dynamics of quantum population and coherence among different network topologies of a quantum network through the quantum spin model coupled to a thermal bosonic reservoir. Our study proceeds in two parts. First, we analyze a small network of Ising spins embedded in a large dissipative bath, modeled via the Lindblad master equation where temperature arises naturally from system-bath coupling. This approach reveals how network topology shapes quantum dissipative dynamics, providing a basis for controlling quantum coherence through tailored network structures. Second, we propose a mean-field approach extending the scale of the network that captures the dissipative dynamics to large-scale network, connecting network topologies to quantum coherence in complex systems and revealing the sensitivity of quantum coherence to complex network structure. Our results highlight how dissipative quantum dynamics changes in network topologies, providing information for the coherent dynamics of entangled states in network. Our results can be extended to the dynamics in complex systems such as opinion propagation in social models, epidemiology, and various condensed phase and biological systems.