Dissipative Quantum Dynamics in Static Network with Different Topologies

TL;DR

This paper explores how the structure of a quantum network influences its dissipative dynamics and coherence, using both small-scale models and mean-field approaches to connect topology with quantum behavior.

Contribution

It introduces a combined analysis of quantum dissipative dynamics in networks of different sizes and topologies, linking network structure to quantum coherence control.

Findings

Network topology significantly affects quantum dissipation and coherence.

A mean-field approach effectively models large-scale quantum networks.

Quantum coherence is highly sensitive to network structure.

Abstract

We investigate the dissipative dynamics of quantum population and coherence among different network topologies of a quantum network using a 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 that extends the network to larger scales and captures dissipative dynamics in large-scale networks, connecting network topology to quantum coherence in complex systems and revealing the sensitivity of quantum coherence to network structure. Our results highlight how dissipative quantum dynamics depend on network topology, providing insight into the coherent dynamics of entangled states in networks. These results may be extended to dynamics in complex systems such as opinion propagation in social models, epidemiology, and various condensed-phase and biological systems.