Coherent Dynamics of Complex Quantum Systems

V. M. Akulin

Wei-Yang Liu, Hsuan‐Wei Lee

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.

Xiang Ying Sun

Wei-Yang Liu, Hsuan-Wei Lee

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.

Marcos G. Alpino, Tiago Debarba, Reinaldo O. Vianna +1 more

We investigate the role of a statistical complexity measure to assign equilibration in isolated quantum systems. While unitary dynamics preserve global purity, expectation values of observables often exhibit equilibration-like behavior, raising the question of whether a measure of complexity can track this process. In addition to examining observable equilibration, we extend our analysis to study how the complexity of the quantum states evolves, providing insight into the transition from initial coherence to equilibrium. We define a classical statistical complexity measure based on observable entropy and deviation from equilibrium, which captures the dynamical progression towards equilibration and effectively distinguishes between complex and non-complex trajectories. In particular, our measure is sensitive to non-complex dynamics. Such dynamics include the quasi-periodic behavior exhibited by low-dimensional initial states, where the system explores a limited region of Hilbert space while preserving coherence. Numerical simulations of an Ising-like non-integrable Hamiltonian spin-chain model support these findings. Our work provides new insight into the emergence of equilibrium behavior from unitary dynamics and advances complexity as a meaningful tool in the study of the emergence of classicality in microscopic systems.

I. Chiorescu, Patrice Bertet, Kouichi Semba +3 more