Dissipative Dynamics of a Quantum System.

S. Alipour, Dariusz Chruściński, Paolo Facchi A +3 more

Abstract Dynamics and features of quantum systems can be drastically different from classical systems. Dissipation is understood as a general mechanism through which quantum systems may lose part or all of their quantum aspects. Here we discuss a method to analyze behaviors of dissipative quantum systems in an algebraic sense. This method employs a time-dependent product between system’s observables which is induced by the underlying dissipative dynamics. We argue that the long-time limit of the algebra of observables defined with this product yields a contractive algebra which reflects the loss of some quantum features of the dissipative system, and it bears relevant information about irreversibility. We illustrate this result through several examples of dissipation in various Markovian and non-Markovian systems.

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.

Kenneth S. Chow

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.

Alberto Acevedo, Manuel Berrondo, Jean-François S. Van Huele