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Across all scales of the physical world, dynamical systems can often be usefully represented as abstract networks that encode the systems units and inter-unit interactions. Understanding how physical rules shape the topological structure of those networks can clarify a systems function and enhance our ability to design, guide, or control its behavior. In the emerging area of quantum network science, a key challenge lies in distinguishing between the topological properties that reflect a systems underlying physics and those that reflect the assumptions of the employed conceptual model. To elucidate and address this challenge, we study networks that represent non-equilibrium quantum-electronic transport through quantum antidot devices -- an example of an open, mesoscopic quantum system. The network representations correspond to two different models of internal antidot states: a single-particle, non-interacting model and an effective model for collective excitations including Coulomb interactions. In these networks, nodes represent accessible energy states and edges represent allowed transitions. We find that both models reflect spin conservation rules in the network topology through bipartiteness and the presence of only even-length cycles. The models diverge, however, in the minimum length of cycle basis elements, in a manner that depends on whether electrons are considered to be distinguishable. Furthermore, the two models reflect spin-conserving relaxation effects differently, as evident in both the degree distribution and the cycle-basis length distribution. Collectively, these observations serve to elucidate the relationship between network structure and physical constraints in quantum-mechanical models. More generally, our approach underscores the utility of network science in understanding the dynamics and control of quantum systems.
Using flow equations, equilibrium and non-equilibrium dynamics of a two-level system are investigated, which couples via non-commuting components to two independent oscillator baths. In equilibrium the two-level energy splitting is protected when the
The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phase transition in a spinless dissi
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