Network architecture of energy landscapes in mesoscopic quantum systems

Mesoscopic quantum systems exhibit complex many-body phenomena. Even simple, non-interacting theories display a rich landscape of energy states, where many-particle configurations are linked by spin- and energy-dependent transition rates. This collective energy landscape is difficult to characterize, especially in regimes of frustration. Here, we use network science to quantify the organization of these state transitions. Using a computational model of electronic transport through quantum antidots, we construct networks where nodes represent energy states and edges represent allowed transitions. We explore how current and conductance, which measure transport, are reflected in the network topology in response to changes in external voltages. We find that the state-transition networks exhibit Rentian scaling, which is characteristic of efficient computer and neural circuitry, and which measures the interconnection complexity of a network. Remarkably, networks corresponding to points of frustration in transport exhibit enhanced complexity relative to networks not experiencing frustration. Our results demonstrate that network-based analyses can capture salient properties of quantum transport, and motivate future efforts using network science to understand complex quantum systems.