Magnetic field switching in parallel quantum dots

We show that the Coulomb blockade in parallel dots pierced by magnetic flux $\Phi$ completely blocks the resonant current for any value of $\Phi$ except for integer multiples of the flux quantum $\Phi_0$. This non-analytic (switching) dependence of the current on $\Phi$ arises only when the dot states that carry the current are of the same energy. The time needed to reach the steady state, however, diverges when $\Phi\to n\Phi_0$.Comment: additional explanations added, Europhysics Letters, in pres

The Study of Highway for Lifelong Multi-Agent Path Finding

In modern fulfillment warehouses, agents traverse the map to complete endless tasks that arrive on the fly, which is formulated as a lifelong Multi-Agent Path Finding (lifelong MAPF) problem. The goal of tackling this challenging problem is to find the path for each agent in a finite runtime while maximizing the throughput. However, existing methods encounter exponential growth of runtime and undesirable phenomena of deadlocks and rerouting as the map size or agent density grows. To address these challenges in lifelong MAPF, we explore the idea of highways mainly studied for one-shot MAPF (i.e., finding paths at once beforehand), which reduces the complexity of the problem by encouraging agents to move in the same direction. We utilize two methods to incorporate the highway idea into the lifelong MAPF framework and discuss the properties that minimize the existing problems of deadlocks and rerouting. The experimental results demonstrate that the runtime is considerably reduced and the decay of throughput is gradually insignificant as the map size enlarges under the settings of the highway. Furthermore, when the density of agents increases, the phenomena of deadlocks and rerouting are significantly reduced by leveraging the highway