Quantum traffic theory
J R Barker and S Babiker
Queuing theory, a branch of the mathematics of stochastic systems, is being developed for the quantum mechanical many-body problem of electrons mving through systems of conducting islands in nanoelectronic structures. The conditions for queuing occur when the effects of Coulomb charging energy become significant, typically in systems with very small capacitances. These range from single electronic devices, to hopping systems in low dimensional semiconductors to redox centre chains in chemical systems and to electron transfer in coonducting polymers and enzymes.
Queuing theory produces some unexpected results, for example Braess paradox states that if one attempts to relieve congestion on a particular network by providing relief routes between different parts of the network, the congestion may actually increase! These surprising results are relevant to road traffic, telephone communication systems, wiring problems in VLSI and now to the transport of interacting electrons in nanostructures.
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