Unexpected emergence of delay equations in quantum transport control
Transport through quantum nanostructures can be described in terms of trajectories consisting of electron jumps into and out of the device. These trajectories offer a very physical way of introducing a control formalism in which, conditioned on the detection of the electron jumps, control operations are performed on the device.
By allowing electrons that tunnel during a control operation to themselves initiate further control operations (which initiate further control prcoesses, and so on...), a infinite regression is implied. Remarkably, the statistics of charge transfer in this situation can be mapped onto a system of coupled differential delay equations.