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Collaborative Research Center 910Unexpected emergence of delay equations in quantum transport control

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Unexpected emergence of delay equations in quantum transport control

Abstract:
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.

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