We describe the transport properties of a point contact under the influenceof a classical two-level fluctuator. We employ a transfer matrix formalismallowing us to calculate arbitrary correlation functions of the stochasticprocess by mapping them on matrix products. The result is used to obtain thegenerating function of the full counting statistics of a classical pointcontact subject to a classical fluctuator, including extensions to a pair oftwo-level fluctuators as well as to a quantum point contact. We show that thenoise in the quantum point contact is a sum of the (quantum) partitioning noiseand the (classical) noise due to the two-level fluctuator. As a side result, weobtain the full counting statistics of a quantum point contact withtime-dependent transmission probabilities.
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