Quantum transport and counting statistics in closed systems

A current can be induced in a closed device by changing control parameters. The amount Q of particles that are transported via a path of motion is characterized by its expectation value 〈 Q 〉, and by its variance Var (Q). We show that quantum mechanics invalidates some common conceptions about this statistics. We first consider the process of a double path crossing, which is the prototype example for counting statistics in multiple path non-trivial geometry. We find out that contrary to the common expectation, this process does not lead to partition noise. Then we analyze a full stirring cycle that consists of a sequence of two Landau-Zener crossings. We find out that quite generally counting statistics and occupation statistics become unrelated, and that quantum interference affects them in different ways.