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.