Full counting statistics of a general quantum mechanical variable

We present a quantum mechanical framework for defining the statistics of measurements of integral dt (A) over cap (t), A(t) being a quantum mechanical variable. This is a generalization of the so-called full counting statistics proposed earlier for DC electric currents. We develop an influence functional formalism that allows us to study the quantum system along with the measuring device while fully accounting for the back action of the detector on the system to be measured. We define the full counting statistics of an arbitrary variable by means of an evolution operator that relates the initial and final density matrices of the measuring device. In this way we are able to resolve inconsistencies that occur in earlier definitions. We suggest two schemes to observe the so defined statistics experimentally.