Abstract
A theory of electron-counting processes is formulated in terms of the Liouville space method. The developed model is based on the quantum Markov processes developed by Davies and Srinivas. The time evolution of an electron system interacting with an electron counter and the counting probability distribution are investigated. The average value, fluctuation, and correlation function of the electron number registered by the counter are calculated, and the sub-Poissonian distribution and antibunching correlation of the electrons are obtained for an arbitrary noncorrelated initial state of electrons. For a correlated initial state, depending on the initial correlation among the electrons and on the electron counters used in the measurement, the statistics for the electron number registered by the counter is characterized as a sub-Poissonian, Poissonian, or super-Poissonian distribution, and the intensity correlation function exhibits antibunching or bunching correlation. As an example, the state with correlation between the up-spin and down-spin electrons is considered. The electron counting processes under the influence of a chaotic electron source are also considered, and the effect of the chaotic electron source on the counting statistics is investigated.
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