Full Counting Statistics of Stationary Particle Beams

Details Full Counting Statistics of Stationary Particle Beams Full Counting Statistics of Stationary Particle Beams

2010-09-06

arxiv.org/abs/1009.1109v2

Physics

Quantum Physics

12 pages, 2 figures. This is an extended version of the previous submission

Scientific paper

We present a general scheme for treating particle beams as many particle systems. This includes the full counting statistics and the requirements of Bose/Fermi symmetry. In the stationary limit, i.e., for longer and longer beams, the total particle number diverges, and a description in Fock space is no longer possible. We therefore extend the formalism to include stationary beams. These beams exhibit a well-defined "local" counting statistics, by which we mean the full counting statistics of all clicks falling into any given finite interval. We treat in detail a model of a source, creating particles in a fixed state, which then evolve under the free time evolution, and we determine the resulting stationary beam in the far field. In comparison to the one-particle picture we obtain a correction due to Bose/Fermi statistics, which depends on the emission rate. We also consider plane waves as stationary many particle states, and determine the distribution of intervals between successive clicks in such a beam.

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