Full Counting Statistics of Stationary Particle Beams

TL;DR

This paper develops a formalism for analyzing stationary particle beams, including full counting statistics and quantum symmetries, and applies it to models of particle sources and plane waves, revealing quantum statistical effects.

Contribution

It extends counting statistics to stationary beams, incorporating Bose/Fermi symmetry and addressing the divergence in particle number in the infinite-beam limit.

Findings

Stationary beams have well-defined local counting statistics.

Quantum statistics cause corrections depending on emission rate.

Distribution of intervals between clicks is characterized for plane waves.

Abstract

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.