Full counting statistics of stationary particle beams

J. Kiukas, A. Ruschhaupt, R. F. Werner
2013 Journal of Mathematical Physics  
We present a general theoretical framework for treating particle beams as timestationary limits of many particle systems. Due to stationarity, the total particle number diverges, and a description in Fock space is no longer possible. Nevertheless, we show that when describing the particle detection via second quantized arrival time observables, such beams exhibit a well-defined "local" counting statistics, that is, full counting statistics of all clicks falling into any given finite time
more » ... finite time interval. We also treat in detail a realization of such a beam via the long time limit of a source creating particles in a fixed initial state from which they then evolve freely. From the mathematical point of view, the beam is described by a quasi-free state which, in the one-particle level, is locally trace class with respect to the operator valued measure describing the time observable; this ensures the existence of a Fredholm determinant defining the characteristic function of the counting statistics. C 2013 AIP Publishing LLC. [http://dx.This is again Poisson, and depends only on the integral σ = μ(dt)σ (t). The corresponding state on full Fock space is N 042109-11 Kiukas, Ruschhaupt, and Werner J. Math. Phys. 54, 042109 (2013) statistics. In quantitative terms, the operator norm σ ∞ (the largest eigenvalue) measures well the maximal effect of statistics, in some sense the maximal phase space density:
doi:10.1063/1.4801780 fatcat:rt2gp3y4ynfuvefgy4o6hsx5fa