TY - JOUR

T1 - Full counting statistics of stationary particle beams

AU - Kiukas, J.

AU - Ruschhaupt, A.

AU - Werner, R. F.

N1 - Funding Information:
The authors acknowledge support by the BMBF (Ephquam project), the EU project CORNER, and the Academy of Finland.
Copyright:
Copyright 2013 Elsevier B.V., All rights reserved.

PY - 2013/4/23

Y1 - 2013/4/23

N2 - We present a general theoretical framework for treating particle beams as time-stationary 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 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.

AB - We present a general theoretical framework for treating particle beams as time-stationary 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 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.

UR - http://www.scopus.com/inward/record.url?scp=84877685701&partnerID=8YFLogxK

U2 - 10.1063/1.4801780

DO - 10.1063/1.4801780

M3 - Article

AN - SCOPUS:84877685701

SN - 0022-2488

VL - 54

JO - Journal of Mathematical Physics

JF - Journal of Mathematical Physics

IS - 4

M1 - 042109

ER -