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Characterization of Classical and Quantum Poisson Systems by Thinnings and Splittings
Author(s) -
Fichtner Karl–Heinz,
Freudenberg Wolfgang,
Liebscher Volkmar
Publication year - 2000
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/1522-2616(200010)218:1<25::aid-mana25>3.0.co;2-y
Subject(s) - poisson distribution , cox process , point process , mathematics , statistical physics , independence (probability theory) , quantum , characterization (materials science) , gaussian , gaussian process , poisson point process , thinning , quantum mechanics , mathematical analysis , physics , poisson process , statistics , optics , ecology , biology
There exist several well–known characterizations of Poisson and mixed Poisson point processes (Cox processes) by thinning and splitting procedures. So a point process is necessarily a Cox process if for arbitrary small thinning parameter it can be obtained by a thinning of some other point process [30]. Poisson processes are characterized by the independence of the two random subconfigurations obtained by an independent splitting of the configuration into two parts [11]. For quantum mechanical particle systems beam splittings which are well–known in quantum optics provide analogous procedures. It is shown that coherent states respectively mixtures of them can be characterized in the same way as Poisson processes and Cox processes. Moreover, for the position distributions of these states which are “classical” point processes just the above mentioned characterizations are obtained. As example of mixed coherent states we consider Gaussian states which arise as equilibrium states of ideal Bose gases.