A Cox Process Involved in the Bose–Einstein Condensation |
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Authors: | Nathalie Eisenbaum |
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Institution: | (1) Laboratoire de probabilités et modéles aléatoires, UMR 7599 – CNRS, Universités Paris 6 et 7, 4, Place Jussieu, Case 188, F-75252 Paris Cedex 05, France |
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Abstract: | The point process corresponding to the configurations of bosons in standard conditions is a Cox process driven by the square
norm of a centered Gaussian process. This point process is infinitely divisible. We point out the fact that this property
is preserved by the Bose–Einstein condensation phenomenon and show that the obtained point process after such a condensation
occured, is still a Cox process but driven by the square norm of a shifted Gaussian process, the shift depending on the density
of the particles. This law provides an illustration of a “super”- Isomorphism Theorem existing above the usual Isomorphism
Theorem of Dynkin available for Gaussian processes.
Submitted: February 8, 2008. Accepted: March 5, 2008. |
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Keywords: | |
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