Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check

Details Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check Normalization of Collisional Decoherence: Squaring the Delta Function, and an Independent Cross-Check

2006-07-17

arxiv.org/abs/quant-ph/0607109v3

J.Phys. A39 (2006) 14067-14074

Physics

Quantum Physics

Tex: 14 pages 7/30/06: revisions to introduction, and references added 9/29/06: further minor revisions and references added

Scientific paper

10.1088/0305-4470/39/45/015

We show that when the Hornberger--Sipe calculation of collisional decoherence is carried out with the squared delta function a delta of energy instead of a delta of the absolute value of momentum, following a method introduced by Di\'osi, the corrected formula for the decoherence rate is simply obtained. The results of Hornberger and Sipe and of Di\'osi are shown to be in agreement. As an independent cross-check, we calculate the mean squared coordinate diffusion of a hard sphere implied by the corrected decoherence master equation, and show that it agrees precisely with the same quantity as calculated by a classical Brownian motion analysis.

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