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arXiv:1009.5345 · Physical Review A

Reply to “Comment on ‘Quantum linear Boltzmann equation with finite intercollision time’ ”

Lajos Diósi

Published Sep 27, 2010• 1 citation
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Abstract

Hornberger and Vacchini [Phys. Rev. A 82, 036101 (2010)] claim that the specific collisional momentum decoherence, pointed out in my recent work [Phys. Rev. A 80, 064104 (2009)], is already described by their theory. However, I have performed a calculation whereby I disprove the authors' claim and refute their conclusion that my recent work had no advantage over theirs.

DOI
10.1103/physreva.82.036102

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Comment on “Quantum linear Boltzmann equation with finite intercollision time”

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Inconsistencies are pointed out in a recent proposal [L.Diósi, Phys. Rev. A 80, 064104 (2009)] for a quantum version of the classical linear Boltzmann equation.

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Vacchini Replies:

Bassano Vacchini

This is the reply to a Comment by R. F. O'Connell (Phys. Rev. Lett. 87 (2001) 028901) on a paper written by the author (B. Vacchini, ``Completely positive quantum dissipation'', Phys.Rev.Lett. 84 (2000) 1374, arXiv:quant-ph/0002094).

arXiv:quant-ph/0107046•Physical Review Letters•Jun 20, 2001•16 citations
Hornberger and Vacchini [Phys. Rev. A 82, 036101 (2010)] claim that the specific collisional momentum decoherence, pointed out in my recent work [Phys. Rev. A 80, 064104 (2009)], is already described by their theory. However, I have performed a calculation whereby I disprove the authors' claim and refute their conclusion that my recent work had no advantage over theirs.
A reexamination of the results of my earlier paper [Phys. Rev. E 50, 3116 (1994)] is supplied using entirely straightforward methods, i.e., without appealing to operator formalism. This reexamination confirms the consistency of the work in that paper by extracting a term proportional to time that Dembrinski et al. [Phys. Rev. E 53, 4243 (1996)] claim is not present. The arguments of Dembinski et al. are not refuted, but it is pointed out that they are based upon methods within which one readily encounters paradoxes such [p${\mathrm{^}}^{2}$,p^]\ensuremath{\ne}0 and [x^,p^]\ensuremath{\ne}i^. The present exposition avoids such methods. Unfortunately I am not prepared to address their numerical results. This will have to await further investigation. However, an example of numerical results of my own is presented in order to illustrate the richness of the dynamics of the model. \textcopyright{} 1996 The American Physical Society.