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Erratum to “Fractional exclusion statistics in general systems of interacting particles” [Phys. Lett. A 372 (2008) 5745]
Physics Letters A 376 (2012) 892
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Physics Letters A www.elsevier.com/locate/pla
Erratum
Erratum to “Fractional exclusion statistics in general systems of interacting particles” [Phys. Lett. A 372 (2008) 5745] Dragos-Victor ¸ Anghel Horia Hulubei National Institute of Physics and Nuclear Engineering, 30 Reactorului Street, P.O. Box MG-6, RO-077125, M˘agurele, Jud. Ilfov, Romania
a r t i c l e
i n f o
Article history: Received 19 December 2011 Accepted 21 December 2011 Available online 28 December 2011 Communicated by C.R. Doering
A mistake appeared in Eqs. (15) and (16) of Ref. [1]. This is only a technical detail and it does not affect any of the conclusions of the Letter. In what follows I shall use the notation R1 for Ref. [1] and (nR1) for the equation number n of R1. The first line of Eq. (15R1) reads
δ G (˜ M −1 , ˜ M ) = σ (M )δ M − σ (M −1 )δ M −1 ,
(1)
where by δ M I denoted δ (˜ M , ˜ i ), of Eq. (14R1). By writing σ (M −1 ) = σ (M )−[dσ (M )/dM ](M − M −1 ) and δ M −1 = δ M − [d(δ M )/d M ]( M − M −1 ) and keeping only the terms which are linear in M − M −1 , I obtain
δ G (˜ M −1 , ˜ M ) ≈
δ M + σ (M ) d(δ M ) (M − M −1 ) d M d M
dσ ( )
DOI of original article: 10.1016/j.physleta.2008.07.044. E-mail address: [email protected]. 0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.12.038
(2a)
≡
d d M
σ (M )δ M (M − M −1 ).
(2b)
The difference between Eq. (2a) and Eq. (15R1) is the second term in the brackets of Eq. (2a). This was mistakenly omitted, by considering it much smaller than the first term. This mistake propagates also in Eq. (16R1) where one should write instead
α˜ M ˜i = (M − M −1 )
d d M
σ (M )[ V (M , i ) + f (˜ M , ˜i )] , ∂ V (M , ) 1+ 0M σ ( )n( ) d ∂ M
(3)
i.e., include the term δ M of (14R1) under the derivative. All the conclusions and comments remain the same as in R1, with the only exception that δ G (˜ M −1 , ˜ M ) and therefore α˜ M ˜i may be different from zero even if dσ ( M )/d M = 0. References [1] D.V. Anghel, Phys. Lett. A 372 (2008) 5745, arXiv:0710.0728.
Contents lists available at SciVerse ScienceDirect
Physics Letters A www.elsevier.com/locate/pla
Erratum
Erratum to “Fractional exclusion statistics in general systems of interacting particles” [Phys. Lett. A 372 (2008) 5745] Dragos-Victor ¸ Anghel Horia Hulubei National Institute of Physics and Nuclear Engineering, 30 Reactorului Street, P.O. Box MG-6, RO-077125, M˘agurele, Jud. Ilfov, Romania
a r t i c l e
i n f o
Article history: Received 19 December 2011 Accepted 21 December 2011 Available online 28 December 2011 Communicated by C.R. Doering
A mistake appeared in Eqs. (15) and (16) of Ref. [1]. This is only a technical detail and it does not affect any of the conclusions of the Letter. In what follows I shall use the notation R1 for Ref. [1] and (nR1) for the equation number n of R1. The first line of Eq. (15R1) reads
δ G (˜ M −1 , ˜ M ) = σ (M )δ M − σ (M −1 )δ M −1 ,
(1)
where by δ M I denoted δ (˜ M , ˜ i ), of Eq. (14R1). By writing σ (M −1 ) = σ (M )−[dσ (M )/dM ](M − M −1 ) and δ M −1 = δ M − [d(δ M )/d M ]( M − M −1 ) and keeping only the terms which are linear in M − M −1 , I obtain
δ G (˜ M −1 , ˜ M ) ≈
δ M + σ (M ) d(δ M ) (M − M −1 ) d M d M
dσ ( )
DOI of original article: 10.1016/j.physleta.2008.07.044. E-mail address: [email protected]. 0375-9601/$ – see front matter © 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.physleta.2011.12.038
(2a)
≡
d d M
σ (M )δ M (M − M −1 ).
(2b)
The difference between Eq. (2a) and Eq. (15R1) is the second term in the brackets of Eq. (2a). This was mistakenly omitted, by considering it much smaller than the first term. This mistake propagates also in Eq. (16R1) where one should write instead
α˜ M ˜i = (M − M −1 )
d d M
σ (M )[ V (M , i ) + f (˜ M , ˜i )] , ∂ V (M , ) 1+ 0M σ ( )n( ) d ∂ M
(3)
i.e., include the term δ M of (14R1) under the derivative. All the conclusions and comments remain the same as in R1, with the only exception that δ G (˜ M −1 , ˜ M ) and therefore α˜ M ˜i may be different from zero even if dσ ( M )/d M = 0. References [1] D.V. Anghel, Phys. Lett. A 372 (2008) 5745, arXiv:0710.0728.