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Newton series expansion of bosonic operator functions
by Jürgen König, Alfred Hucht
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Submission summary
Authors (as registered SciPost users): | Alfred Hucht · Jürgen König |
Submission information | |
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Preprint Link: | https://arxiv.org/abs/2008.11139v1 (pdf) |
Date submitted: | Aug. 26, 2020, 11:56 a.m. |
Submitted by: | Hucht, Alfred |
Submitted to: | SciPost Physics |
Ontological classification | |
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Academic field: | Physics |
Specialties: |
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Approach: | Theoretical |
Abstract
We show how series expansions of functions of bosonic number operators are naturally derived from finite-difference calculus. The scheme employs Newton series rather than Taylor series known from differential calculus, and also works in cases where the Taylor expansion fails. For a function of number operators, such an expansion is automatically normal ordered. Applied to the Holstein-Primakoff representation of spins, the scheme yields an exact series expansion with a finite number of terms. As a second example, we show that factorial moments and factorial cumulants arising in the context of photon or electron counting are a natural consequence of Newton series expansions.
Current status:
Reports on this Submission
Report #3 by Anonymous (Referee 3) on 2020-10-7 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2008.11139v1, delivered 2020-10-07, doi: 10.21468/SciPost.Report.2057
Strengths
There is also a nice discussion of the application of the method to photon statistics, with an emphasis on the value of the “factorial moments” over the more conventional raw (or ordinary) moments.
Weaknesses
Report
I believe the acceptance criteria have been met.
Report #2 by Anonymous (Referee 2) on 2020-9-24 (Invited Report)
- Cite as: Anonymous, Report on arXiv:2008.11139v1, delivered 2020-09-24, doi: 10.21468/SciPost.Report.2021
Strengths
Weaknesses
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Requested changes
A minor suggestion would be not to use abbreviations such as "w.l.o.g.", which might not be known to all readers.
Report #1 by Dirk Schuricht (Referee 1) on 2020-9-16 (Contributed Report)
- Cite as: Dirk Schuricht, Report on arXiv:2008.11139v1, delivered 2020-09-16, doi: 10.21468/SciPost.Report.1997
Report
In my view, the article can be seen as a neat little note pointing out a fairly simple yet usually unknown mathematical method which can be applied in quantum mechanics to simplify and clarify operator-valued functions. As such I find the ideas of the note worthwhile publishing (maybe in SciPost Physics Core). However, I would appreciate some additions or remarks on further applications or generalisations, eg, on the applicability of the approach to operators that do not possess a spectrum of equally spaced real values, fermionic system, or systems with several degrees of freedom.
As a minor remark, I think the notation in (2) is somewhat imprecise regarding to which part of the expression the derivative is applied.