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Newton series expansion of bosonic operator functions

by Jürgen König, Alfred Hucht

Submission summary

As Contributors: Fred Hucht
Arxiv Link: https://arxiv.org/abs/2008.11139v1 (pdf)
Date submitted: 2020-08-26 11:56
Submitted by: Hucht, Fred
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Quantum Physics
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.

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Submission 2008.11139v1 on 26 August 2020

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