Improved recursive computation of clebsch-Gordan coefficients

Xu, Guanglang

doi:10.1016/j.jqsrt.2020.107210

Cited by 3 publications

(3 citation statements)

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“…these matrices always exhibit a sparsity higher than 95% and are thus very efficient to store. Moreover, since iterative methods exist to compute the Clebsch-Gordan coefficients [48], they are also calculated extremely fast, which also entails that the coefficients (39) are rapidly determined, resulting in very quick simulations. Furthermore, the interactions ( 36) and ( 37) remain consistent across numerical experiments involving different devices, with the only difference being their respective far-field expansion coefficients (e r , m r ) and (e t , m t ), required to compute (39).…”

Section: Theorymentioning

confidence: 99%

Efficient Modeling of On-Body Passive UHF RFID Systems in the Radiative Near-Field

Felaco

Kapusuz

Rogier

et al. 2022

IEEE Trans. Antennas Propagat.

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A novel method is presented to accurately determine the operational range of an on-body, passive ultra-high-frequency (UHF) radio-frequency identification (RFID) system operating in the radiative near-field, based on its far-field radiation patterns. To this end, an efficient algorithm based on 3-D multipole expansion of the electromagnetic fields is formulated. By combining the new operator with the simulated or measured standalone far-field radiation patterns of the on-body RFID system, a comprehensive and accurate range determination is obtained. Compared with commercial software tools and measurements, we prove the accuracy and improved speed of the novel technique.

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Section: Theorymentioning

confidence: 99%

Efficient Modeling of On-Body Passive UHF RFID Systems in the Radiative Near-Field

Felaco

Kapusuz

Rogier

et al. 2022

IEEE Trans. Antennas Propagat.

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“…The reason is that we might well have several fundamental solutions. For instance, if D=10 and N =9, then we have the fundamental solutions (7, 2), (13,4) and (57,18). Golomb [89] defined a powerful number to be a positive integer r such that p 2 divides r whatever the prime p divides r, and discussed consecutive pairs of powerful numbers which fall into one of two categories; type 1: pairs of consecutive powerful numbers one of which is a perfect square, and type 2: pairs of consecutive numbers neither of which is a perfect square.…”

Section: Pell Diophantine Equation and Powerful Numbersmentioning

confidence: 99%

“…Ritchie's method [15,16] is particularly well suited to calculating lists of Clebsch-Gordan coefficients "on-the-fly" for different magnetic quantum numbers being projections of the same angular momentum, thus avoiding the need for large or complex in-memory storage schemes. Very recently, Xu proposed an improved recursive computation of Clebsch-Gordan coefficients [18]; the method separates the recursion process into sign-recursion and exponentrecursion. The Clebsch-Gordan values can be obtained after the computation of their signs and exponents.…”

Section: Introductionmentioning

confidence: 99%

Some properties of Wigner 3j coefficients: non-trivial zeros and connections to hypergeometric functions

Pain

2020

Eur. Phys. J. A

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The contribution of Jacques Raynal to angular-momentum theory is highly valuable. In the present article, I intend to recall the main aspects of his work related to Wigner 3j symbols. It is well known that the latter can be expressed with a hypergeometric series. The polynomial zeros of the 3j coefficients were initially characterized by the number of terms of the series minus one, which is the degree of the coefficient. A detailed study of the zeros of the 3j coefficient with respect to the degree n for J = a + b + c ≤ 240 (a, b and c being the angular momenta in the first line of the 3j symbol) by Raynal revealed that most zeros of high degree had small magnetic quantum numbers. This led him to define the order m to improve the classification of the zeros of the 3j coefficient. Raynal did a search for the polynomial zeros of degree 1 to 7 and found that the number of zeros of degree 1 and 2 are infinite, though the number of zeros of degree larger than 3 decreases very quickly as the degree increases. Based on Whipple's symmetries of hypergeometric 3F2 functions with unit argument, Raynal generalized the Wigner 3j symbols to any arguments and pointed out that there are twelve sets of ten formulas (twelve sets of 120 generalized 3j symbols) which are equivalent in the usual case. In this paper, we also discuss other aspects of the zeros of 3j coefficients, such as the role of Diophantine equations and powerful numbers, or the alternative approach involving Labarthe patterns.

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