Rejection of the Light Quantum: The Dark Side of Niels Bohr

Evidence is recalled of the strong opposition of Niels Bohr, at the time of the Old Quantum Theory 1.913-25, to the Lichtquanten hypothesis of Einstein. Some episodes with H.A. Kramers, J.C. Slater and W. Heisenberg are recollected; Bohr's changing point of view is traced back to some philosophical antecedents and to his endeavour to deduce quantum results from the Correspondence Principle. Some consequences for the future interpretation of Quantum Mechanics, specially to the Complementarity Principle, are considered.Comment: 15 page

Relation of the cyclotomic equation with the harmonic and derived series

We associate some (old) convergent series related to definite integrals with the cyclotomic equation $x^m-1= 0$, for several natural numbers $m$; for example, for $m = 3$, $x^3-1 = (x-1)(1+x+x^2)$, leads to $\int_0^1dx\frac{1}{(1+x+x^2)} = \frac{\pi}{(3\sqrt{3})} = (1-\frac{1}{2}) + (\frac{1}{4}-\frac{1}{5}) + (\frac{1}{7}-\frac{1}{8}) + \ldots$ . In some cases, we express the results in terms of the Dirichlet characters. Generalizations for arbitrary $m$ are well defined, but do imply integrals and/or series summations rather involved.Comment: This paper has been accepted in The Scientific World Journal, and will appear in brie

Introduction to Sporadic Groups for physicists

We describe the collection of finite simple groups, with a view on physical applications. We recall first the prime cyclic groups $Z_p$, and the alternating groups $Alt_{n>4}$. After a quick revision of finite fields $\mathbb{F}_q$, $q = p^f$, with $p$ prime, we consider the 16 families of finite simple groups of Lie type. There are also 26 \emph{extra} "sporadic" groups, which gather in three interconnected "generations" (with 5+7+8 groups) plus the Pariah groups (6). We point out a couple of physical applications, including constructing the biggest sporadic group, the "Monster" group, with close to $10^{54}$ elements from arguments of physics, and also the relation of some Mathieu groups with compactification in string and M-theory.Comment: This paper is published in: Journal of Physics A, (vol.) 46, (2013), as Topical Revie

V2X Meets NOMA: Non-Orthogonal Multiple Access for 5G Enabled Vehicular Networks

Benefited from the widely deployed infrastructure, the LTE network has recently been considered as a promising candidate to support the vehicle-to-everything (V2X) services. However, with a massive number of devices accessing the V2X network in the future, the conventional OFDM-based LTE network faces the congestion issues due to its low efficiency of orthogonal access, resulting in significant access delay and posing a great challenge especially to safety-critical applications. The non-orthogonal multiple access (NOMA) technique has been well recognized as an effective solution for the future 5G cellular networks to provide broadband communications and massive connectivity. In this article, we investigate the applicability of NOMA in supporting cellular V2X services to achieve low latency and high reliability. Starting with a basic V2X unicast system, a novel NOMA-based scheme is proposed to tackle the technical hurdles in designing high spectral efficient scheduling and resource allocation schemes in the ultra dense topology. We then extend it to a more general V2X broadcasting system. Other NOMA-based extended V2X applications and some open issues are also discussed.Comment: Accepted by IEEE Wireless Communications Magazin