Cambridge University Press, Cambridge, 1995, p 255]) emphasize that in the limits of the models studied both at T ϭ 0 and T 0, the "cross-over" from a BCS-type to a BEC-type superconductor is continuous. The BCS and BEC "end points" seem to be well-established. However, in the intermediate region-home to fulleride and high temperature superconductors-considerable extrapolation of the models must be done as there still is no exact theory. Yet, considerable current literature is devoted to what appears to be more "singular-type phenomena" such as quantum critical points, "stripe" formation, insulator to superconductor phase transitions, loss of validity of the Fermi liquid theory, etc. Using a connection we have made with "cold" atom fermion-boson crossover theory [Chen, Stajic, Levin, 2005, e-print cond-mat/0508603], we can establish that the resonance previously discussed [Squire and March, Int J Quant Chem, 2006, 106, 3343] is a result of the crossing of the fermion band by the boson band. While the ground state appears to remain continuous, the paired energy gap becomes transformed. We discuss features of the resonance and the experimentally observed pre-formed "BEC Cooper pair" formation, essential to the boson-fermion resonance theory. In addition some of the various singular phenomena discussed above can be put more into perspective. Finally, in both limits the relation of characteristic lengths to the inverse Fermi momentum is strongly emphasized, as is the role of the chemical potential near the pseudogap regime.

ABSTRACT:After a brief discussion of the four classes of superconducting materials, attention is focused on the fullerides. More critically, motivated by the work of Herzberg and Longuet-Higgins (HLH), especially in the context of the Berry phase, and the topological superconducting model of Wiegmann we propose a microscopic model of C 60 superconductivity. One key is the relationship of the HLH phase sign change of the wave function circling a degeneracy. The sign change is related to a topological quantity, a Chern number, which is a requirement specified for a topological superconductor, following Weigmann. Thus, it seems vibrational modes are topologically and coherently coupled to the electronic wave function. We establish a microscopic basis for topological superconductivity using Weigmann's generalization of Frö hlich's 1-D model to two dimensions. This necessarily invokes the nonlinear sigma model and the addition of topological terms. We then reinterpret the work of Auerbach et al. and O'Brien by suggesting that vibrational analysis of C 60 with Jahn-Teller distortions that produce a collective mode(s) that could be described by a soliton or, equivalently, a skyrmion model. The soliton (skyrmion) statistics are such that both fermions and bosons result depending on the number of electrons, n. Superconductivity is predicted for n ϭ 3, and possibly 5 electrons, and n ϭ 2 and 4 should be insulators. The strong coupling theory developed seems appropriate for describing a molecular superconductor.

ABSTRACT:We propose a microscopic mechanism for superconductivity in an alkali-metal doped fulleride. Support is given for the notion that a fulleride doped with two electrons exhibits Wigner-like correlations. Doping a third electron into this system leads to a transition to superconductivity. The present work has expanded interactions to include not only Wigner-like correlations between electrons, but also phonons and plasmons. The strength and influence of the numerous interactions are discussed. In the latter context, a "Marel plot" is briefly considered along with electron energy loss measurements. Lastly, we propose that a "soft" electron-pair quasi-particle is involved in pairing.

The manuscript defines and discusses the products of a successful cyber‐physical system in the chemical industry using two examples. The first is the ability to make the correct decision quickly regarding an unforecasted large sale of a product. The second is the automatic availability of critically needed information, accessible anywhere in the world which provides endless possibilities for the chemical industry. Concerns and some resolutions are also discussed. © 2014 American Institute of Chemical Engineers Process Saf Prog 33: 329–332, 2014