Yoichiro Nambu and the Concept of Apparent Vacuum: A Stepping Stone to Spontaneous Symmetry Breaking

The processes of discovery and concept formation are as mysterious as they are intriguing. In this article, they give a sketch of Yoichiro Nambu's long path toward the concept of spontaneous symmetry breaking focusing on the pivotal role played by his notion of “apparent vacuum”. This is instrumental to draw the original analogical correspondence between the vacuum of quantum field theory and solid matter, which, transforming over time in its use and purpose, enables Nambu to arrive at the concept of spontaneous symmetry breaking. From this historical episode they draw a methodological lesson and emphasise the broad cultural influences that conditioned the conceptual development.     

On the determination of the average molecular weight,radius of gyration,and mass/length ratio of polydisperse solutions of polymerizing rod‐like macromolecular monomers by multi‐angle static light scattering

The angular dependence of the light scattered from polydisperse solutions of rod‐like or worm‐like linear polymers formed by the polymerization of rod‐like macromolecular monomers was studied with the aid of computer simulations. Except at very low conversion degrees, these ensembles are characterized by curved Zimm‐like plots. An appraisal of the use of polynomial fittings for the derivation of the weight‐average molecular weight (M_w) and of the z‐average square radius of gyration (<R_g²>_z) from such plots is presented and discussed. Depending on the average size and shape distribution, the use of polynomial fittings allows the applicability of the Zimm method well beyond the standard condition q²<R_g²>_z<<1, q being the scattering wavevector. In addition, the derivation of the w/z‐average mass/length ratio M_L of the polymers from only partially linear Casassa plots, from which large errors in the derived M_L values can be made, is analyzed. By combining the Casassa method with the complementary Holtzer plots, it is usually possible to assess the reliability of the results and give an estimate of their accuracy. However, it was also found that apparently linear Casassa plots, allowing a good estimate of the M_L value, may arise in particular situations even when the Holtzer plot would indicate otherwise.