The Love of His Life

The solid state physics community is electrified when Bardeen, Cooper, and Schrieffer (BCS) announce their discovery of a microscopic model capable of explaining the phenomenon of superconductivity,which is observed in some metals at very low temperature. To understand Anderson’s contributions to this subject, this chapter begins with the phenomenology of superconductivity and then sketches a few key aspects of many-electron theory, including the concepts of collective excitations and quasiparticles. Anderson explains the apparent lack of gauge invariance of the BCS approach and then uses a sophisticated approximation to study the excited states of a superconductor. He travels to Russia where his theory gains the approval of Lev Landau and he demonstrates how to analyze so-called dirty superconductors. He collaborates indirectly with Robert Schrieffer to generalize the BCS model into a full-blown theory capable of describing any material where the electron-phonon interaction drives superconductivity.

Ratios of negative-to-positive parity level densities in Mo isotopes

The ratios of negative-to-positive parity level densities in ^94,96,98Mo isotopes are calculated using a microscopic formalism based on the BCS model. In this calculation, the single-particle energies are obtained with the Nilsson model. Mass number, shell and deformation effects on the parity equilibration phenomena in these isotopes are discussed in this work.

Biomimetic Artificial Membrane Permeability Assay over Franz Cell Apparatus Using BCS Model Drugs

A major parameter controlling the extent and rate of oral drug absorption is permeability through the lipid bilayer of intestinal epithelial cells. Here, a biomimetic artificial membrane permeability assay (Franz–PAMPA Pampa) was validated using a Franz cells apparatus. Both high and low permeability drugs (metoprolol and mannitol, respectively) were used as external standards. Biomimetic properties of Franz–PAMPA were also characterized by electron paramagnetic resonance spectroscopy (EPR). Moreover, the permeation profile for eight Biopharmaceutic Classification System (BCS) model drugs cited in the FDA guidance and another six drugs (acyclovir, cimetidine, diclofenac, ibuprofen, piroxicam, and trimethoprim) were measured across Franz–PAMPA. Apparent permeability (Papp) Franz–PAMPA values were correlated with fraction of dose absorbed in humans (Fa%) from the literature. Papp in Caco-2 cells and Corti artificial membrane were likewise compared to Fa% to assess Franz–PAMPA performance. Mannitol and metoprolol Papp values across Franz–PAMPA were lower (3.20 × 10−7 and 1.61 × 10−5 cm/s, respectively) than those obtained across non-impregnated membrane (2.27 × 10−5 and 2.55 × 10−5 cm/s, respectively), confirming lipidic barrier resistivity. Performance of the Franz cell permeation apparatus using an artificial membrane showed acceptable log-linear correlation (R2 = 0.664) with Fa%, as seen for Papp in Caco-2 cells (R2 = 0.805). Data support the validation of the Franz–PAMPA method for use during the drug discovery process.

Quantitative and qualitative centrality of a social representation's core elements: The use of the Basic Cognitive Schemes model

The general aim of this research was to investigate the use of the Basic Cognitive Schemes (BCS) model in examining the qualitative vs. quantitative centrality of a social representation’s (SR) core elements. Firstly, we examined the internal structure of the social representation of the European integration (Study 1, N = 71) according to Central Core Theory of the structural approach of social representations. Secondly, we investigated the qualitative vs. quantitative centrality of its core elements (Study 2, N = 106) using the BCS model. The study included young people from Eastern Romania enrolled in a Psychology undergraduate degree. The results permitted the identification of the elements defining the internal structure of the SR of the European integration among young Romanians. We identified five central elements with prescriptive functions (i.e., mobility, unity, opportunity, European funds, and civilization). Furthermore, after checking their qualitative and quantitative centrality using the BCS model, only three of them were confirmed as both qualitatively and quantitatively central. Thus, the results also underlined the importance of the BSC model in better understanding the relationships between the SR’s internal elements. Theoretical and practical implications of the results are discussed.

Ground-state energy of a Richardson-Gaudin integrable BCS model

We investigate the ground-state energy of a Richardson-Gaudin integrable BCS model, generalizing the closed and open p+ip models. The Hamiltonian supports a family of mutually commuting conserved operators satisfying quadratic relations. From the eigenvalues of the conserved operators we derive, in the continuum limit, an integral equation for which a solution corresponding to the ground state is established. The energy expression from this solution agrees with the BCS mean-field result.

Multi-Band Superconductivity and the Steep Band/Flat Band Scenario

The basic features of multi-band superconductivity and its implications are derived. In particular, it is shown that enhancements of the superconducting transition temperature take place due to interband interactions. In addition, isotope effects differ substantially from the typical BCS scheme as soon as polaronic coupling effects are present. Special cases of the model are polaronic coupling in one band as realized e.g., in cuprates, coexistence of a flat band and a steep band like in MgB2, crossovers between extreme cases. The advantages of the multiband approach as compared to the single band BCS model are elucidated and its rather frequent realization in actual systems discussed.