Reverse engineering in many-body quantum physics: Correspondence between many-body systems and effective single-particle equations

The mapping, exact or approximate, of a many-body problem onto an effective single-body problem is one of the most widely used conceptual and computational tools of physics. Here, we propose and investigate the inverse map of effective approximate single-particle equations onto the corresponding many-particle system. This approach allows us to understand which interacting system a given single-particle approximation is actually describing, and how far this is from the original physical many-body system. We illustrate the resulting reverse engineering process by means of the Kohn-Sham equations of density-functional theory. In this application, our procedure sheds light on the nonlocality of the density-potential mapping of density-functional theory, and on the self-interaction error inherent in approximate density functionals.

Morphological and morphometric appraisal of the spermatophore of the southern hermit crab Isocheles sawayai Forest and Saint Laurent, 1968 (Anomura: Diogenidae), with comments on gonopores in both sexes

The spermatophore morphology of the hermit crab Isocheles sawayai from Southwestern Atlantic (Brazil) is described. The spermatophores show similarities with those described for other members of the family Diogenidae, especially with the recently described Loxopagurus loxochelis. The spermatophore is composed of three major regions: a sperm filled head or ampulla, a columnar stalk and a foot or pedestal. The spermatophores show specific morphology in having a circular ampulla, and a constriction or neck between the ampulla (100 mu m) and the thin (27 mu m), long stalk (500 mu m). The stalk penetrates less than half way into the spermatophore head. Most spermatophores show one or the small posterior projections on the underside of the ampulla as being bigger than the other, making it asymmetrical. The size of the spermatophore is related to hermit crab size with direct relationships found between spermatophore ampulla width, total length, and peduncle length with shield length of the hermit crab. The morphological characteristics of the spermatophore of L sawayai. are species-specific distinguishing it from other members of the family, and are useful to infer further phylogenetic relationships. (C) 2008 Elsevier GmbH. All rights reserved.