R A Fisher, design theory, and the Indian connection.

Design Theory, a branch of mathematics, was born out of the experimental statistics research of the population geneticist R A Fisher and of Indian mathematical statisticians in the 1930s. The field combines elements of combinatorics, finite projective geometries, Latin squares, and a variety of further mathematical structures, brought together in surprising ways. This essay will present these structures and ideas as well as how the field came together, in itself an interesting story.

Efimov states and their Fano resonances in a neutron-rich nucleus.

Asymmetric resonances in elastic n+19C scattering are attributed to Efimov states of such neutron-rich nuclei, that is, three-body bound states of the n+n+18C system when none of the pairs is bound or some of them are only weakly bound. By fitting to the general resonance shape described by Fano, we extract the resonance position, width, and the "Fano profile index." While Efimov states have been discussed extensively in many areas of physics, there is only one very recent experimental observation in trimers of cesium atoms. The conjunction that we present of the Efimov and Fano phenomena may lead to experimental realization in nuclei.

Embedding dissipation and decoherence in unitary evolution schemes.

Dissipation and decoherence, and the evolution from pure to mixed states in quantum physics, are handled through master equations for the density matrix. By embedding elements of this matrix in a higher-dimensional Liouville-Bloch equation, the methods of unitary integration are adapted to solve for the density matrix as a function of time, including the nonunitary effects of dissipation and decoherence. The input requires only solutions of classical, initial value time-dependent equations. Results are illustrated for a damped, driven two-level system.

Biological scaling and physics.

Kleiber's law in biology states that the specific metabolic rate (metabolic rate per unit mass) scales as M- 1/4 in terms of the mass M of the organism. A long-standing puzzle is the (- 1/4) power in place of the usual expectation of (- 1/3) based on the surface to volume ratio in three-dimensions. While recent papers by physicists have focused exclusively on geometry in attempting to explain the puzzle, we consider here a specific law of physics that governs fluid flow to show how the (- 1/4) power arises under certain conditions. More generally, such a line of approach that identifies a specific physical law as involved and then examines the implications of a power law may illuminate better the role of physics in biology.

Excitation and decay of correlated atomic States.

Doubly excited states of atoms and ions in which two electrons are excited from the ground configuration display strong radial and angular electron correlations. They are prototypical examples of quantum-mechanical systems with strong coupling. Two distinguishing characteristics of these states are: (i) their organization into successive families, with only weak coupling between families, and (ii) a hierarchical nature of this coupling, with states from one family decaying primarily to those in the next lower family. A view of the pair of electrons as a single entity, with the electron-electron repulsion between them divided into an adiabatic and a nonadiabatic piece, accounts for many of the dominant features. The stronger, adiabatic part determines the family structure and the weaker, nonadiabatic part the excitation and decay between successive families. Similar considerations extend to three-electron atomic states, which group into five different classes. They are suggestive of composite models for quarks in elementary particle physics, which exhibit analogous groupings into families with a hierarchical arrangement of masses and electroweak decays.