Colloquium Fall 1998
The standard theory of metals, and of the Fermi surface instabilities that produce low temperture ordered states in metals (of which BCS theory is the most notable and successful example) are all based on the idea that the electron kinetic energy dominates the physics, and that interaction effects can be treated as an afterthought. The normal state is thus, essentially, the ground-state of the kinetic energy, and the instabilities are "potential" driven. In highly correlated materials, and especially in doped antiferromagnets (or more generally, doped Mott insulators) the short-range piece of the electron-electron repulsion is the dominant energy, which means that the kinentic energy is strongly frustrated so the normal state is not a Fermi liquid, and any order that develops on cooling tends to be "kinetic energy driven." From this viewpoint, the various transitions and crossovers that have been observed in the most studied example of a doped antiferromagnet, the high temperature superconductors, can be understood as successive levels of self-organization whereby the zero-point kinetic energy is minimized: a) Local and global charge "stripe" order is a manifestation of Coulomb frustrated kinetic phase separation, whereby locally metallic regions are created in the insulating matrix. b) Pseudo-gap formation, which plays the role of superconducting pairing in conventional superconductors, is driven virtual tunnelling of pairs from the metallic stripe regions into their immediate environement, a mechanism which we have named "the spin-gap proximity effect". c) Superconducting long-range order is triggered by phase ordering, whereby the superconducting pairs delocalize between stripes.
Granular materials can exhibit a static, solid-like character because thermal energies are not sufficient to move grains around one another. Granular materials can also exhibit a liquid-like character in which they flow and deform smoothly when acted on by large external forces. A central questions in understanding such flows, then, is the fate of the energy supplied by the driving forces. Rather than shake or tilt a sandpile, we have thus created two dynamical systems in which energy is supplied continuously and homogeneously throughout the medium at a known rate. The first consists of a rectangular hopper, or hourglass, with uniform cross section , while the second is a gas-fluidized bed in which motion is excited by an upward flow of gas . In both cases we probe the resulting grain dynamics via diffusing-wave spectroscopy (DWS). We find that grains fly ballistically between collisions with the typical mean free times and paths being far too short to be measured by conventional imaging techniques: 10-5 s and 10 nm, respectively, for 0.1 mm diameter grains. Though surprising, these scales are in rough accord with energy conservation, showing that random collisions (the so-called ``granular temperature'') rather than kinetic friction, can dominate the dissipation even in slow dense flows. This phenomenon is intrinsically nonlinear: the collisional dynamics are determined by the hydrodynamic flow, rather than KbT, while the hydrodynamic flow itself is determined by the collisional dynamics.
 N. Menon and D. J. Durian, "Diffusing-wave spectroscopy of dynamics in a three-dimensional granular flow," Science 275, 1920-1922 (1997).
 N. Menon and D. J. Durian, "Particle motion in a gas-fluidized bed of sand," Phys. Rev. Lett. 79, 3407-3410 (1997).
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