Broken symmetry and strangeness of the semiconductor impurity band metal-insulator transition

The filamentary model of the metal-insulator transition in randomly doped semiconductor impurity bands is geometrically equivalent to similar models for continuous transitions in dilute antiferromagnets and even to the λ transition in liquid He, but the critical behaviors are different. The origin of these differences lies in two factors: quantum statistics and the presence of long range Coulomb forces on both sides of the transition in the electrical case. In the latter case, in addition to the main transition, there are two satellite transitions associated with disappearance of the filamentary structure in both insulating and metallic phases. These two satellite transitions were first identified by Fritzsche in 1958, and their physical origin is explained here in geometrical and topological terms that facilitate calculation of critical exponents.

Contribution of S opponent cells to color appearance

We measured the regions in isoluminant color space over which observers perceive red, yellow, green, and blue and examined the extent to which the colors vary in perceived amount within these regions. We compared color scaling of various isoluminant stimuli by using large spots, which activate all cone types, to that with tiny spots in the central foveola, where S cones, and thus S opponent (So) cell activity, are largely or entirely absent. The addition of So input to that from the L and M opponent cells changes the chromatic appearance of all colors, affecting each primary color in different chromatic regions in the directions and by the amount predicted by our color model. Shifts from white to the various chromatic stimuli we used produced sinusoidal variations in cone activation as a function of color angle for each cone type and in the responses of lateral geniculate cells. However, psychophysical color-scaling functions for 2° spots were nonsinusoidal, being much more peaked. The color-scaling functions are well fit by sine waves raised to exponents between 1 and 3. The same is true for the color responses of a large subpopulation of striate cortex cells. The narrow color tuning, the discrepancies between the spectral loci of the peaks of the color-scaling curves and those of lateral geniculate cells, and the changes in color appearance produced by eliminating So input provide evidence for a cortical processing stage at which the color axes are rotated by a combination of the outputs of So cells with those of L and M opponent cells in the manner that we postulated earlier. There seems to be an expansive response nonlinearity at this stage.