Nonlinear aspects of band structure in liquids. I. Neat liquids

Abstract

One can make significant inroads into the problems of identifying the collective linear excitations (band structure) of liquids using what have been called ‘‘single-site’’ theories. In the context of liquid-theory methods for band structure, such theories arise from linear liquid theories such as the mean spherical approximation. However, at low densities, and when certain levels of eigenvector information are required, these theories are manifestly inadequate. We show here how a nonlinear theory for band structure in liquids can be constructed based on the EXP liquid theory. When tested against simulations of electronic s bands, the predictions are found to be quantitatively accurate in both low-density fluids and in impurity-band situations with uncorrelated dopants. Beyond its ramifications for band structure, the calculation presented here is also of some technical interest as an example of a nonlinear treatment of fluctuating internal degrees of freedom in liquids.