Scattering and Coxeter groups

Abstract

The Peierls instability in chain-like substances is re-examined and a two-step Peierls transition theory is developed. The weak inter-chain coupling makes the CDW transition and the associated metal-insulator transition occur at different temperatures and allows the CDW to co-exist with the metallic feature. The resistivity anomaly in TaS3 between 215 and 270 K and the pressure-induced metal-insulator transition in (DMe-DcNQI),Cu are well explained.

Diffusion in the Lorentz Gas

“…For billiards inside polygons, angles of the form π/n are removable singularities. Thus the polygons with angles (π/2, π/2, π/2, π/2), (π/2, π/4, π/4), (π/2, π/3, π/6) and (π/3, π/3, π/3) are completely regular, as are polyhedra associated with Coxeter groups [150]. Other polygons with angles a rational multiple of π can be mapped to translation surfaces of finite genus, and any trajectory can have only a finite number of velocity directions.…”