Discontinuous behavior of effective transport coefficients in quasiperiodic media

We investigate the effective conductivity^* of a quasiperiodic medium in ^d and the discontinuous dependence, found in ref. 1, of^* on the wavelengths of the system. It was shown there, for example, that the effective conductivity^*(k) for a layered medium with a one-dimensional local conductivity_k(x)=A+cosx+coskx, A>2, is discontinuous ink. An explicit class of higherdimensional examples which exhibit the discontinuity is constructed here. The conductivity^*(k, L) of a sample of lengthL in one dimension asL is also analyzed and shown to have a plateau structure for any irrationalk well approximated by rationals.