EXOTIC SPECTRA, WAVE-FUNCTIONS AND TRANSPORT IN INCOMMENSURATE LATTICES

We present numerical results on a range of related issues for a number of incommensurate TBM's, each of which shows a metal-insulator type t ransition as a binding-to-hopping ratio is made to increase through so me limiting value. These supplement a series of similar results on a c ouple of 1D lattices in a number of recent works (see below). A brief review pertaining to spectral properties and wavefunctions in incommen surate lattices is followed by results on the above TBM's relating to an interesting correlation between the gross features of wavefunctions and the energies arranged in a particular sequence termed the lattice -ordered sequence, and also between the lattice-ordered energies and t he on-site potentials. We present a qualitative explanation of these c orrelations on the basis of perturbation theory. Basic results on dyna mics of wavepackets in relation to spectral characteristics of incomme nsurate TBM's are also reviewed. Features of lattice-ordered energies and wavefunctions for the TBM's under study are used in the framework of the so-called Maryland construction, leading to a qualitative predi ction of criteria for recurrent and non-recurrent wavepacket dynamics in these lattices, and these predictions are checked against numerical iterations of the relevant 'quantum maps'. Closely related to the dyn amics of wavepackets are the transport properties of these lattices. R esults are available to indicate that the unusual spectral characteris tics of pseudorandom lattices lead to novel features in transport prop erties of these systems. In this context, low temperature a.c conducti vity in these lattices is a good probe for the spectral characteristic s and wavefunctions. However, not much is known about the a.c conducti vity, excepting a set of early results pertaining to the low frequency regime, principally because of the fact that the a.c conductivity dep ends on global characteristics of the spectrum and the entire set of w avefunctions. We present a simple model whereby the;gross structure of variation of the a.c conductivity with frequency can be obtained from a knowledge of the spectrum alone for the set of TBM's under consider ation. Numerical computations show that despite its simplicity, the mo del leads to results in good agreement with those from the Kubo-Greenw ood formula for a.c conductivity.