We study the localization-delocalization transition in one-dimensional incommensurate crystals both numerically and analytically. From the numerical point of view we provide an implementation of the renormalization method, which allows to process with high accuracy millions of sites (whenever necessary). From the analytic point of view we extend the envelope function concepts to incommensurate potentials, smoothly varying on lattice constant scale. The control of the transition is made by numerical calculation of the Lyapunov exponent: it presents surprising aspects of universality and simplicity, with plateaux, linear regions and, at times, much more complicated behaviours. The envelope function method, together with semi-analytic considerations, allows to understand, in a number of situations, the presence of mobility edges, pseudo-mobility edges, and gaps in the energy spectrum.
RENORMALIZATION AND ENVELOPE FUNCTION FORMALISM FOR INCOMMENSURATE SYSTEMS
GROSSO, GIUSEPPE;
1993-01-01
Abstract
We study the localization-delocalization transition in one-dimensional incommensurate crystals both numerically and analytically. From the numerical point of view we provide an implementation of the renormalization method, which allows to process with high accuracy millions of sites (whenever necessary). From the analytic point of view we extend the envelope function concepts to incommensurate potentials, smoothly varying on lattice constant scale. The control of the transition is made by numerical calculation of the Lyapunov exponent: it presents surprising aspects of universality and simplicity, with plateaux, linear regions and, at times, much more complicated behaviours. The envelope function method, together with semi-analytic considerations, allows to understand, in a number of situations, the presence of mobility edges, pseudo-mobility edges, and gaps in the energy spectrum.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
