Fractal Concepts in Condensed Matter Physics

Abstract

Library of Congress Cataloging-in-Publication Data: Nakayama, T. (Tsuneyoshi), 1945-. Fractal concepts in condensed matter physics/ T. Nakayama, K. Yakubo. p. cm. -(Springer series in solid-state sciences, ISSN 0171-1873; 140). Includes bibliographical references and index.(alk.paper) 1. Condensed matter-Mathematics. 2.Fractals. I.

Study of off-diagonal disorder using the typical medium dynamical cluster approximation

“…Thus, TMM provides good data for a finite size scaling analysis to capture the critical points and the corresponding exponents. In our calculations, the transmission of states down a three-dimensional bar of widths M = [6,12] and length L = 2 × 10 4 M are studied by adding the products of the transfer matrices with random initial states. The multiplication of transfer matrices is numerically unstable.…”

“…These mean field approaches describe the effective medium using the average density of states which is not critical at the tran-sition 12,[35][36][37] . Thus, theories which rely on such averaged quantities will fail to properly characterize Anderson localization.…”

Harmonic vibrational excitations in graded elastic networks: Transition from phonons to gradons

“…1,2,3,4,5,6 Notable examples include disorder-induced localized states (i.e., the Anderson localization of lattice vibrations), fractal-induced localization (i.e., fractons 7 ), modes contributing the boson peak, 8 the connection of excess of low-frequency modes with the jamming-unjamming transition in particle packings, 9 intrinsic localized modes (ILMs)…”

High-Resolution Studies of Domain Switching Behavior in Nanostructured Ferroelectric Polymers

“…42 Fractal analysis provides a simple description of the effect of spatial correlations in a disordered medium on polarization reversal. In this context, lateral domain growth is viewed as a flow of dipole rotations in the randomly distributed internal potential, which forms a random percolating network.…”