Fifty years of Anderson localization

Abstract

What began as a prediction about electron diffusion has spawned a rich variety of theories and experiments on the nature of the metal–insulator transition and the behavior of waves—from electromagnetic to seismic—in complex materials.

Phonon localization drives polar nanoregions in a relaxor ferroelectric

“…The disappearance of the flat resonance mode intensity profile is also expected since the resonance modes become coherently bound to the Anderson-localized phonons, which causes them to lose their fully localized incoherent character. This interpretation is supported quantitatively by noting that Anderson localization is exponential [32][33][34][35] and, as illustrated in Fig. 4d, exponential localization of a phonon in real space transforms in reciprocal space to a q-space convolution of the phonon at the resonance wave vector, q 0 ¼ (2p/a)K 0 , with a Lorentzian function (a ¼ lattice parameter).…”

“…Figure 4a shows a resonance mode radiating energy in the form of ferroelectric TO phonons at the resonance wave vector, q 0 . Arranging these randomly in 3D allows for the coherent trapping of phonons at the resonance via Anderson localization [32][33][34][35] , Fig. 4b.…”

“…The ILM frequency then slows below that of the TO phonon into the frequency gap between the TA and TO phonons, and eventually vanishes as PNRs become static [25][26][27] . There is an additional phonon localization mechanism for disordered systems; coherent multiple scattering interference from random, strongly scattering sites can produce localized regions of trapped standing waves-an effect known as Anderson localization [32][33][34][35] . Originally proposed to explain the localization of electron wavefunctions in disordered materials 32 , Anderson localization has since been observed for a variety of systems ranging from ultrasound in an elastic network 33 to ultra cold atoms 34,35 , but it has not been observed for phonons.…”

High Frequency Acoustics in Colloid-Based Meso- and Nanostructures by Spontaneous Brillouin Light Scattering

“…[153,162] Another possible explanation for strong localization that does not require a periodic structure, but, moreover, has 'large' disorder as a precondition, is the Anderson localization of sound. [163,164] Only recently, John Page and coworkers could show the realization of the localization of ultrasound in a three-dimensional elastic network consisting of disordered, sintered, monodisperse aluminum beads. [165] However, the theoretical treatment of Anderson localization is extremely demanding.…”

Anomalous low frequency dissipation processes in metal springs

“…Crystalline defects (not all line dislocations) appearing as often as every 200 lattice spacings [8,15], are required to generate the electron scattering necessary to explain the measured metal resistivity in pure metals. Many of these defects are dislocations of various kind.…”