Uncovered: The essential structure of waves close to the transition point

Waves usually diffuse through random materials. This fact allows light to travel through thick clouds and electrons to conduct through metals. But disorder can sometimes bring wave propagation to a complete halt. This remarkable phase transition from conductor to insulator, suggested by Philip Anderson in 1958, is known as Anderson localization. Now a group of Dutch, Canadian, and French researchers has uncovered the essential structure of waves close to the transition point.

The researchers studied ultrasound propagation in a disordered network of aluminum beads. Just below the Anderson transition threshold wildly fluctuating forked wave-patterns, so-called multifractals, arise. The observation of multifractality in waves finally brings theories of the structure of the localization transition developed over the last 25 years, face to face with reality. The Anderson localization transition, once such an out-of-reach complex theory that Philip Anderson called his seminal paper "the unrecognizable monster" in his 1977 Nobel prize lecture, has evolved into a sub-branch of condensed matter theory with applications found in electronic conductivity of solids, transport of light and sound in multiple-scattering media, the quantum hall transition, high-T_c superconductivity, and the conductivity of Graphene. In fact, the concept of multifractality extends beyond localization. Multifractals are found in many complex systems such as turbulence, earthquakes, and patterns of rainfall.

Reference:
Observation of Multifractality in Anderson Localization of Ultrasound
Phys. Rev. Lett. 103, 155703 (2009)

The FOM press release (Dutch only)

Please contact: Sanli Faez (Researcher Photon Scattering group, first author) or Melissa van der Sande (Communications department). Tel. (00 31) (0)20 7547100.

Figure 1 (a) The multifractal wave pattern below the Anderson localization transition point. The pattern is characterized by spikes of sound of all different sizes. (b) The random diffuse "gurgle" of noise that typically results from random scattering of sound.

Figure 2. The sample is a collection of aluminum beads contained in a box.