Anderson localization of waves in three dimensions

6 problems

• Why measured cold-atom mobility edges in 3D speckle disagree with numerics

  Open

  Atoms released into a random pattern of laser light (speckle) can be trapped by disorder if their energy is below a threshold, the mobility edge. The measured thresholds lie well above the values computed for the same disorder.

• Universality class of three-dimensional localization of elastic waves

  Partially resolved

  Sound waves in a random network of welded metal beads have been seen to stop spreading, which is Anderson localization of elastic waves. Multifractal intensity patterns at the transition have been measured, but whether its critical exponent matches the electron transition, despite two kinds of waves (compression and shear) that convert into each other, is untested.

• Can light localize in any three-dimensional disordered dielectric?

  Open

  Light trapping by disorder in three dimensions has been predicted for decades, but dense clouds of tiny scatterers do not localize because their near fields couple them too strongly. Whether any non-absorbing disordered dielectric can trap light remains unknown.

• Critical exponent of the real-space 3D Anderson transition for atoms

  Open

  Near the mobility edge, the size of trapped wave packets grows without bound following a power law whose exponent is believed to be universal. It has been measured only in a momentum-space analogue, never for atoms spreading in real three-dimensional disorder.

• Is replica symmetry breaking in random lasers a true glass phase?

  Contested

  Shot-to-shot fluctuations of random-laser spectra have been read as a sign of a glassy state like that of spin glasses, where many configurations compete. Whether this is a real phase of the coupled light modes or a misreading of ordinary fluctuations is disputed.

• First-principles statistics of lasing modes in random lasers

  Open

  A random laser has no mirrors: light bounces among random scatterers in a material with gain until it lases. A theory that predicts how many modes lase, what they look like and how their output fluctuates from shot to shot is still missing.