Critical exponent of the real-space 3D Anderson transition for atoms
In plain words
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.
Precise statement
For noninteracting matter waves in 3D speckle, the localization length $\xi \sim \mid E - E_c\mid^{-\nu}$ below $E_c$ and diffusion constant $D \sim (E - E_c)^s$ above it, with Wegner scaling $s = \nu$ in 3D. Numerics for the orthogonal symmetry class (time-reversal symmetric, spinless) give $\nu$ approximately 1.57; the quasiperiodic kicked rotor gave $\nu$ near 1.6. An answer is a real-space measurement of $\nu$ with an uncertainty below 0.1, and whether it matches the orthogonal class.
What would settle it
Finite-time scaling analysis of real-space expansion of energy-selected atoms in 3D speckle across $E_c$.