Transport speed of Weierstrass crystals

Determine the transport speed of Weierstrass crystals, particularly in parameter regimes where their spectrum is purely singular continuous.

Background

The paper relates regularity of Floquet functions to transport, proving finite-time blow-up of the second moment for sufficiently irregular Weierstrass crystals. It does not determine the full transport behavior across the parameter space, especially in regimes expected to have singular continuous spectrum.

References

What is the speed of transport for Weierstrass crystals, in particular in regimes where the spectrum is purely singular continuous?

— Arbitrarily Fast Quantum Dispersion in Long-Range Crystals  (2608.27326 - Leclerc et al., 27 Aug 2026) in Section 7, subsection “Speed of transport”

if $\lambda=\mu{-1}$, we conjecture that the spectrum is purely singular continuous;

— Arbitrarily Fast Quantum Dispersion in Long-Range Crystals  (2608.27326 - Leclerc et al., 27 Aug 2026) in Section 7, subsection “Spectrum”