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Anderson delocalization at weak disorder

Absence of eigenvalues alone does not exclude singular continuous spectrum.

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Understand the problem ↓

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Understanding the problem

Read the background

Absence of eigenvalues alone does not exclude singular continuous spectrum. The target is a nonempty purely absolutely continuous interval at weak disorder.

Dimension is fixed and disorder must be sufficiently small. The claim concerns the specified independent uniform potential law and energy interval, not every disorder strength or distribution.

Why it matters

If correct, establishes the stated weak-disorder absolutely continuous spectral regime in every fixed dimension at least three.

What counts as progress

A sourced resolution or substantial advance on the precise target, with hypotheses, prior context, and verification evidence stated separately.

What to watch for

  • Assess the precise statement and assumptions before comparing results.
  • Dimension is fixed and disorder must be sufficiently small. The claim concerns the specified independent uniform potential law and energy interval, not every disorder strength or distribution.
  • Track independent assessments, dependencies, corrections, and withdrawals separately from importance.

Background review: 2026-10-11. Selected sources:

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