Harmonic rigidity at fixed spectral gap in one dimension
Abstract
Abstract We resolve the static isoperimetric problem underlying the Mandelstam–Tamm limit: among one-dimensional confining potentials at fixed gap Δ, the harmonic trap uniquely maximizes Var 0 ( x ) , yielding the exact geometric quantum speed limit g x x ⩽ ( 2 m Δ ) − 1 with an iff criterion. Beyond the extremum we prove quantitative rigidity (Thomas–Reiche–Kuhn-tail and structural L 2 control), extend to magnetic settings (longitudinal iff; transverse guiding-center bounds), and note applications to static polarizability, quantum-metric limits, and trap benchmarking.
Fields of Study & Subjects
Spectral Theory in Mathematical Physics
Quantum Mechanics and Applications
Advanced Mathematical Physics Problems
Publication details
- Journal / source
- Journal of Physics A Mathematical and Theoretical
- Volume
- 59
- Issue
- 2
- Pages
- 025201–025201
- Publication date
- 14 January 2026