Harmonic rigidity at fixed spectral gap in one dimension

• URL: http://arxiv.org/abs/2512.24790v1
• Date: Wed, 31 Dec 2025 11:20:31 GMT
• Title: Harmonic rigidity at fixed spectral gap in one dimension
• Authors: Arseny Pantsialei,
• Abstract summary: We prove that the harmonic trap is the unique maximizer of the ground-state position variance.<n>We obtain a sharp geometric quantum speed-limit bound on the position-position component of the quantum metric.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We solve the static isoperimetric problem underlying the Mandelstam-Tamm bound. Among one-dimensional confining potentials with a fixed spectral gap, we prove that the harmonic trap is the unique maximizer of the ground-state position variance. As a consequence, we obtain a sharp geometric quantum speed-limit bound on the position-position component of the quantum metric, and we give a necessary-and-sufficient condition for when the bound is saturated. Beyond the exact extremum, we establish quantitative rigidity. We control the Thomas-Reiche-Kuhn spectral tail and provide square-integrable structural stability for potentials that nearly saturate the bound. We further extend the analysis to magnetic settings, deriving a longitudinal necessary-and-sufficient characterization and transverse bounds expressed in terms of guiding-center structure. Finally, we outline applications to bounds on static polarizability, limits on the quantum metric, and benchmarking of trapping potentials.

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