Error Bounds in Spectroscopy and Nonequilibrium Statistical Mechanics

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Abstract
Upper and lower bounds are derived for the response of a system initially in equilibrium to a weak damped‐harmonic perturbation. The only information required in the construction of these error bounds are equilibrium properties of the unperturbed system, in particular, the equilibrium moments of the spectral density corresponding to the perturbation are used. The error bounds are shown to be the most precise possible, given only this equilibrium information. As an example, error bounds are obtained for the shape of a nuclear‐resonance spectrum due to dipolar broadening in solids, and good agreement is obtained with nuclear‐magnetic resonance experiments on CaF2. The error bounds are applicable to many other areas of spectroscopy and nonequilibrium statistical mechanics.