Model-Independent Sum Rule Analysis Based on Limited-Range Spectral Data

Partial sum rules are widely used in physics to separate low- and high-energy degrees of freedom of complex dynamical systems. Their application, though, is challenged in practice by the always finite spectrometer bandwidth and is often performed using risky model-dependent extrapolations. We show that, given spectra of the real and imaginary parts of any causal frequency-dependent response function (for example, optical conductivity, magnetic susceptibility, acoustical impedance etc.) in a limited range, the sum-rule integral from zero to a certain cutoff frequency inside this range can be safely derived using only the Kramers-Kronig dispersion relations without any extra model assumptions. This implies that experimental techniques providing both active and reactive response components independently, such as spectroscopic ellipsometry in optics, allow an extrapolation-independent determination of spectral weight 'hidden' below the lowest accessible frequency.Comment: 5 pages, 3 figure

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National Highway Traffic Safety Administration, Office of Research and Traffic Records, Washington, D.C.Mode of access: Internet.Author corporate affiliation: Schulman, Ronca and Bucuvalas, Inc., Silver Spring, Md.Subject code: HCESubject code: NMCSubject code: PDDSubject code: PDEKSubject code: PDIESubject code: RCBDLSubject code: SBEDTSubject code: XPCSubject code: YC