Density Fluctuations at Low Temperatures

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Abstract
The applicability to a quantum liquid of the standard classical formula connecting the compressibility with the coherent scattering cross section for large wavelengths, questioned by the author in a previous paper, is examined. The correctness of the standard formula is proved (a) at absolute zero (the density fluctuations being infranormal); (b) under quantum conditions for all temperatures at which the Wigner expansion converges (it is conjectured that for liquid helium the expansion may diverge below the lambdapoint); and (c) for a one-dimensional crystal for all temperatures. These results, while they stop short of a complete proof of the standard classical formula for all conditions, do extend considerably our knowledge of its range of validity.

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