Density fluctuations and the structure of a nonuniform hard sphere fluid
arXiv:cond-mat/0008124 · doi:10.1103/PhysRevLett.86.440
Abstract
We derive an exact equation for density changes induced by a general external field that corrects the hydrostatic approximation where the local value of the field is adsorbed into a modified chemical potential. Using linear response theory to relate density changes self-consistently in different regions of space, we arrive at an integral equation for a hard sphere fluid that is exact in the limit of a slowly varying field or at low density and reduces to the accurate Percus-Yevick equation for a hard core field. This and related equations give accurate results for a wide variety of fields.
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