Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Pair correlation functions and the wavevector-dependent surface tension
  in a simple density functional treatment of the liquid-vapour interface   We study the density-density correlation function $G({\bf r},{\bf r}')$ in
the interfacial region of a fluid (or Ising-like magnet) with short-ranged
interactions using square gradient density functional theory. Adopting a simple
double parabola approximation for the bulk free-energy density, we first show
that the parallel Fourier transform $G(z,z';q)$ and local structure factor
$S(z;q)$ separate into bulk and excess contributions. We attempt to account for
both contributions by deriving an interfacial Hamiltonian, characterised by a
wavevector dependent surface tension $\sigma(q)$, and then reconstructing
density correlations from correlations in the interface position. We show that
the standard crossing criterion identification of the interface, as a surface
of fixed density (or magnetization), does not explain the separation of
$G(z,z';q)$ and the form of the excess contribution. We propose an alternative
definition of the interface position based on the properties of correlations
between points that "float" with the surface and show that this describes the
full $q$ and $z$ dependence of the excess contributions to both $G$ and $S$.
However, neither the "crossing-criterion" nor the new "floating interface"
definition of $\sigma(q)$ are quantities directly measurable from the total
structure factor $S^{tot}(q)$ which contains additional $q$ dependence arising
from the non-local relation between fluctuations in the interfacial position
and local density. Since it is the total structure factor that is measured
experimentally or in simulations, our results have repercussions for earlier
attempts to extract and interpret $\sigma(q)$.

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The categories of this paper are: q-bio
1
The categories of this paper are: cs
31
The categories of this paper are: ao-sci
28
The categories of this paper are: alg-geom
2
The categories of this paper are: math
17
The categories of this paper are: q-fin
33
The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
18
The categories of this paper are: econ
23
The categories of this paper are: solv-int
21
The categories of this paper are: adap-org
25
The categories of this paper are: patt-sol
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The categories of this paper are: nucl-th
30
The categories of this paper are: q-alg