Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elastic Chain in a Random Potential: Simulation of the Displacement
  Function $<(u(x)-u(0))^2>$ and Relaxation   We simulate the low temperature behaviour of an elastic chain in a random
potential where the displacements $u(x)$ are confined to the {\it longitudinal}
direction ($u(x)$ parallel to $x$) as in a one dimensional charge density
wave--type problem. We calculate the displacement correlation function $g(x)=<
(u(x)-u(0))^2>$ and the size dependent average square displacement
$W(L)=<(u(x)-\bar{u})^2>$. We find that $g(x)\sim x^{2\eta}$ with
$\eta\simeq3/4$ at short distances and $\eta\simeq3/5$ at intermediate
distances. We cannot resolve the asymptotic long distance dependence of $g$
upon $x$. For the system sizes considered we find $g(L/2)\propto W\sim
L^{2\chi}$ with $\chi\simeq2/3$. The exponent $\eta\simeq3/5$ is in agreement
with the Random Manifold exponent obtained from replica calculations and the
exponent $\chi\simeq2/3$ is consistent with an exact solution for the chain
with {\it transverse} displacements ($u(x)$ perpendicular to $x$).The
distribution of nearest distances between pinning wells and chain-particles is
found to develop forbidden regions.

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The categories of this paper are: mtrl-th
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The categories of this paper are: dg-ga
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The categories of this paper are: nlin
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: econ
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The categories of this paper are: nucl-th
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-lat
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The categories of this paper are: chao-dyn
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The categories of this paper are: ao-sci