Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Topological Constraints in Directed Polymer Melts   Polymers in a melt may be subject to topological constraints, as in the
example of unlinked polymer rings. How to do statistical mechanics in the
presence of such constraints remains a fundamental open problem. We study the
effect of topological constraints on a melt of directed polymers, using
simulations of a simple quasi-2D model. We find that fixing the global topology
of the melt to be trivial changes the polymer conformations drastically.
Polymers of length $L$ wander in the transverse direction only by a distance of
order $(\ln L)^\zeta$ with $\zeta \simeq 1.5$. This is strongly suppressed in
comparison with the Brownian $L^{1/2}$ scaling which holds in the absence of
the topological constraint. It is also much smaller than the predictions of
standard heuristic approaches - in particular the $L^{1/4}$ of a
mean-field-like `array of obstacles' model - so our results present a sharp
challenge to theory. Dynamics are also strongly affected by the constraints,
and a tagged monomer in an infinite system performs logarithmically slow
subdiffusion in the transverse direction. To cast light on the suppression of
the strands' wandering, we analyse the topological complexity of subregions of
the melt: the complexity is also logarithmically small, and is related to the
wandering by a power law. We comment on insights the results give for 3D melts,
directed and non-directed.

17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
0
The categories of this paper are: hep-ph
32
The categories of this paper are: atom-ph
35
The categories of this paper are: mtrl-th
9
The categories of this paper are: nlin
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
33
The categories of this paper are: plasm-ph
20
The categories of this paper are: acc-phys
11
The categories of this paper are: hep-lat
12
The categories of this paper are: nucl-th
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex