Fluctuations of the winding number of a directed polymer in a random medium

Details Fluctuations of the winding number of a directed polymer in a random medium Fluctuations of the winding number of a directed polymer in a random medium

2003-10-15

arxiv.org/abs/cond-mat/0310342v1

Phys. Rev. E 68, 041101 (2003)

Physics

Condensed Matter

Disordered Systems and Neural Networks

22 pages

Scientific paper

10.1103/PhysRevE.68.041101

For a directed polymer in a random medium lying on an infinite cylinder, that is in 1+1 dimensions with finite width and periodic boundary conditions on the transverse direction, the winding number is simply the algebraic number of turns the polymer does around the cylinder. This paper presents exact expressions of the fluctuations of this winding number due to, first, the thermal noise of the system and, second, the different realizations of the disorder in the medium.

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