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Title: Finite-temperature perturbation theory for the random directed polymer problem

We study the random directed polymer problem-the short-scale behavior of an elastic string (or polymer) in one transverse dimension subject to a disorder potential and finite temperature fluctuations. We are interested in the polymer short-scale wandering expressed through the displacement correlator Left-Pointing-Angle-Bracket [{delta}u(X)]{sup 2} Right-Pointing-Angle-Bracket , with {delta}u(X) being the difference in the displacements at two points separated by a distance X. While this object can be calculated at short scales using the perturbation theory in higher dimensions d > 2, this approach becomes ill-defined and the problem turns out to be nonperturbative in the lower dimensions and for an infinite-length polymer. In order to make progress, we redefine the task and analyze the wandering of a string of a finite length L. At zero temperature, we find that the displacement fluctuations Left-Pointing-Angle-Bracket [{delta}u(X)]{sup 2} Right-Pointing-Angle-Bracket {proportional_to} LX{sup 2} depend on L and scale with the square of the segment length X, which differs from a straightforward Larkin-type scaling. The result is best understood in terms of a typical squared angle Left-Pointing-Angle-Bracket {alpha}{sup 2} Right-Pointing-Angle-Bracket {proportional_to} L, where {alpha} = {partial_derivative}{sub x}u, from which the displacement scaling for the segment X follows naturally, Left-Pointing-Angle-Bracket [{delta}u(X)]{sup 2} Right-Pointing-Angle-Bracket {proportional_to} Left-Pointing-Angle-Bracket {alpha}{supmore » 2} Right-Pointing-Angle-Bracket X{sup 2}. At high temperatures, thermal fluctuations smear the disorder potential and the lowest-order results for disorder-induced fluctuations in both the displacement field and the angle vanish in the thermodynamic limit L {yields} {infinity}. The calculation up to the second order allows us to identify the regime of validity of the perturbative approach and provides a finite expression for the displacement correlator, albeit depending on the boundary conditions and the location relative to the boundaries.« less
Authors:
 [1] ; ;  [2]
  1. Russian Academy of Sciences, Landau Institute for Theoretical Physics (Russian Federation)
  2. Theoretische Physik (Switzerland)
Publication Date:
OSTI Identifier:
22210467
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 117; Journal Issue: 3; Other Information: Copyright (c) 2013 Pleiades Publishing, Inc.; http://www.springer-ny.com; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; BOUNDARY CONDITIONS; DISTANCE; FLUCTUATIONS; LENGTH; PERTURBATION THEORY; POLYMERS; POTENTIALS; RANDOMNESS; SCALING; TEMPERATURE RANGE 0400-1000 K