Directed Polymers with Constrained Winding Angle

Abstract

In this article we study from a non-perturbative point of view the entanglement of two directed polymers subjected to repulsive interactions given by a Dirac $\delta -$function potential. An exact formula of the so-called second moment of the winding angle is derived. This result is used to provide a thorough analysis of entanglement phenomena in the classical system of two polymers subjected to repulsive interactions and related problems. No approximation is made in treating the constraint on the winding angle and the repulsive forces. In particular, we investigate how repulsive forces influence the entanglement degree of the two-polymer system. In the limit of ideal polymers, in which the interactions are switched off, we show that our results are in agreement with those of previous works.

34 pages, LaTeX + RevTeX 4, minor typos corrected, 2 figures added, a major revision of Section V

References in corpus (2)

• Chern-Simons Field Theories with Non-semisimple Gauge Group of Symmetry
• Topologically Linked Polymers are Anyon Systems

Cited by in corpus (5)

• An approximation to the Woods-Saxon potential based on a contact interaction
• Band spectra of periodic hybrid $\delta$-${\delta }^{\prime }$ structures
• The Birman-Schwinger Operator for a Parabolic Quantum Well in a Zero-Thickness Layer in the Presence of a Two-Dimensional Attractive Gaussian Impurity
• Application of a quantum wave impedance method for zero-range singular potentials
• Self-consistent treatment of electrostatics in molecular DNA braiding through external forces