Probability Distributions of Line Lattices in Random Media from the 1D Bose Gas

Abstract

The statistical properties of a two dimensional lattice of elastic lines in a random medium are studied using the Bethe ansatz. We present a novel mapping of the dilute random line lattice onto the weak coupling limit of a pure Bose gas with delta-function interactions. Using this mapping, we calculate the cumulants of the free energy in the dilute limit exactly. The relation between density and displacement correlation functions in the two models is examined and compared with existing results from renormalization group and variational ansaetze.

38 pages, 2 figures

Cited by in corpus (14)

• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Universal tree structures in directed polymers and models of evolving populations
• Ground state energy of the $\delta$-Bose and Fermi gas at weak coupling from double extrapolation
• The crossing probability for directed polymers in random media
• Fluctuations of the winding number of a directed polymer in a random medium
• Test of Replica Theory: Thermodynamics of 2D Model Systems with Quenched Disorder
• Crossing probability for directed polymers in random media: exact tail of the distribution
• Population Extinction on a Random Fitness Seascape
• Super-rough phase of the random-phase sine-Gordon model: Two-loop results
• Distribution of Brownian coincidences
• Is there a Glass Transition in Planar Vortex Systems?
• Relation between directed polymers in random media and random bond dimer models
• A stationary model of non-intersecting directed polymers
• Love--Lieb integral equations: applications, theory, approximations, and computation