Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation
Statistical Mechanics
2014-10-07 v1 Soft Condensed Matter
Pattern Formation and Solitons
Abstract
We discuss the mode spectrum in both the deterministic and noisy Burgers equations in one dimension. Similar to recent investigations of vortex depinning in superconductors, the spectrum is given by a non-Hermitian eigenvalue problem which is related to a `quantum' problem by a complex gauge transformation. The soliton profile in the Burgers equation serves as a complex gauge field engendering a {\em mode transmutation} of diffusive modes into propagating modes and giving rise to a {\em dynamical pinning} of localized modes about the solitons.
Cite
@article{arxiv.cond-mat/0005182,
title = {Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation},
author = {Hans C. Fogedby},
journal= {arXiv preprint arXiv:cond-mat/0005182},
year = {2014}
}
Comments
4 pages, Revtex file, 2 figures, submitted to Phys. Rev. Lett