Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation

Details Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation Dynamical pinning and non-Hermitian mode transmutation in the Burgers equation

2000-05-10

arxiv.org/abs/cond-mat/0005182v1

Physics

Condensed Matter

Statistical Mechanics

4 pages, Revtex file, 2 figures, submitted to Phys. Rev. Lett

Scientific paper

10.1007/PL00011097

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.

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