English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

The noisy Burgers equation in one spatial dimension is analyzed by means ofthe Martin-Siggia-Rose technique in functional form. In a canonical formulationthe morphology and scaling behavior are accessed by mean of a principle ofleast action in the asymptotic non-perturbative weak noise limit. The ensuingcoupled saddle point field equations for the local slope and noise fields,replacing the noisy Burgers equation, are solved yielding nonlinear localizedsoliton solutions and extended linear diffusive mode solutions, describing themorphology of a growing interface. The canonical formalism and the principle ofleast action also associate momentum, energy, and action with asoliton-diffusive mode configuration and thus provides a selection criterionfor the noise-induced fluctuations. In a ``quantum mechanical'' representationof the path integral the noise fluctuations, corresponding to different pathsin the path integral, are interpreted as ``quantum fluctuations'' and thegrowth morphology represented by a Landau-type quasi-particle gas of ``quantumsolitons'' with gapless dispersion and ``quantum diffusive modes'' with a gapin the spectrum. Finally, the scaling properties are dicussed from a heuristicpoint of view in terms of a``quantum spectral representation'' for the slopecorrelations. The dynamic eponent z=3/2 is given by the gapless solitondispersion law, whereas the roughness exponent zeta =1/2 follows from aregularity property of the form factor in the spectral representation. Aheuristic expression for the scaling function is given by spectralrepresentation and has a form similar to the probability distribution for Levyflights with index $z$.Comment: 30 pages, Revtex file, 14 figures, to be submitted to Phys. Rev.

Soliton approach to the noisy Burgers equation: Steepest descent method