Soliton approach to the noisy Burgers equation: Steepest descent method

Details Soliton approach to the noisy Burgers equation: Steepest descent method Soliton approach to the noisy Burgers equation: Steepest descent method

1997-10-14

arxiv.org/abs/cond-mat/9710133v1

Physics

Condensed Matter

Statistical Mechanics

30 pages, Revtex file, 14 figures, to be submitted to Phys. Rev. E

Scientific paper

10.1103/PhysRevE.57.4943

The noisy Burgers equation in one spatial dimension is analyzed by means of the Martin-Siggia-Rose technique in functional form. In a canonical formulation the morphology and scaling behavior are accessed by mean of a principle of least action in the asymptotic non-perturbative weak noise limit. The ensuing coupled saddle point field equations for the local slope and noise fields, replacing the noisy Burgers equation, are solved yielding nonlinear localized soliton solutions and extended linear diffusive mode solutions, describing the morphology of a growing interface. The canonical formalism and the principle of least action also associate momentum, energy, and action with a soliton-diffusive mode configuration and thus provides a selection criterion for the noise-induced fluctuations. In a ``quantum mechanical'' representation of the path integral the noise fluctuations, corresponding to different paths in the path integral, are interpreted as ``quantum fluctuations'' and the growth morphology represented by a Landau-type quasi-particle gas of ``quantum solitons'' with gapless dispersion and ``quantum diffusive modes'' with a gap in the spectrum. Finally, the scaling properties are dicussed from a heuristic point of view in terms of a``quantum spectral representation'' for the slope correlations. The dynamic eponent z=3/2 is given by the gapless soliton dispersion law, whereas the roughness exponent zeta =1/2 follows from a regularity property of the form factor in the spectral representation. A heuristic expression for the scaling function is given by spectral representation and has a form similar to the probability distribution for Levy flights with index $z$.

Affiliated with

Also associated with

No associations

Rating

Soliton approach to the noisy Burgers equation: Steepest descent method does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Soliton approach to the noisy Burgers equation: Steepest descent method, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Soliton approach to the noisy Burgers equation: Steepest descent method will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-166228