Bethe solution for the dynamical-scaling exponent of the noisy Burgers equation

Leh Hun Gwa, Herbert Spohn

Research output: Contribution to journalArticlepeer-review

279 Scopus citations

Abstract

We approximate the noisy Burgers equation by the single-step model, alias the asymmetric simple exclusion process. The generator of the corresponding master equation is identical to the ferromagnetic Heisenberg spin chain with a purely imaginary XY coupling. We Bethe diagonalize this nonsymmetric Hamiltonian. We show that the gap between the ground state and first excited state scales as N-3/2 for large system size N. The gap between the largest and next-largest eigenvalue scales as N-1. This property hints at conformal invariance. We also explain the connection to the six-vertex model.

Original languageEnglish
Pages (from-to)844-854
Number of pages11
JournalPhysical Review A
Volume46
Issue number2
DOIs
StatePublished - 1992
Externally publishedYes

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