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

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