Continuum limit, Galilean invariance, and solitons in the quantum equivalent of the noisy Burgers equation

Abstract

A continuum limit of the non-Hermitian spin-1/2 chain, conjectured recently to belong to the universality class of the noisy Burgers or, equivalently, Kardar-Parisi-Zhang equation, is obtained and analyzed. The Galilean invariance of the Burgers equation is explicitly realized in the operator algebra. In the quasi-classical limit we find nonlinear soliton excitations exhibiting the $\omega \propto k^z$ dispersion relation with dynamical exponent $z=3/2$.

12 pages, latex, no figures

References in corpus (1)

• Two-Loop Renormalization Group Analysis of the Burgers-Kardar-Parisi-Zhang Equation

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