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

Hans C. Fogedby·Anders B. Eriksson·Lev V. Mikheev
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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 $ω\propto k^z$ dispersion relation with dynamical exponent $z=3/2$.

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Hans C. Fogedby, Anders B. Eriksson, Lev V. Mikheev. 1995-03-06. Continuum limit, Galilean invariance, and solitons in the quantum equivalent of the noisy Burgers equation. https://doi.org/10.1103/physrevlett.75.1883

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