Finite-temperature dynamical structure factor of the one-dimensional Bose gas: From the Gross-Pitaevskii equation to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena

Manas Kulkarni, Austen Lamacraft

arXiv:1201.6363Physical Review AAug 8, 201376 citations

Physica

Remarks on critical phenomena

R. Brout

Published Nov 1, 1970• 7 citations

Publisher

DOI: 10.1016/0031-8914(70)90058-3

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Finite-temperature dynamical structure factor of the one-dimensional Bose gas: From the Gross-Pitaevskii equation to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena

Manas Kulkarni, Austen Lamacraft

We study the finite-temperature dynamical structure factor $S(k,\ensuremath{\omega})$ of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in $S(k,\ensuremath{\omega})$ has a width $\ensuremath{\propto}$ ${|k|}^{3/2}$ at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena.We study the finite-temperature dynamical structure factor $S(k,\ensuremath{\omega})$ of a one-dimensional Bose gas using numerical simulations of the Gross-Pitaevskii equation appropriate to a weakly interacting system. The line shape of the phonon peaks in $S(k,\ensuremath{\omega})$ has a width $\ensuremath{\propto}$${|k|}^{3/2}$ at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena.

arXiv:1201.6363Physical Review AAug 8, 201376 citations

{|k|}^{3/2}

at low wave vectors. This anomalous width arises from resonant three-phonon interactions, and reveals a remarkable connection to the Kardar-Parisi-Zhang universality class of dynamical critical phenomena.