Dynamic properties of the multicomponent Bose fluid

The hydrodynamic properties of an $m$-component Bose fluid are explored, with attention to the consequences of the invariance of the Hamiltonian under the group $\mathrm{U}\mathrm{}\left(m\right)\mathrm{}$ of unitary transformations in the component space. It is pointed out that the hydrodynamics of the multicomponent systems ($m\ge 2$) differs in significant respects from that of the ordinary superfluid ($m=1\mathrm{}$). For example, in the superfluid phase, the multicomponent system has propagating modes with $\omega \propto k^2$ at long wavelengths, similar to the spin wave in a Heisenberg ferromagnet. In the normal phase, the multicomponent system has $m^2-1\mathrm{}$ new diffusive modes, corresponding to the conserved generators of the group $\mathrm{SU}\mathrm{}\left(m\right)\mathrm{}$, whose fluctuations diverge in the critical region. On the basis of dynamic scaling and the mode-mode coupling approach applied to these new modes, we predict a dynamic critical exponent $z=\frac{\varphi }{\nu }$, where $\varphi$ is the cross-over exponent for a symmetry-breaking perturbation of the axial type.