Physics – Condensed Matter – Other Condensed Matter
Scientific paper
2007-09-16
Physics
Condensed Matter
Other Condensed Matter
Scientific paper
Transition to condensate state in the degenerate gas of bosons is studied using the Gross-Pitaevskii equation. It is shown that adiabatic invariance of an enstrophy (mean squared vorticity) based on a generalized vorticity $curl (|\psi|^2 {\bf v})/|\psi|^2$, controls dynamics of the transitional turbulence just before formation of the condensate with its tangles of quantized vortices ($|\psi|^2 {\bf v}$ is the weighted velocity field defined on the macroscopic wave function $\psi$). Scaling of the angle-averaged occupation number spectrum, $N_k \sim k^{-1}$, has been obtained for the free developing transitional turbulence for the weak nonlinear (and completely disordered) initial conditions. Results of the three-dimensional numerical simulations have been used to support the theoretical consideration.
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