Biswas, A. C. ; Shenoy, S. R.
(1977)
*The Ginzburg-Pitaevskii equation and microscopic quantum hydrodynamics*
Physica B+C, 90
(2).
pp. 265-268.
ISSN 0378-4363

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Official URL: http://www.sciencedirect.com/science/article/pii/0...

Related URL: http://dx.doi.org/10.1016/0378-4363(77)90116-4

## Abstract

We show that for local equilibrium the microscopically derived phase and continuity equations, neglecting certain terms, yield an equation similar to the Ginzburg-Pitaevskii equation at absolute zero. The complex wave function is ψ = √p(r) × exp{i( < Φ(itr) > + μt/ℏ} where μ is the uniform chemical potential in strict equilibrium. A length scale ξ(0) = ℏ/√nρ_{0}V_{0} appears naturally, where V_{0} is the spatially integrated potential. With experimental values for the uniform total number density ρ_{0} and a hard sphere radius of 1 Å, ξ(0)~1.35 Å, comparable to the phenomenological GP length ~4 Å. Deviations of macroscopic quantities from their equilibrium values must be small, e.g.|ρ(r)-ρ|/ρ_{0} ≪ 1 and we must have 2mξ^{2}(0)/hρ_{0})| Δ · {j(r)-ρ(r)}ν_{s}(r)}| ≪ 1, where ν_{s}(r) = (ℏ/m Δ < Φ(r) >. In the above, j(r), ρ(r) and < φ(r) > are the total number current and number density, and the mean phase, respectively, in local equilibrium.

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ID Code: | 46048 |

Deposited On: | 30 Jun 2011 09:54 |

Last Modified: | 30 Jun 2011 09:54 |

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