An application of quantum fluid dynamics |
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Authors: | Masashi Himi Kenji Fukushima |
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Institution: | Department of Physics, Tokyo Metropolitan University, Tokyo 158, Japan |
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Abstract: | Hydrodynamics is often applied to quantum phenomena such as heavy-ion collisions. But here it should be noted that local equilibrium is not always realized in these collision processes and also the quantum effect is not fully taken into account in hydrodynamics. In this sense, a fluid-dynamical treatment of quantum many-body systems which does not presuppose local equilibrium is required. As an attempt in this direction, we derive simultaneous equations governing the motion of local variables such as the particle density ρ(r, t) and velocity field ν(r, t) by averaging a many-body wave function. The equations obtained will be shown to unify into a single nonlinear Schrödinger-type equation. Hence this is worthy of being called a quantum fluid dynamics (QFD). In deriving the QFD, we have employed the time-dependent Hartree-Fock and the generalized scaling approximation. Particularly, in order to attain self-containedness, we have assumed a certain relation which is valid in the case of the locally isotropic strain tensor. The introduction of anisotropy requires other local variables reflecting explicitly the deviation from local equilibrium and thus has been left as a future task. |
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