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Journal of Physics A Mathematical and General

Quantum fluid dynamics within a relativistic density-functional framework

S K Ghosh, B M Deb

Published Jan 1, 1985• 0 citations
Publisher
DOI
10.1088/0305-4470/18/1/529

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The authors explore certain interconnections between density-functional theory and quantum fluid dynamics of many-electron systems, in the relativistic domain following the hydrodynamical approach adopted by Takabayashi for the one-particle Dirac equation. In order to build a 'classical' hydrodynamical interpretation, the spinor formulation is transformed into a tensor formulation by defining a number of density functions (local observables). These lead to six 'classical' fluid dynamic equations, together with two subsidiary conditions, for a complete specification of the system. The various density functions and the hydrodynamical equations are physically interpreted. The relativistic hydrodynamics discussed here correspond to a 'spinning' fluid. The net many-electron fluid consists of components each of which is characterised by fluid dynamic quantities corresponding to each spinor. The net hydrodynamical quantities are obtained by summing over the occupied spinors. Thus, the earlier nonrelativistic 'classical' picture of the many-electron fluid as a collection of individual fluid components is also valid in the relativistic domain.
Abstract We develop a relativistic (quasi-)hydrodynamic framework, dubbed gyrohydrodynamics, to describe the fluid dynamics of many-body systems with spin under strong vorticity based on entropy-current analysis. This framework generalizes the recently developed spin hydrodynamics to the regime where the spin density is at the leading order in derivatives but suppressed by another small parameter, the Planck constant ℏ, due to its quantum nature. Our analysis shows that the complete first-order constitutive relations of gyrohydrodynamics involve 17 transport coefficients and are highly anisotropic.
We propose new ideal hydrodynamics in the function space which describes a fluid composed of the 1+1 dimensional real scalar field in the framework of the stochastic variational method (SVM). In the derivation, the thermal equilibrium is assumed to the internal state of fluid elements in the function space of the scalar-field configuration. The deterministic trajectory of the functional fluid element is related to the functional generalization of the Bohmian trajectory in relativistic quantum field theory. To find the correspondence relation to standard hydrodynamics, a further coarse-graining should be introduced. Thus functional hydrodynamics is regarded as a mesoscopic theory such as the Boltzmann equation in the dynamical hierarchy of many-body systems. Functional hydrodynamics reproduces the exact behaviors of relativistic quantum field theory in a certain limit. We thus expect that our theory is applicable to study the influence of quantum-field theoretical fluctuation in collective flows of produced particles in relativistic heavy-ion collisions.