Quantum hydrodynamics: Construction of equations and critical scaling of viscosity

Abstract

A systematic method is proposed for deriving hydrodynamic equations for microscopic quantum field models. All terms of the equations are constructed from composite operators based on the Schwinger equations and are subsequently transformed into closed form using functional integral techniques. This scheme is applied to derive an analog of the Navier–Stokes equation for a quantum Bose liquid. The critical dimensions of the shear and bulk viscosity coefficients near the \(\lambda\) point are presented.