Nonrelativistic hydrodynamics from quantum field theory. I. Normal fluid composed of spinless Schrödinger fields
As the author describes in the abstract, this manuscript deals with the derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schrödinger fields, assuming that an initial density operator takes a special form of the local Gibbs distribution. An optimized/renormalized perturbation theory for real-time evolution that helps to evaluate dissipative and no dissipative parts of constitutive relations is developed. The author shows that the path integral formula for local thermal equilibrium together with the symmetry properties of the resulting action provides a systematic way to derive the no dissipative part of constitutive relations and those dissipative parts are accompanied with the entropy production operator together with two kinds of fluctuation theorems. After obtaining the exact expression for constitutive relations, the author performs the derivative expansion and derives the first-order hydrodynamic (Navier-Stokes) equation using the Green-Kubo formula for transport coefficients.
renormalized/optimized perturbation theory
scientific article