Nonrelativistic Hydrodynamics from Quantum Field Theory: (I) Normal Fluid Composed of Spinless Schrödinger Fields

We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schrödeinger fields, assuming that an initial density operator takes a special form of the local Gibbs distribution. The constructed optimized/renormalized perturbation...

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Bibliographic Details
Published in:Journal of statistical physics 2019-03, Vol.174 (5), p.1038-1079
Main Author: Hongo, Masaru
Format: Article
Language:English
Subjects:
Computational fluid dynamics
Constitutive relationships
Field theory
Fluid flow
Formulas (mathematics)
Hydrodynamic equations
Hydrodynamics
Isomorphism
Mathematical and Computational Physics
Operators (mathematics)
Perturbation theory
Physical Chemistry
Physics
Physics and Astronomy
Quantum field theory
Quantum Physics
Quantum theory
Statistical Physics and Dynamical Systems
Symmetry
Theoretical
Thermodynamics
Transport properties
Variation
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Summary:We provide a complete derivation of hydrodynamic equations for nonrelativistic systems based on quantum field theories of spinless Schrödeinger fields, assuming that an initial density operator takes a special form of the local Gibbs distribution. The constructed optimized/renormalized perturbation theory for real-time evolution enables us to separately evaluate dissipative and nondissipative parts of constitutive relations. It is shown that the path-integral formula for local thermal equilibrium together with the symmetry properties of the resulting action—the nonrelativistic diffeomorphism and gauge symmetry in the thermally emergent Newton–Cartan geometry—provides a systematic way to derive the nondissipative part of constitutive relations. We further show that dissipative parts are accompanied with the entropy production operator together with two kinds of fluctuation theorems by the use of which we derive the dissipative part of constitutive relations and the second law of thermodynamics. After obtaining the exact expression for constitutive relations, we perform the derivative expansion and derive the first-order hydrodynamic (Navier–Stokes) equation with the Green–Kubo formula for transport coefficients.
ISSN:0022-4715
1572-9613
DOI:10.1007/s10955-019-02224-4