Microscopic derivation of nonlinear fluctuating hydrodynamics for crystalline solid

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Materials Science

Background:

• Understanding the macroscopic behavior of solids from microscopic interactions is crucial.
• Existing hydrodynamic equations often lack a rigorous microscopic foundation for nonlinear effects.

Purpose of the Study:

• To derive a nonlinear fluctuating hydrodynamic equation for crystalline solids from first principles.
• To establish a microscopic basis for nonlinear elastic properties and mode-coupling in solids.

Main Methods:

• Microscopic derivation from a Hamiltonian description of a many-particle system.
• Projection onto coarse-grained fields, including the displacement field.
• Long-wavelength expansion and application of the stationarity condition of the Fokker-Planck equation.

Main Results:

• A microscopic expression for the displacement field that reproduces nonlinear elastic properties.
• Identification of nonlinear mode-coupling terms in reversible currents consistent with phenomenological equations.
• Establishment of a connection between microscopic dynamics and macroscopic hydrodynamic behavior.

Conclusions:

• The study provides a rigorous microscopic foundation for nonlinear fluctuating hydrodynamics in crystalline solids.
• The derived equation accurately describes nonlinear elastic phenomena and mode-coupling.
• This work bridges the gap between microscopic Hamiltonians and macroscopic continuum theories.