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An Analog Macroscopic Technique for Studying Molecular Hydrodynamic Processes in Dense Gases and Liquids
Published on: December 4, 2017
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Dynamic correlators of Fermi-Pasta-Ulam chains and nonlinear fluctuating hydrodynamics
Christian B Mendl1, Herbert Spohn2
1Zentrum Mathematik, Technische Universität München, 85747 Garching, Germany.
Physical Review Letters
|January 31, 2014
Summary
We predict dynamic correlations in classical anharmonic chains using nonlinear fluctuating hydrodynamics. This approach, applicable to 1D Hamiltonian systems, offers insights into conserved fields and fluid dynamics.
Area of Science:
- Physics
- Statistical Mechanics
- Condensed Matter Physics
Background:
- Classical anharmonic chains exhibit complex dynamics.
- Understanding equilibrium time correlations is crucial for these systems.
- Existing models may not fully capture the behavior of conserved fields.
Purpose of the Study:
- To predict the dynamic correlator of conserved fields in classical anharmonic chains.
- To generalize a prediction scheme based on nonlinear fluctuating hydrodynamics.
- To explore the applicability of this scheme to other 1D Hamiltonian systems.
Main Methods:
- Employing nonlinear fluctuating hydrodynamics, a system of nonlinear conservation laws with noise.
- Utilizing a one-loop approximation for systems with multiple modes.
- Deriving mode-coupling equations with a quadratic memory kernel.
Main Results:
- The mode-coupling equations describe the time evolution of the 3x3 correlator matrix for locally conserved fields.
- Analytical computation of long-time asymptotics.
- Numerical simulation for finite-time properties.
Conclusions:
- Nonlinear fluctuating hydrodynamics provides a framework for predicting dynamic correlators in classical anharmonic chains.
- The developed scheme is general and potentially applicable to classical and quantum fluids.
- The one-loop approximation and mode-coupling equations offer valuable insights into the system's dynamics.
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