Nonlinear fluctuating hydrodynamics with many conserved fields: The case of a three-dimensional anharmonic chain

Area of Science:

• Condensed matter physics
• Statistical mechanics
• Nonlinear dynamics

Background:

• Understanding the vibrational dynamics of atomic chains is crucial for material properties.
• Previous studies successfully applied nonlinear fluctuating hydrodynamic theory to 1D chains.
• Investigating 3D chains with anharmonic potentials under tension presents unique challenges.

Purpose of the Study:

• To propose and analyze a theoretical model for a three-dimensional vibrating chain with anharmonic interatomic potentials and external tension.
• To identify and characterize the different modes of vibration (heat and sound) within this model.
• To compare theoretical predictions with molecular dynamics simulations for validation.

Main Methods:

• Development of a theoretical model for a 3D vibrating chain incorporating anharmonic potentials and external tension.
• Application of nonlinear fluctuating hydrodynamic theory to derive mode properties.
• Conducting molecular dynamics simulations to replicate and validate the theoretical model.
• Analysis of spatiotemporal correlations for heat and sound modes.

Main Results:

• The model predicts one heat mode, two longitudinal sound modes, and four transverse sound modes.
• Theoretical results show good agreement with molecular dynamics simulations, particularly at high temperatures.
• Transverse sound modes exhibit diffusive behavior.
• Heat and longitudinal sound modes display superdiffusive behavior.

Conclusions:

• The proposed model accurately describes the vibrational dynamics of a 3D anharmonic chain under tension.
• The distinct diffusive and superdiffusive behaviors of different modes offer insights into energy and momentum transport.
• Further exploration of scaling functions and characteristic exponents is warranted for a comprehensive understanding.