Subdiffusive energy transport in a strongly nonlinear ϕ^{4} lattice.

Area of Science:

• Nonlinear dynamics
• Statistical physics
• Condensed matter physics

Background:

• Classical homogeneous Hamiltonian systems were thought to forbid subdiffusion due to finite Poincaré recurrence times.
• Recent findings suggest subdiffusion can occur, particularly when induced by long-range interactions.

Purpose of the Study:

• To investigate the possibility of subdiffusion in a classical homogeneous system without disorder or long-range interactions.
• To explore the role of strong nonlinearity in energy transport within a one-dimensional φ⁴ lattice.

Main Methods:

• Studied a one-dimensional φ⁴ lattice model.
• Analyzed energy transport characteristics under strong nonlinearity.
• Calculated energy diffusivity and conductivity.
• Examined the relationship between power spectra and phonon band structure.

Main Results:

• Presented evidence for subdiffusive energy transport in the φ⁴ lattice under strong nonlinearity.
• Demonstrated quantitative consistency between calculated energy diffusivity and conductivity.
• Identified the normal-to-subdiffusive transition mechanism.

Conclusions:

• Subdiffusion is possible in classical homogeneous Hamiltonian systems with strong nonlinearity, even without disorder or long-range interactions.
• The observed subdiffusion is linked to the interplay between the system's power spectra and phonon band structure.
• Findings challenge the conventional understanding of energy transport limitations in such systems.