Transport, correlations, and chaos in a classical disordered anharmonic chain

Area of Science:

• Condensed Matter Physics
• Statistical Mechanics
• Nonlinear Dynamics

Background:

• Understanding heat transport in disordered systems is crucial for materials science and statistical mechanics.
• Quantum many-body localization (MBL) describes a phenomenon where disorder prevents thermalization in quantum systems.
• Classical analogs of MBL are sought to understand the fundamental mechanisms of localization.

Purpose of the Study:

• To investigate heat transport properties in a disordered nonlinear chain of classical harmonic oscillators.
• To identify classical regimes exhibiting behavior analogous to quantum many-body-localized systems.
• To analyze the dependence of conductivity on system size, disorder strength, and temperature.

Main Methods:

• Extensive numerical simulations of a nonlinear chain of classical harmonic oscillators.
• Connecting the system to heat baths at different temperatures to achieve a nonequilibrium steady state.
• Computing heat current, temperature profiles, and conductivity as a function of system parameters (N, Δ, T).
• Analyzing equilibrium dynamical correlation functions and the role of chaos using out-of-time-ordered commutators.

Main Results:

• The system exhibits a regime analogous to quantum many-body localization.
• Conductivity (κ) saturates to a nonzero value (κ_∞ > 0) in the large system size limit.
• For Δ > 0, conductivity approaches zero faster than any power of temperature T in the (T/Δ)→0 limit, following κ_∞ ~ exp(-B|ln(CΔ/T)|^3).
• Finite-size effects on conductivity depend on whether the system is in the weak or strong disorder regime.

Conclusions:

• Disordered nonlinear classical oscillator chains can display phenomena similar to quantum many-body localization.
• The observed temperature dependence of conductivity suggests a unique transport mechanism driven by chaotic islands.
• The study provides insights into the fundamental differences in chaos propagation in weak and strong chaos regimes.