Establish the microscopic origin of subdiffusive energy transport

Establish the microscopic mechanisms that generate energy subdiffusion and its associated antipersistent current correlations in many-body Hamiltonian lattices with long-range interactions.

Background

The review discusses numerical evidence for subdiffusive energy transport in the mean-field or σ = 0 long-range FPUT system, including a mean-squared-displacement exponent below one and negative, antipersistent energy-current correlations.

Although subdiffusion is observed in several settings, the physical mechanism responsible for its emergence in many-body Hamiltonian systems remains unresolved. The authors specifically distinguish this problem from the more extensively studied subdiffusion of individual particles.

References

However, most studies focus only on particle motion and subdiffusion within energy transport types and their corresponding fundamental physical mechanisms is still unclear.

— Recent progress on thermal transport in one-dimensional long-range interacting Fermi-Pasta-Ulam-Tsingou lattice systems  (2609.18765 - Xiong et al., 16 Sep 2026) in Section 3.2, “Subdiffusive Thermal Transport at σ = 0”

The exact hydrodynamics of $H_z$ is unknown, and our numerical results suggest that it does not alter the subdiffusive behavior.

— Unraveling the Emergence of Slow Dynamics in U(1) Lattice Gauge Theories  (2609.26599 - Andreoni et al., 22 Sep 2026) in Section 5.3, “Emergent hydrodynamics”