Observable dependence of ETH spectral-function plateaus

Characterize how the extent of the low-frequency plateaus in ETH spectral functions depends on the observable considered, including observables that overlap with different powers of the Hamiltonian or with other conserved quantities such as magnetization.

Background

The paper studies low-frequency plateaus in the ETH spectral functions of total energy-current and spin-current operators in clean and disordered spin ladders. These plateaus are associated with random-matrix statistics of observable matrix elements and are compared with spectral-form-factor and transport frequencies.

The authors identify the dependence of plateau extent on the choice of observable as an unresolved direction for future study. They specifically point to observables overlapping with different powers of the Hamiltonian and with additional conserved quantities, such as magnetization, as relevant cases for determining whether the observed plateau behavior is universal or observable-dependent.

References

A potentially related question that is left for future studies is how the extent of the plateaus in the spectral functions depends on the observable considered.

— Random-matrix and transport frequencies in eigenstate spectral functions  (2609.24602 - Çeven et al., 21 Sep 2026) in Section Summary and outlook (Sec. Conclusions)

We cannot, however, rule out the finite-size effects, and that in the thermodynamic limit, both the spin and energy autocorrelations ultimately decay with the same power law.

— 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”