# Stochastic self-consistent harmonic approximation

Barium titanate's electro-optic coefficient falls markedly as modulation frequency rises, limiting modulator bandwidth. Using machine-learned potentials trained on PBE and HSE data and Green–Kubo molecular dynamics for the fixed-cell ionic coefficient, the work finds that nonharmonic damping and atomic displacement correlations spanning many unit cells, rather than phonon frequency itself, set both the low-frequency amplitude and the attenuation frequency. The HSE potential gives about 590 pm/V and about 137 GHz, against experimental values of 480 pm/V and 72.6 GHz.

Barium titanate's electro-optic coefficient falls markedly as modulation frequency rises, limiting modulator bandwidth. Using machine-learned potentials trained on PBE and HSE data and Green–Kubo molecular dynamics for the fixed-cell ionic coefficient, the work finds that nonharmonic damping and atomic displacement correlations spanning many unit cells, rather than phonon frequency itself, set both the low-frequency amplitude and the attenuation frequency. The HSE potential gives about 590 pm/V and about 137 GHz, against experimental values of 480 pm/V and 72.6 GHz.