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This work presents the design and performance characterization of the optical calibration systems produced for the Pacific Ocean Neutrino Experiment (P-ONE), which target gain, energy and time calibration in the detector. These systems include novel light-pulse driver circuitry based on gallium nitride field-effect transistor technology and its application to directional and isotropic, self-monitoring optical calibration instruments. A total of 330 directional light pulsers and two isotropic, 17-inch calibration modules (P-CALs) were produced for the first P-ONE line. We present the designs and performance of both the directional and isotropic calibration devices and perform detailed optical characterizations of both full-production batches. In a wavelength range of 365 ─ 520 nm, our developed driver circuits achieve emission intensities up to 10<SUP>11</SUP> photons and pulse widths as small as 1.4 ns, respectively. Light-pulse drivers and self-monitoring electronics in the P-CAL were characterized using the same experimental setup, and the instrument's optical-isotropy design was optimized in combination with a dedicated GEANT4-based simulation framework. The optimized P-CAL achieves a simulated isotropy grade of 1.00 ± 0.01 across the entire 4π solid angle range. These simulation investigations were explicitly confirmed by dedicated measurements in both air and water using two independent experimental setups, and we report the results. With this, a detailed performance estimate for deployed P-CAL modules in P-ONE was possible.

We have incorporated a hadron interaction tuning based on accelerator data into our atmospheric neutrino flux calculation, which has been used to analyze atmospheric neutrino oscillations at Super-Kamiokande. This new approach enables a more direct evaluation of the flux uncertainty than a conventional tuning using atmospheric muons. The neutrino flux calculated with this new tuning is 5%--10% smaller but still consistent with our previously published prediction within its uncertainty. The flavor ratio <inline-formula><tex-math>$(\nu _{\mu }+\bar{\nu }_{\mu })/(\nu _e+\bar{\nu }_e)$</tex-math></inline-formula> and <inline-formula><tex-math>$\bar{\nu }/\nu$</tex-math></inline-formula> ratio were consistent with the previous prediction. Based on the measurement errors of the accelerator data, we evaluated the flux uncertainty associated with the new tuning to be 7%--9% in the <inline-formula><tex-math>$E_{\nu } \lt $</tex-math></inline-formula> 1 GeV region, which was difficult to assess with the conventional tuning. The flux uncertainty in the <inline-formula><tex-math>$1\lt E_{\nu }\lt 10$</tex-math></inline-formula> GeV region was evaluated to be 5%--7%, which is an improvement over the conventional tuning.

We explore how perturbations of a Schwarzschild black hole can redistribute energy among scalar modes and seed turbulent-like cascades. We make use of the van der Pol-Krylov-Bogoliubov averaging method and derive coupled mode equations that describe near-resonant interactions between neighboring multipoles. We compare two routes to instability, namely the difference-frequency mixing between adjacent modes and the diagonal (Mathieu) self-modulation channel. We show that, at high multipole number (eikonal limit), the difference-frequency route dominates and drives a one-way cascade from higher to lower frequencies. We chart the corresponding instability regions (``tongues'') and quantify their detuning dependence. The framework provides a simple, quantitative mechanism for energy transfer in black hole ringdowns and clarifies when and how turbulent signatures can arise within linear probes on a weakly perturbed background.