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First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon (e-ph) interactions being a prime example. However, these techniques use large matrices encoding the interactions on dense momentum grids, which reduces computational efficiency and obscures interpretability. For e-ph interactions, existing interpolation techniques leverage locality in real space, but the high dimensionality of the data remains a bottleneck to balance cost and accuracy. Here we show an efficient way to compress e-ph interactions based on singular value decomposition (SVD), a widely used matrix and image compression technique. Leveraging (un)constrained SVD methods, we accurately predict material properties related to e-ph interactions—including charge mobility, spin relaxation times, band renormalization, and superconducting critical temperature—while using only a small fraction (1%–2%) of the interaction data. These findings unveil the hidden low-dimensional nature of e-ph interactions. Furthermore, they accelerate state-of-the-art first-principles e-ph calculations by about 2 orders of magnitude without sacrificing accuracy. Our Pareto-optimal parametrization of e-ph interactions can be readily generalized to electron-electron and electron-defect interactions, as well as to other couplings, advancing quantitative studies of condensed matter. 

Abstract Formed in the aftermath of a core-collapse supernova or neutron star merger, a hot proto–neutron star (PNS) launches an outflow driven by neutrino heating lasting for up to tens of seconds. Though such winds are considered potential sites for the nucleosynthesis of heavy elements via the rapid neutron capture process (r-process), previous work has shown that unmagnetized PNS winds fail to achieve the necessary combination of high entropy and/or short dynamical timescale in the seed nucleus formation region. We present three-dimensional general-relativistic magnetohydrodynamical simulations of PNS winds which include the effects of a dynamically strong (B≳ 10¹⁵G) dipole magnetic field. After initializing the magnetic field, the wind quickly develops a helmet-streamer configuration, characterized by outflows along open polar magnetic field lines and a “closed” zone of trapped plasma at lower latitudes. Neutrino heating within the closed zone causes the thermal pressure of the trapped material to rise in time compared to the polar outflow regions, ultimately leading to the expulsion of this matter from the closed zone on a timescale of ∼60 ms, consistent with the predictions of Thompson. The high entropies of these transient ejecta are still growing at the end of our simulations and are sufficient to enable a successful second-peakr-process in at least a modest ≳1% of the equatorial wind ejecta. 

Abstract We explore the effects of rapid rotation on the properties of neutrino-heated winds from proto-neutron stars (PNS) formed in core-collapse supernovae or neutron-star mergers by means of three-dimensional general-relativistic hydrodynamical simulations with M0 neutrino transport. We focus on conditions characteristic of a few seconds into the PNS cooling evolution when the neutrino luminosities obey $L_{{\nu }_e}+L_{{\overline{\nu }}_e}\approx 7\times {10}^{51}$erg s⁻¹, and over which most of the wind mass loss will occur. After an initial transient phase, all of our models reach approximately steady-state outflow solutions with positive energies and sonic surfaces captured on the computational grid. Our nonrotating and slower rotating models (angular velocity relative to Keplerian Ω/Ω_K≲ 0.4; spin periodP≳ 2 ms) generate approximately spherically symmetric outflows with properties in good agreement with previous PNS wind studies. By contrast, our most rapidly spinning PNS solutions (Ω/Ω_K≳ 0.75;P≈ 1 ms) generate outflows focused in the rotational equatorial plane with much higher mass-loss rates (by over an order of magnitude), lower velocities, lower entropy, and lower asymptotic electron fractions, than otherwise similar nonrotating wind solutions. Although such rapidly spinning PNS are likely rare in nature, their atypical nucleosynthetic composition and outsized mass yields could render them important contributors of light neutron-rich nuclei compared to more common slowly rotating PNS birth. Our calculations pave the way to including the combined effects of rotation and a dynamically important large-scale magnetic field on the wind properties within a three-dimensional GRMHD framework.