Publications

A new scheme is proposed to construct an (n)-times differentiable function extension of an (n)-times differentiable function defined on a smooth domain, (D,) in (d)-dimensions. The extension scheme relies on an explicit formula consisting of a linear combination of (n+1) function values in (D,) which extends the function along directions normal to the boundary. Smoothness tangent to the boundary is automatic. The performance of the scheme is illustrated by using function extension as part of a numerical solver for the Poisson equation on domains with complex geometry in both two and three dimensions. Although the cost of extending the function increases mildly with the extension order, it remains a small fraction of the overall algorithm. Moreover, the modest additional work required for high order function extensions leads to considerably more accurate solutions of the partial differential equation.

Generalizing atomistic machine learning models from small molecular clusters to bulk systems is a significant challenge in computational chemistry and materials science. While models trained on clusters can leverage high-accuracy quantum chemical data, their performance in bulk environments often deteriorates. In this work, we systematically investigate the factors influencing "clusters-to-bulk" generalization for several state-of-the-art atomistic learning architectures. We identify "the good"—effective strategies for data selection and representation that enhance transferability; "the bad"—common pitfalls such as overfitting to cluster-specific motifs and neglecting long-range interactions; and "the ugly"—inherent limitations of local descriptors in capturing bulk emergent properties. Our findings provide a detailed assessment of current methodologies and offer practical recommendations for developing more robust and generalizable atomistic potentials for complex condensed-phase systems.

Neural network parametrizations have increasingly been used to represent the ground and excited states in variational Monte Carlo (VMC) with promising results. However, traditional VMC methods only optimize the wave function in regions of peak probability. The wave function is uncontrolled in the tails of the probability distribution, which can limit the accuracy of the trained wavefunction approximation. To improve the approximation accuracy in the probability tails, this paper interprets VMC as a gradient flow in the space of wave functions, followed by a projection step.

The force-balance equation of time-dependent density-functional theory presents a promising route toward obtaining approximate functionals; however, so far, no practical correlation functionals have been derived this way. In this work, starting from a correlated wave function proposed originally by Colle and Salvetti [Theoret. Chim. Acta 37, 329 (1975)], we derive an analytical correlation-energy functional for the ground state based on the force-balance equation. The new functional is compared to the local-density correlation of the homogeneous electron gas, and we find an increased performance for atomic systems, while it performs slightly worse on solids. From this point onward, the new force-based correlation functional can be systematically improved.

The solid-electrolyte interphase (SEI) is a complex, multicomponent film that forms on the lithium metal anode in lithium-ion batteries. The SEI is formed through the decomposition of the electrolyte, which is a process that is mediated by the lithium metal surface. In this work, we use machine learning potentials to study the reaction dynamics of lithium-mediated electrolyte decomposition. We use a combination of active learning and enhanced sampling to efficiently explore the reaction pathways and calculate the free energy profiles of the decomposition reactions. Our results show that the decomposition of the electrolyte is a complex process that involves multiple steps and intermediate species. We also find that the lithium metal surface plays a crucial role in the decomposition process, as it provides a platform for the reactions to occur and stabilizes the reaction intermediates. Our work provides new insights into the mechanism of SEI formation and highlights the power of machine learning potentials for studying complex chemical reactions in battery systems.

Extreme light confinement in plasmonic nanosystems enables novel applications in photonics, sensor technology, energy harvesting, biology, and quantum information processing. Fullerenes represent an extreme case for nanoplasmonics: They are subnanometer carbon-based molecules showing high-energy and ultrabroad plasmon resonances; however, the fundamental mechanisms driving the plasmonic response and the corresponding collective electron dynamics are still elusive. Here, we uncover the dominant role of electron correlations in the dynamics of the giant plasmon resonance (GPR) of the subnanometer system C60 by using attosecond photoemission chronoscopy. We find a characteristic photoemission delay of up to about 300 attoseconds that is purely induced by coherent large-scale electron correlations in the plasmonic potential. These results provide insights into the nature of the plasmon resonances in subnanometer systems and open perspectives for advancing nanoplasmonic applications. Attosecond photoemission chronoscopy reveals the role of electron correlations in the plasmonic dynamics of C60 fullerene.

Optical selection rules endorsed by symmetry are crucial for understanding the optical properties of quantum materials and the associated ultrafast spectral phenomena. Here, we introduce momentum-resolved Floquet optical selection rules using group theory to elucidate the pump-probe photoemission spectral distributions of monolayer black phosphorus (BP), which are governed by the symmetries of both the material and the lasers. Using time-dependent density functional theory (TDDFT), we further investigate the dynamical evolution of Floquet(-Volkov) states in the photoemission spectra of monolayer BP, revealing their spectral weights at specific momenta for each sideband. These observations are comprehensively explained by the proposed Floquet optical selection rules. Our framework not only clarifies experimental photoemission spectra but also uncovers unexplored characteristics under different pump-probe configurations. Our results are expected to deepen the understanding of light-induced ultrafast spectra in BP and can be extended to other Floquet systems. Symmetry-based Floquet optical selection rules determine the visibility of light-induced sidebands in TrARPES intensity plots.

Chirality, the breaking of improper rotational symmetry, is a fundamental concept spanning diverse scientific domains. In condensed matter physics, chiral phonons, originating from circular atomic motions that carry angular momentum, have sparked intense interest due to their coupling to magnetic degrees of freedom, enabling potential phonon-controlled spintronics. However, modes and their counter-rotating counterparts are typically degenerate at the Brillouin zone center. Selective excitation of a single-handed circulating phonon requires external stimuli that break the degeneracy. Whether energetically nondegenerate circularly polarized phonons can appear spontaneously without structural or external symmetry breaking remains an open question. Here, we demonstrate that nondegenerate elliptically polarized phonon pairs can be induced by coupling to magnons with same helicity in the van der Waals antiferromagnet FePSe

Mamba has recently emerged as a promising alternative to Transformers, demonstrating competitive performance in many language modeling tasks with linear-time computational complexity. Theoretical characterization of Mamba has largely focused on its approximation power for solving certain tasks through specific constructions. However, it remains unclear whether Mamba trained with gradient descent can learn such constructions. As a first step to address this gap, we perform a mechanistic study of simplified Mamba models on associative recall tasks. By analyzing the learned model weights and the hidden state evolution, we uncover the mechanisms used by simplified Mamba models to perform associative recall. We complement our study with theoretical analysis on the optimization dynamics of simplified Mamba models that give rise to such mechanisms.

The randomized singular value decomposition (SVD) has become a popular approach to computing cheap, yet accurate, low-rank approximations to matrices due to its efficiency and strong theoretical guarantees. Recent work by Boullé and Townsend [Found. Comput. Math., 23 (2023), pp. 709–739] presents an infinite-dimensional analogue of the randomized SVD to approximate Hilbert–Schmidt operators. However, many applications involve computing low-rank approximations to symmetric positive semi-definite matrices. In this setting, it is well established that the randomized Nyström approximation is usually preferred over the randomized SVD. This paper explores an infinite-dimensional analogue of the Nyström approximation to compute low-rank approximations to non-negative self-adjoint trace-class operators. We present an analysis of the method and, along the way, improve the existing infinite-dimensional bounds for the randomized SVD. Our analysis yields bounds on the expected value and tail bounds for the Nyström approximation error in the operator, trace, and Hilbert–Schmidt norms. Numerical experiments on integral operators arising from Gaussian process sampling and Bayesian inverse problems are used to validate the proposed infinite-dimensional Nyström algorithm.