Large Coulomb Systems

Christopher C. Gerry, James B. Togeas

A phase integral approximation, based on the notion that large N is a semiclassical limit, is presented for spherically symmetric systems of the Coulomb type. Since the dynamical group SO(2,1) is the spectrum generating group for the radial point Coulomb problem and the Casimir operators of O(N) and SO(2,1) are coupled, the authors write a path integral expression of the Green function in terms of SO(2,1) coherent states. The resulting phase integral approximation is applied to the Yukawa potential and the Coulomb plus linear r confining potential.

Élliott H. Lieb

Shi‐Hai Dong

Fazeleh Kazemian, Jorge Luis Galvez Vallejo, Giuseppe M. J. Barca

Predicting the chemico-physical properties of large molecular systems is a formidable challenge in chemistry and materials science. Traditional quantum mechanical methods, while accurate, have impractical scaling for large molecules with thousands of atoms, which are crucial in the development of novel therapeutics, catalysts, and nanomaterials. To address this, molecular fragmentation algorithms have been proposed to improve scalability and enable extensive parallelism. In this article, we introduce a significant enhancement to the Fragment Molecular Orbital (FMO) method, termed the Coulomb-Perturbed Fragmentation (CPF) method. CPF incorporates algorithmic improvements and implementation enhancements to optimize performance on heterogeneous computing systems equipped with a large number of GPUs. Key developments include a significant simplification of iteratitve self-consistent field (SCF) algorithm, advanced data management through a one-sided communication model, topology-aware optimizations, and a hybrid communication strategy for intra-group exchanges. Moreover, CPF integrates a distributed dynamic multi-layer load balancing scheme to optimise fragment distribution and workload management across nodes and GPUs. Performance evaluations on a 420-atom benzene molecule system comprising 35 fragments reveal that CPF outperforms existing GPU/CPU-based FMO algorithms in both efficiency and accuracy. When deployed on the Gadi supercomputer, CPF achieves over 97% parallel efficiency on 20 nodes, with scalability maintaining above 98% and 90% efficiency in weak-scaling tests for smaller and larger systems, respectively. Notably, CPF matches or exceeds the computational accuracy of conventional FMO methods, marking a substantial progress in the field of computational chemistry for fragmentation-based large-scale molecular modelling.

B. Szymanski, Romain Dubessy, B. Dubost +3 more

We designed and operated a surface ion trap with an ion-substrate distance of 500 μm, realized with standard printed-circuit-board techniques. The trap has been loaded with up to a few thousand Sr+ ions in the Coulomb-crystal regime. An analytical model of the pseudo-potential allowed us to determine the parameters that drive the trap into anisotropic regimes in which we obtain large (N>150) purely two dimensional (2D) ion Coulomb crystals. These crystals may open a simple and reliable way to experiments on quantum simulations of large 2D systems.