Discoveries in quantum mechanics as a result of the Polish project run on LUMI

The “DYNAmics of STrongly interacting nuclei in neutron star’s inner crust” (DYNASTy) was one of the Polish projects granted to run on the LUMI supercomputer. Dr Daniel Pęcak (Warsaw University of Technology), the project’s principal investigator, shares the preliminary results and some remarks on utilising LUMI.

– When heavy stars explode, they can transform into neutron stars, which are exotic objects with about two solar masses packed into a mere 30 km in diameter. Due to their extreme density, neutron stars can be considered enormous nuclei bound by their gravity. To correctly describe their properties, quantum mechanics is necessary. Nuclear interactions occur on a femtometer scale (10–15 m), while observations like pulsar timing or gravitational waves originate on a kilometre scale (104 m). No single physical theory can describe phenomena across such a wide range of magnitudes. Therefore, a phenomenological theory, characterised by effective parameters, is required to bridge the gap between these extremes – introduces Dr Pęcak.

The research required the use of a full quantum description to study the dynamics in a layer of a neutron star known as the inner crust, where nuclei coexist with superfluid neutrons. The presence of both components, nuclei, and superfluid, which strongly interact with each other, makes the problem very complex. However, by conducting numerical experiments on LUMI, the DYNASTy team could extract effective parameters, such as the effective mass of nuclei, which is crucial for describing significant physical effects with simpler models.

– Our primary objective was to numerically measure the effective mass of nuclei in various layers of the inner crust of a neutron star. An impurity interacting with its environment is a problem that can be found across different fields of physics. The general idea is to remove the environment from the description and include the complex effect of interaction as a change in the impurity’s mass – informs the researcher.

– We compared our results with other models previously used in the literature, where approximate methods were employed. It is noteworthy that the complexity of the problem arises not only from the strong nuclear interaction between the nucleus and superfluid neutrons but also from the fact that the nucleus is not a sphere with sharp edges but rather an object with “fuzzy” borders. Moreover, by the law of quantum mechanics, the neutrons inside the nucleus are indistinguishable from neutrons that form the superfluid – continues Dr Pęcak, with the statement that those issues make the problem challenging.

What came as a solution were the numerical experiments. They enabled the research team not only to extract effective masses but also to demonstrate how energy is dissipated and how quantum vortex rings can form in the system. As explained by Dr Pęcak, those are analogues of vortex rings that can form from air bubbles underwater or clouds that form over a volcano. The researcher is convinced that the obtained results will benefit the neutron star community by providing estimates of the effective mass of nuclei, which might help in a more accurate estimation of the properties of the crystalline structure in the inner crust.

Image: Visualization of a nucleus moving through a superfluid neutron medium. The red sphere represents protons, and the magenta sphere represents neutrons bound in nucleus. The uniform neutron medium is depicted as transparent for clarity. Green contours indicate three vortex rings generated by the nucleus’s violent movement through the superfluid. This is the primary channel for energy dissipation from the nucleus. The arrows represent the neutron velocity field.

Undoubtedly, the aforementioned numerical experiments were possible thanks to the state-of-the-art computing infrastructure.

– Our group consistently seeks access to the latest high-performance computing (HPC) machines. These resources are essential for exploring Fermi systems with the necessary high resolution and large volumes, which are crucial for studying the microscopic properties of neutron stars. The requirement to model not only the nucleus but also the superfluid adds significant complexity, making it challenging to consider finite-size effects accurately – explains Dr Pęcak – The choice of LUMI comes naturally, given that it is the most powerful machine of its kind in Europe and the fifth in the world. Our research can be viewed as a numerical experiment, with results analysed after generation. With supercomputing resources, studying effective mass using our approach is possible. Therefore, LUMI’s contribution to our research is invaluable. After utilising LUMI, we can analyse the results on a local cluster or even a laptop.

Asked to evaluate the general performance of LUMI from the point of view of the project manager, Dr Pęcak replies:

– Given that this was my first experience with the AMD MI250x GPU architecture, I was pleasantly surprised. I assess the performance very positively. Mathematically, we solve a coupled set of hundreds of thousands of nonlinear equations known in the literature as the Bogoliubov-de-Gennes or Hartree-Fock-Bogoliubov equations. Additionally, we need to explore a large parameter space, requiring many simulations. Therefore, we need top-tier supercomputers. The engine was already tested and benchmarked in the pilot phase by Prof. Gabriel Wlazłowski so that we could utilise the total capacity of the software for this project. The code extensively uses the ELPA (Eigenvalue soLvers for Petaflop Applications) library. To facilitate collaboration within this captivating field of neutron star’s inner crust, we decided to release our code as open-source software, W-BSk Toolkit. We have already extensively tested it on LUMI.

The researcher briefly yet positively evaluates the application process and the contact with the LUMI User Support Team (LUST). To conclude the interview, Dr Pęcak points out some further challenges in research on the Fermi systems:

– At this point, we are investigating either a single nucleus or two nuclei. The scientific consensus states that the inner crust is composed of a crystalline lattice of nuclei immersed in a superfluid. In the future, it might be crucial to access and probe larger volumes containing more nuclei to limit finite-size effects. This capability would be valuable for accurately modeling interactions with vortices, essential for understanding glitches — sudden spin-ups of neutron stars. Another topic sensitive to finite-size effects is the so-called pasta phase, a region in neutron stars where spherical nuclei may deform into geometric structures like lines and sheets. These shapes resemble various types of Italian pasta, hence the name.

The preprint of the DYNASTy team paper (currently under review) is available here. The authors encourage you to watch one of the simulations on Prof. Wlazłowski’s channel. This work was financially supported by the (Polish) National Science Center Grants No. 2021/40/C/ST2/00072, 2021/43/B/ST2/01191, and 2022/45/B/ST2/00358.

Author: Kamil Mucha, Cyfronet