In a groundbreaking study, physicists have used the rules of chess, specifically the knight’s tour, to design intricate mazes. These complex labyrinths, made up of Hamiltonian cycles, could revolutionize the way we approach challenges in various industries. The research is set to be published in Physical Review X and is available on the arXiv preprint server.
The Hamiltonian cycles, a loop through a structure visiting each stopping point only once, were constructed in irregular structures that describe exotic matter known as quasicrystals. Unlike traditional crystals, quasicrystals do not follow the regular arrangement of atoms, instead taking on a more mysterious formation that can be described mathematically as slices through six-dimensional crystals existing in our three-dimensional universe. Only three natural quasicrystals have been found, with the first artificial one being discovered accidentally after the Trinity Test in 1945.
The uniquely complex mazes formed by these Hamiltonian cycles have potential applications in various fields, including scanning tunneling microscopy. By following the faster routes created by these cycles, complex images can be generated in less time. Improvements in efficiency could significantly streamline processes that take months to complete using current technology.
One potentially impactful application of these quantum mazes is in adsorption—a key industrial process in which molecules stick to the surfaces of crystals, such as in carbon capture and storage applications. Quasicrystals have been found to be highly efficient in adsorption, offering potential advancements in this area. Furthermore, efficient adsorption could also make quasicrystals surprising candidates for catalysts, boosting industry efficiency by lowering the energy of chemical reactions involved in processes like Haber-Bosch catalysis, used in the production of ammonia fertilizers for farming.
Lead author of the study, Dr. Felix Flicker, highlighted that the new findings render seemingly impossible problems tractable, providing new opportunities that could impact different realms of science. This work was the outcome of collaboration between the University of Bristol and Cardiff University, and the results add to our understanding of quasicrystals, with potential industry-wide implications.
