Physicists at Heidelberg University have developed a theory that unifies two competing explanations of how a single foreign particle behaves when immersed in a dense quantum environment made up of fermions, such as electrons, protons, or neutrons.
The work, carried out at the university's Institute for Theoretical Physics, focuses on what happens when an impurity particle sits inside a so-called Fermi sea. Depending on how mobile that impurity is, physicists have historically used two very different models to describe the resulting behavior — models that, until now, had never been formally connected.
Two pictures, one framework
The first model centers on quasiparticles. When an impurity moves through a crowd of fermions, it interacts with and effectively drags along nearby particles, forming a composite object called a Fermi polaron. According to Eugen Dizer, a doctoral candidate involved in the research, this quasiparticle picture has become a standard tool for studying strongly interacting systems, including ultracold atomic gases, solid-state materials, and nuclear matter.
The second model applies when the impurity is extremely heavy and barely moves at all. In that case, a different phenomenon known as Anderson's orthogonality catastrophe emerges: the heavy impurity so thoroughly disturbs the surrounding fermions that their wave functions lose their original form, preventing the coordinated motion that quasiparticles require.
For decades, no theory bridged these two extremes. The Heidelberg team, using a range of analytical techniques, has now shown that both descriptions can be captured within a single mathematical framework.
"The theoretical framework we developed explains how quasiparticles emerge in systems with an extremely heavy impurity, connecting two paradigms that have long been treated separately," Dizer said. He is part of the Quantum Matter Theory working group led by Prof. Dr. Richard Schmidt.
The key insight, according to the researchers, is that even a very heavy impurity is never perfectly still. As the surrounding fermions adjust to its presence, the impurity undergoes subtle motions that create a small energy gap — and it is this gap that allows quasiparticles to form out of what would otherwise be an unruly, highly correlated quantum background. The framework also accounts for how quantum systems shift between what are known as polaronic and molecular states.
Why it matters for future experiments
Schmidt said the theory offers a flexible way to describe quantum impurities across different spatial dimensions and interaction types. "Our research not only advances the theoretical understanding of quantum impurities but is also directly relevant for ongoing experiments with ultracold atomic gases, two-dimensional materials, and novel semiconductors," he said.
The study was conducted through Heidelberg University's STRUCTURES Cluster of Excellence and the ISOQUANT Collaborative Research Centre 1225, and was published in Physical Review Letters.