Three physicists born in Britain but now working in the United States were awarded the Nobel Prize in Physics on Tuesday for research into the bizarre properties of matter in extreme states, including superconductors, superfluids and thin magnetic films.

David J. Thouless of the University of Washington was awarded half of the prize of 8 million Swedish kronor, or about $930,000, while F. Duncan M. Haldane of Princeton University and J. Michael Kosterlitz of Brown University shared the other half.

The scientists relied on advanced mathematical models to study “theoretical discoveries of topological phase transitions and topological phases of matter,” in the words of the Royal Swedish Academy of Sciences in Stockholm.

Their studies may have major applications in electronics, materials science and computing. In an email, Michael S. Turner, a physicist at the University of Chicago, described the work as “truly transformational, with long-term consequences both practical and fundamental.”