High-temperature superconductor cooled with liquid nitrogen. The prediction if and when a material becomes superconducting depends decisively on whether excitations require energy or not. However, a prediction of that property is more difficult than imagined, as an underlying mathematical problem has proven to be unsolvable in principle. - Photo: Ulli Benz / TUM
A mathematical problem underlying fundamental questions in particle and quantum physics is provably unsolvable, according to scientists at UCL, Universidad Complutense de Madrid - ICMAT and Technical University of Munich. It is the first major problem in physics for which such a fundamental limitation could be proven. The findings are important because they show that even a perfect and complete description of the microscopic properties of a material is not enough to predict its macroscopic behavior. A small spectral gap - the energy needed to transfer an electron from a low-energy state to an excited state - is the central property of semiconductors. In a similar way, the spectral gap plays an important role for many other materials. When this energy becomes very small - i.e. the spectral gap closes - it becomes possible for the material to transition to a completely different state. An example of this is when a material becomes superconducting.
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