The spectral gap represents the energy required to transfer an electron from a low energy state to an excited state. For example, a small spectral gap is the central property of semiconductors. Similarly, this amount plays a role in many other materials.
When the spectral gap becomes small, ie, it is closed, the material can change to another state entirely different, what happens, for example, when a material becomes superconducting.
“The possibility of extrapolating the microscopic description of the material properties of the solid is one of the most important tools in finding superconducting materials at room temperature or other properties of interest, “says David Pérez García, researcher and member of the UCM ICMAT.
Perez is one of the authors of a study published in Nature showing a fundamental limitation in this approach. With sophisticated mathematics, the authors have shown that even providing a complete microscopic description of a quantum materials, whether or not spectral gap is unspeakable problem.
“Alan Turing is known for his role in . decoding the Enigma machine but in mathematics and computer science community is much more famous his work in logic showed that some mathematical questions are unspeakable words, they are neither true nor false simply they are beyond the scope of.. math, “says Toby Cubitt, a researcher at University College London (UCL) Computer Science, co-author of the results.
” We have shown that the spectral gap is one of those problems, which means that no may be a general method to determine if a system described by quantum mechanics or not it has spectral gap. This limits the scope that can have our predictions of quantum materials, and even elementary particle physics, “adds the expert.
A million dollars to gain
The most famous on the spectral gap problem is whether the theory that governs the elementary particles of matter (the called standard model of particle physics) has a spectral gap. The particle physics experiments, such as those developed at CERN (European Laboratory for Particle Physics), and simulations on supercomputers, indicate that there exists in this case, a spectral gap.
However, there is still a mathematical proof of the matter, known as the hop mass conjecture of Yang-Mills. Whoever finds it will receive one million dollars prize Clay Mathematics Institute, which selected the problem as one of the seven Millennium Problems.
“There are particular cases that do have the problem solution although the general formulation is unspeakable, so it is still possible that someone wins a million dollars. But our result opens the possibility that some of the major problems of theoretical physics have no solution, “says Toby Cubitt.
“From the work of Turing and Gödel in the 1930s is known that, in principle, could be untold trouble, but so far this only affected the theory of computation and the more abstract mathematical logic. No one had seriously considered these ideas may affect the heart of theoretical physics, “says Michael Wolf, a researcher at the Technical University of Munich.
” From a philosophical perspective, the result also questions the reductionist view reality because the insurmountable difficulty of the problem is moving from the microscopic description of macroscopic properties, “continues
.
not all bad news
“Not all bad news,” said David Perez-Garcia. “Our results also predict the existence of quantum systems with properties not observed yet. For example, that adding a single particle to a cluster of art can, in principle, to radically change its properties.”
“The history of physics teaches us that often new and exotic properties translate like this, sooner or later, technological advances,” adds the scientist.
Now, researchers want see if their findings can be extended beyond the artificial mathematical models on which they have worked, to more realistic quantum materials that may occur in the laboratory
. Source: http: / /www.agenciasinc.es /
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