For more than 10 years, mathematicians around the world have been studying the amazing similarity of equations describing two seemingly completely different physical processes: the curvature of space-time and the interaction of systems consisting of many particles. Scientists have recently used this mathematical similarity to reproduce the operation of a “standard” superconducting device. Although the results so far do not show any new breakthroughs, the full agreement of theory with experiment gives hope for future active progress in the study of other condensed matter.

Very often, the parameters of the border of a certain area of ​​space strongly affect what happens inside this area. Some scientists call this phenomenon the “holographic principle” by analogy with how two-dimensional holograms contain information about three-dimensional reality. Based on this general principle, back in 1997, an American theorist from the Institute for Advanced Study in Princeton put forward the assumption that there is a mathematical similarity between two completely different theoretical constructs. One of them is string theory, in particular, which describes the peculiarities of the curvature of space-time in gravitational fields; the second is quantum theory, which describes strongly interacting particles in ordinary space-time (which in this case can be considered as the boundary of curved space-time, i.e., assume a lower dimension for it). The scientist’s hypothesis was that at the boundary it is always possible to transform the physical equation of string theory in curved space-time to field theory, which has a lower dimension. To date, it has not been proven that this is the case in all cases, but, according to the author of the hypothesis, evidence exists.

At first, the hypothesis was used to understand more about string theory without having to deal with the complexities of curved space. Now the approach is reversed: string theory is being used to understand more about strongly interacting particles. In 2008, the author of the theory and his colleagues proposed a model of a two-dimensional superconductor based on this.

In their new paper, published in Physical Review Letters, they continued their research by proposing a mathematical model for a so-called Josephson device, in which a current flows between two pieces of a superconductor through a narrow band of “normal” material. Mathematical research has shown that as the quantum phase difference between superconductors increases, the current changes in a sinusoidal manner. This feature gives rise to so-called superconducting quantum interference devices (SQUIDs), which are extremely sensitive to magnetic fields. The calculations performed turned out to be in good agreement with the practical results.

Although scientists, in fact, have offered further evidence in favor of the existence of mathematical duality, their colleagues perceive the work with caution. It is not yet clear if the similarity hypothesis will work just as well on other substances and other spatial constructs.

Source: sci-lib.com