Already more than 10 years of mathematics of the whole world are engaged in studying of surprising similarity of the equations describing two, apparently, of absolutely various physical process: a curvature of space-time and interaction of the systems consisting of set of particles. Recently scientific used this mathematical similarity to reproduce work of the "standard" superconducting device. Though results at present do not show any new breaks, full conformity of the theory to experiment gives hope of the future active advancement in studying of other condensed environments.

Very often parametres of border of a certain area of space strongly influence that occurs in this area. Some scientists name this phenomenon «a holographic principle» by analogy to how two-dimensional hologrammes comprise the information on a three-dimensional reality. On the basis of this general principle in 1997 the American theorist from Institute for Advanced Study in Princeton has put forward the assumption of existence of mathematical similarity between two absolutely different theoretical designs. One of them is a theory of strings, in particular, describing features of a curvature of space-time in gravitational fields; the second – the quantum theory describing strongly co-operating particles in usual space-time (which in this case can be considered as border of bent space-time i.e. to assume for it smaller dimension). The hypothesis of the scientist consisted that on border always it is possible to transform the physical equation of the theory of strings in the bent space-time to the theory of a field having smaller dimension. For today it is not proved that it takes place in all cases, but, according to the author of a hypothesis, proofs exist.

At first the hypothesis was used more to understand about the theory of strings, without facing complexities of the bent space. Now the return approach is applied: the theory of strings is used more to understand about strongly co-operating particles. In 2008 the author of the theory with colleagues has offered on the basis of it model of a two-dimensional superconductor.

In the new work published in magazine Physical Review Letters, they have continued researches, having offered mathematical model for so-called dzhozefsonovskogo devices in which the current proceeds between two fragments of a superconductor through a narrow zone of a "normal" material. Mathematical researches have shown that in process of increase in a quantum difference of phases between superconductors, the current changes under the sinusoidal law. This feature generates so-called superspending interferentsionnye quantum devices (superconducting quantum interference device, SQUID), extremely sensitive to magnetic fields. The carried out calculations have appeared well co-ordinated with practical results.

Though scientists one more proof in favour of existence of a mathematical duality, actually, is offered, their colleagues perceive work with care. For the present it is not clear, whether the similarity hypothesis will work so well on other substances and other spatial designs.

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