Saggio | Universality, Condensed Matter and Quantum Field Theory
Vieri Mastropietro, in questo saggio (pubblicato sul “Bullettin of the International Association of Mathematical Physics”), affronta il problema del rapporto fra la materia condensata e la teoria quantistica dei campi.
Ecco l’incipit del testo:
«Matter is composed by atoms or molecules mutually interacting and obeying to the laws of quantum mechanics; the delicate interplay of quantum mechanical effects and collective phenomena related to the enormous number of particles is at the origin of the remarkable properties exhibited at low temperatures by several materials, superconductivity being a classical example. The structure of matter is extremely complex and depending on an enormous number of parameters, and one should expect that this is reected by a very complicated dependence of the macroscopic observables on such parameters. It is an experimental fact, on the contrary, that certain quantities exhibit independence from the underlying structure, having the same value in large classes of systems with different microscopic composition. This universal behavior suggests that certain macroscopic properties are sensitive more to abstract mathematical structures than to the microscopic details, and can therefore be the same also in the idealized models accessible to theoretical analysis. This opens the possibility of exact quantitative predictions for real systems starting from ideal or very approximate models. The situation recalls the emergence of gaussian law in central limits in probability, where a similar independence from details is found in a much simpler setting; remarkably, universality in condensed matter regards even the precise value of certain physical observables and not simply distribution laws».