Huzihiro Araki

Who is Huzihiro Araki?

Huzihiro Araki is a Japanese mathematical physicist and mathematician.

Araki is the son of the University of Kyoto physics professor Gentarō Araki, with whom he studied and with whom in 1954 he published his first physics paper. He earned his diploma under Hideki Yukawa and in 1960 he attained his doctorate at Princeton University with thesis advisors Rudolf Haag and Arthur Strong Wightman. He was since 1966 professor at the University of Kyoto, at the Research Institute for Mathematical Sciences, of which he was also the director.

Araki works on axiomatic quantum field theory and statistical mechanics in particular on application of operator algebras. He already at the beginning of the 1960s at Princeton made important contributions to the "local quantum physics" of Haag and Kastler and also to the scattering theories of Haag and David Ruelle. He also supplied important contributions in the mathematical theory of operator algebras, classifying type-III factors of von Neumann algebras. Araki originated the concept of relative entropy of states of Von Neumann algebras. In the 1970s he showed the equivalence in quantum thermodynamics of, on the one hand, the KMS condition for the characterization of quantum mechanical states in thermodynamic equilibrium with, on the other hand, the variational principle for quantum mechanical spin systems on lattices. With Yanase he worked on the foundations of quantum mechanics. Stated in more precise terms, they proved that an exact measurement of an operator, which additively replaces the operator with a conserved size, is impossible. However, Araki did prove that the uncertainty of the measurement can be made arbitrarily small, provided that the measuring apparatus is sufficiently large.