Kôdi Husimi

From Wikipedia

Kôdi Husimi (June 29, 1909 – May 8, 2008, Japanese: 伏見康治) was a Japanese theoretical physicist who served as the president of the Science Council of Japan. [1] Husimi trees in graph theory, the Husimi Q representation in quantum mechanics, and Husimi's theorem in the mathematics of paper folding are named after him.

Education and career

Husimi studied at the University of Tokyo, graduating in 1933. He spent a year there as an assistant, and then moved to Osaka University in 1934, where he soon began working with Seishi Kikuchi. [1] [2] At Osaka, he became Dean of the Faculty of Science. He moved to Nagoya University in 1961, and directed the plasma institute there. He retired in 1973, and became a professor emeritus of both Nagoya and Osaka. [1]



A 1940 paper by Husimi introduced the Husimi Q representation in quantum mechanics. [3] [4] Husimi also gave the name to the kagome lattice, frequently used in statistical mechanics. [5]

Graph theory

In the mathematical area of graph theory, the name "Husimi tree" has come to refer to two different kinds of graphs: cactus graphs (the graphs in which each edge belongs to at most one cycle) and block graphs (the graphs in which, for every cycle, all diagonals of the cycle are edges). Husimi studied cactus graphs in a 1950 paper, [6] and the name "Husimi trees" was given to these graphs in a later paper by Frank Harary and George Eugene Uhlenbeck. [7] Due to an error by later researchers, the name came to be applied to block graphs as well, causing it to become ambiguous and fall into disuse. [8]

Pacifism and world affairs

Husimi was an early member of the Science Council of Japan, joining it in 1949, and it was largely through his efforts that the Science Council in 1954 issued a statement proposing principles for the peaceful use of nuclear power and opposing the continued existence of nuclear weapons. This statement, in turn, led to the Japanese law outlawing military uses of nuclear technology. Later, he served as president of the Science Council of Japan from 1977 to 1982. He was also a frequent participant in the Pugwash Conferences on Science and World Affairs and a leader of the Committee of Seven for World Peace. [1]

Recreational mathematics

Husimi's recreational interests included origami; [1] he designed several variations of the traditional orizuru (paper crane), folded on paper shaped as a rhombus instead of the usual square, [9] and studied the properties of the bird base that allow it to be varied within a continuous family of deformations. [10] With his wife, Mitsue Husimi, he wrote a book on the mathematics of origami, [11] which included a theorem characterizing the folding patterns with four folds meeting at a single vertex that may be folded flat. The generalization of this theorem to arbitrary numbers of folds at a single vertex is sometimes called Husimi's theorem. [12]


  1. ^ a b c d e Konuma, Michiji (2013), "Kodi Husimi, January 01, 1909 — May 08, 2008", Physics Today, doi: 10.1063/PT.4.2210.
  2. ^ Husimi, Kodi; Brown, L. M.; Konuma, M.; Maki, Z. (1991), "6. Nuclear Research at Osaka Imperial University: Interview with Kodi Husimi", Progress of Theoretical Physics Supplement, 105: 78–83, Bibcode: 1991PThPS.105...78H, doi: 10.1143/PTPS.105.78
  3. ^ Kôdi Husimi (1940), "Some formal properties of the density matrix", Proc. Phys.-Math. Soc. Jpn., 22: 264–314.
  4. ^ Groß, Christian (2012), "2.2.2 Visualizing Spin States: The Husimi Q-Representation", Spin Squeezing and Non-linear Atom Interferometry with Bose-Einstein Condensates, Springer, pp. 10–11, Bibcode: 2012ssnl.book.....G, ISBN  9783642256363.
  5. ^ Mekata, Mamoru (February 2003), "Kagome: The story of the basketweave lattice", Physics Today, AIP Publishing, 56 (2): 12–13, Bibcode: 2003PhT....56b..12M, doi: 10.1063/1.1564329
  6. ^ Husimi, Kodi (1950), "Note on Mayers' theory of cluster integrals", Journal of Chemical Physics, 18 (5): 682–684, Bibcode: 1950JChPh..18..682H, doi: 10.1063/1.1747725, MR  0038903
  7. ^ Harary, Frank; Uhlenbeck, George E. (1953), "On the number of Husimi trees, I", Proceedings of the National Academy of Sciences, 39 (4): 315–322, Bibcode: 1953PNAS...39..315H, doi: 10.1073/pnas.39.4.315, MR  0053893, PMC  1063779, PMID  16589268
  8. ^ See, e.g., MR 0659742, a 1983 review by Robert E. Jamison of a paper using the block graph definition, which attributes the ambiguity to an error in a book by Mehdi Behzad and Gary Chartrand.
  9. ^ Kodi Husimi, origamidb, retrieved 2014-07-12.
  10. ^ Maekawa, Jun (2008), "Fundamental Models: Orizuru Transformation", Genuine Origami: 43 Mathematically-based Models, from Simple to Complex, Japan Publications Trading, pp. 27–28, ISBN  9784889962512.
  11. ^ Husimi, K.; Husimi, M. (1979), The Geometry of Origami, Tokyo: Nihon Hyouronsha. 2nd ed., 1984, ISBN  978-4535781399.
  12. ^ Kawasaki, Toshikazu (2005), Roses, Origami & Math, Japan Publications Trading, p. 139, ISBN  978-4-88996-184-3.

Further reading

  • Konuma, Michiji; Otsuka, Masuhiko (May 2009), "Kodi Husimi and 'science and society'", Nippon Butsuri Gakkai-Shi (in Japanese), 64 (5): 357–362