Simon problems

In mathematics, the Simon problems (or Simon's problems) are a series of fifteen questions posed in the year 2000 by Barry Simon, an American mathematical physicist.[1][2] Inspired by other collections of mathematical problems and open conjectures, such as the famous list by David Hilbert, the Simon problems concern quantum operators.[3] In 2014, Artur Avila won a Fields Medal for work including the solution of three Simon problems.[4][5] Among these was the problem of proving that the set of energy levels of one particular abstract quantum system was in fact the Cantor set, a challenge known as the "Ten Martini Problem" after the reward that Mark Kac offered for solving it.[5][6] Eight of the problems pertain to anomalous spectral behavior of Schrödinger operators, and five concern operators that incorporate the Coulomb potential.

Not to be confused with Simon's problem in computational complexity.

The 2000 list was a refinement of a similar set of problems that Simon had posed in 1984.[7][8]

See also
  • "Simon's Problems". MathWorld. Retrieved 2018-06-13.

References
  1. Simon, Barry (2000). "Schrödinger Operators in the Twenty-First Century". Mathematical Physics 2000. Imperial College London. pp. 283–288. doi:10.1142/9781848160224_0014. ISBN 978-1-86094-230-3.
  2. Marx, C. A.; Jitomirskaya, S. (2017). "Dynamics and Spectral Theory of Quasi-Periodic Schrödinger-type Operators". Ergodic Theory and Dynamical Systems. 37 (8): 2353–2393. arXiv:1503.05740. doi:10.1017/etds.2016.16.
  3. Damanik, David. "Dynamics of SL(2,R)-Cocycles and Applications to Spectral Theory; Lecture 1: Barry Simon's 21st Century Problems" (PDF). Beijing International Center for Mathematical Research, Peking University. Retrieved 2018-07-07.
  4. "Fields Medal awarded to Artur Avila". Centre national de la recherche scientifique. 2014-08-13. Retrieved 2018-07-07.
  5. Bellos, Alex (2014-08-13). "Fields Medals 2014: the maths of Avila, Bhargava, Hairer and Mirzakhani explained". The Guardian. Retrieved 2018-07-07.
  6. Tao, Terry (2014-08-12). "Avila, Bhargava, Hairer, Mirzakhani". What's New. Retrieved 2018-07-07.
  7. Simon, Barry (1984). "Fifteen problems in mathematical physics". Perspectives in Mathematics: Anniversary of Oberwolfach 1984. Birkhäuser. pp. 423–454.
  8. Coley, Alan A. (2017). "Open problems in mathematical physics". Physica Scripta. 92 (9): 093003. arXiv:1710.02105. doi:10.1088/1402-4896/aa83c1.
This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.