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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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From atoms to crystals: a mathematical journey
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by Claude Le Bris and Pierre-Louis Lions PDF
Bull. Amer. Math. Soc. 42 (2005), 291-363 Request permission

Abstract:

We present an overview of some works on the models of computational quantum chemistry. We examine issues such as the existence of ground states (both for the electronic structure and the configuration of nuclei), the foundations of the models of the crystalline phase, and the macroscopic limits. We emphasize the connections between the physical modelling, the numerical concerns and the mathematical analysis of the problems.
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Additional Information
  • Claude Le Bris
  • Affiliation: CERMICS, École Nationale des Ponts et Chaussées, 6 & 8, avenue Blaise Pascal, 77455 Marne-La-Vallée, France
  • MR Author ID: 328085
  • Email: lebris@cermics.enpc.fr
  • Pierre-Louis Lions
  • Affiliation: Collège de France, 11, place Marcelin Berthelot, 75231 Paris Cedex 05, France
  • Email: lions@dmi.ens.fr
  • Received by editor(s): November 20, 2004
  • Published electronically: April 18, 2005
  • Additional Notes: This article is an extended version by the two authors of notes based upon a series of lectures given by PLL at Collège de France during the fall semester of the academic year 2003/04.
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Bull. Amer. Math. Soc. 42 (2005), 291-363
  • MSC (2000): Primary 35Bxx, 35Jxx, 35Pxx, 49Kxx, 81Q05, 81Q10, 82Bxx
  • DOI: https://doi.org/10.1090/S0273-0979-05-01059-1
  • MathSciNet review: 2149087