Letters in Mathematical Physics

, Volume 68, Issue 2, pp 103–112

Gaussian Quantum Fluctuations in Interacting Many Particle Systems

  • Michael Hartmann
  • Günter mahler
  • Ortwin Hess

DOI: 10.1023/B:MATH.0000043321.00896.86

Cite this article as:
Hartmann, M., mahler, G. & Hess, O. Letters in Mathematical Physics (2004) 68: 103. doi:10.1023/B:MATH.0000043321.00896.86


We consider a many particle quantum system, in which each particle interacts only with its nearest neighbours. Provided that the energy per particle has an upper bound, we show, that the energy distribution of almost every product state becomes a Gaussian normal distribution in the limit of infinite number of particles. We indicate some possible applications.

quantum central limit theorem quantum many-body systems quantum fluctuations 

Copyright information

© Kluwer Academic Publishers 2004

Authors and Affiliations

  • Michael Hartmann
    • 1
  • Günter mahler
    • 2
  • Ortwin Hess
    • 3
  1. 1.Institute of Thechnical Physics, DLR Stuttgart and Institute of Theoretical Physics IUniversity of StuttgartGermany
  2. 2.Institute of Theoretical Physics IUniversity of StuttgartGermany
  3. 3.Advanced Technology InstituteUniversity of SurreyUnited Kingdom

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