Communications in Mathematical Physics

, Volume 331, Issue 3, pp 1133–1154 | Cite as

Wigner Crystallization in the Quantum 1D Jellium at All Densities

  • S. Jansen
  • P. JungEmail author


The jellium is a model, introduced by Wigner (Phys Rev 46(11):1002, 1934), for a gas of electrons moving in a uniform neutralizing background of positive charge. Wigner suggested that the repulsion between electrons might lead to a broken translational symmetry. For classical one-dimensional systems this fact was proven by Kunz (Ann Phys 85(2):303–335, 1974), while in the quantum setting, Brascamp and Lieb (Functional integration and its applications. Clarendon Press, Oxford, 1975) proved translation symmetry breaking at low densities. Here, we prove translation symmetry breaking for the quantum one-dimensional jellium at all densities.


Point Process Open Loop Thermodynamic Limit Weyl Chamber Brownian Bridge 
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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Fakultät für MathematikRuhr-Universität BochumBochumGermany
  2. 2.University of AlabamaBirminghamUSA

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