Symmetry Breaking in Quasi-1D Coulomb Systems

Abstract

Quasi 1D systems are systems of particles in domains which are of infinite extent in one direction and of uniformly bounded size in all other directions, e.g., a cylinder of infinite length. The main result proven here is that for such particle systems with Coulomb interactions and neutralizing background, the so-called “jellium”, at any temperature and at any finite-strip width, there is translation symmetry breaking. This extends the previous result on Laughlin states in thin, 2D strips by Jansen et al. (Commun Math Phys 285:503–535, 2009). The structural argument which is used here bypasses the question of whether the translation symmetry breaking is manifest already at the level of the one particle density function. It is akin to that employed by Aizenman and Martin (Commun Math Phys 78:99–116, 1980) for a similar statement concerning symmetry breaking at all temperatures in strictly 1D Coulomb systems. The extension is enabled through bounds which establish tightness of finite-volume charge fluctuations.

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Correspondence to Paul Jung.

Additional information

M. Aizenman supported in part by NSF grant DMS-0602360, and BSF grant 710021 on a visit to the Weizmann Institute.

S. Jansen supported in part by DFG Forschergruppe 718 “Analysis and Stochastics in Complex Physical Systems”, NSF grant PHY-0652854 and a Feodor Lynen research fellowship of the Alexander von Humboldt-Stiftung.

P. Jung supported in part by Sogang University research grant 200910039.

Communicated by Jean Bellissard

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Aizenman, M., Jansen, S. & Jung, P. Symmetry Breaking in Quasi-1D Coulomb Systems. Ann. Henri Poincaré 11, 1453–1485 (2010). https://doi.org/10.1007/s00023-010-0067-y

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Keywords

  • Symmetry Breaking
  • Point Process
  • Gibbs Measure
  • Coulomb System
  • Charge Imbalance