## Abstract

The quantum-mechanical ground state of a two-dimensional (2D) N-electron system in a confining potential V(x)=Kv(x) (K is a coupling constant) and a homogeneous magnetic field B is studied in the high-density limit N→∞, K→∞ with K/N fixed. It is proved that the ground-state energy and electronic density can be computed exactly in this limit by minimizing simple functionals of the density. There are three such functionals depending on the way B/N varies as N→∞: A 2D Thomas-Fermi (TF) theory applies in the case B/N→0; if B/N→const≠0 the correct limit theory is a modified B-dependent TF model, and the case B/N→∞ is described by a classical continuum electrostatic theory. For homogeneous potentials this last model describes also the weak-coupling limit K/N→0 for arbitrary B. Important steps in the proof are the derivation of a Lieb-Thirring inequality for the sum of eigenvalues of single-particle Hamiltonians in 2D with magnetic fields, and an estimation of the exchange-correlation energy. For this last estimate we study a model of classical point charges with electrostatic interactions that provides a lower bound for the true quantum-mechanical energy.

Original language | English (US) |
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Title of host publication | The Stability of Matter |

Subtitle of host publication | From Atoms to Stars: Fourth Edition |

Publisher | Springer Berlin Heidelberg |

Pages | 171-190 |

Number of pages | 20 |

ISBN (Print) | 3540420835, 9783540222125 |

DOIs | |

State | Published - 2005 |

## All Science Journal Classification (ASJC) codes

- General Physics and Astronomy