{
  "id": "1303.4505",
  "version": "v4",
  "published": "2013-03-19T08:06:13.000Z",
  "updated": "2013-12-31T08:33:20.000Z",
  "title": "Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field",
  "authors": [
    "Victor Ivrii"
  ],
  "comment": "81 pp. This preprint supersedes my preprints arXiv:1108.4188, arXiv:1112.2487 and arXiv:1112.5538 as it contains more detailed analysis, more results, stronger results and also some corrections. v3: Corrected an error in v1, 2; v.4: Corrected misprint in abstract",
  "categories": [
    "math-ph",
    "math.MP",
    "math.SP"
  ],
  "abstract": "We consider asymptotics of the ground state energy of heavy atoms and molecules in the self-generatedl magnetic field. Namely, we consider $$ H=((D-A)\\cdot\\boldsymbol{\\sigma})^2-V $$ with $$V=\\sum_{1\\le m\\le M} \\frac{Z_m}{|x-y_m|}$$ and a corresponding Multiparticle Quantum Hamiltonian $$ \\mathsf{H}=\\sum_{1\\le n\\le N} H_{x_n} +\\sum_{1\\le n < n'\\le N}|x_n-x_{n'}|^{-1} $$ on the Fock space $\\wedge _{1\\le n\\le N} L^2(\\mathbb{R}^3, \\mathbb{C}^2)$. Here $A$ is a self-generated magnetic fiels. Then the ground state energy is given by $$ \\mathsf{E}(A)=\\inf \\operatorname{Spec}(\\mathsf{H})+\\frac{1}{\\alpha}\\int |\\nabla \\times A|^2\\,dx $$ where the last term is the energy of magnetic field. Under assumption $\\alpha Z\\le \\kappa^*$ (with a small constant $\\kappa^*$) we study the ground State Energy $$ \\mathsf{E}^*=\\inf _{A}\\mathsf{E}(A). $$ We derive its asymptotics including Scott, and Schwinger and Dirac corrections. We also consider related topics: an excessive negative charge, ionization energy and excessive positive charge when atoms can still bind into molecules.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2013-12-31T08:33:20.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "81Q20",
      "35P20"
    ],
    "keywords": [
      "ground state energy",
      "self-generated magnetic field",
      "heavy molecules",
      "asymptotics",
      "self-generatedl magnetic field"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 81,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1303.4505I"
    }
  }
}