Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Asymptotics of the ground state energy of heavy molecules in
  self-generated magnetic field   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.

31
The categories of this paper are: ao-sci
16
The categories of this paper are: stat
32
The categories of this paper are: atom-ph
33
The categories of this paper are: plasm-ph
35
The categories of this paper are: mtrl-th
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
5
The categories of this paper are: gr-qc
9
The categories of this paper are: nlin
34
The categories of this paper are: chem-ph
28
The categories of this paper are: alg-geom
4
The categories of this paper are: cond-mat
20
The categories of this paper are: acc-phys
15
The categories of this paper are: nucl-ex
1
The categories of this paper are: cs
11
The categories of this paper are: hep-lat