Asymptotics of the ground state energy of heavy molecules in self-generated magnetic field

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 $$ \mathsf{H}=\sum_{1\le n\le N} H_{x_n} +\sum_{1\le n &lt; n&#39;\le N}|x_n-x_{n&#39;}|^{-1} $$ on the Fock space $$\wedge _{1\le n\le N} L^{2(\mathbb{R}^3,} \mathbb{C}<sup>2)$$. 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 $\alpha Z\le \kappa<sup>*$ (with a small constant $\kappa<sup>*$) 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.