2013/12/29 by Victor Ivrii, Ivrii, Victor
Mathematics · Physics and Astronomy · #35P20 #81Q20 #Cold Atom Physics and Bose-Einstein Condensates #FOS: Mathematics #Quantum chaos and dynamical systems #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math.SP #msc:35P20 #msc:81Q20
paper · pdf · doi:10.48550/arxiv.1312.7533
115 pp. v3: added new results
openalex publication_date 2013/12/29 · arxiv created 2014/03/27 · arxiv updated 2014/03/28 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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)⋅\boldsymbolσ)2-V with V=∑1≤ m≤ M (Zm)/(|x-ym|) and a corresponding Multiparticle Quantum Hamiltonian H=∑1≤ n≤ N Hxn +∑1≤ n < n'≤ N|xn-xn'|-1 on the Fock space \wedge 1≤ n≤ N L2(ℝ3, ℂ2). Here A=A0+A' where A0=(1)/(2)(-B x2, B x1,0) is an external magnetic field and A' is self-generated magnetic field. Then the ground state energy is given by E(A)=inf Spec(H)+\frac1α∫ |∇ × A'|2 dx where the last term is the energy of magnetic field. Under assumptions αZ≤ κ^* (with a small constant κ^*) and M=1 (atomic case) we study the ground State Energy E^*=infA'E(A). We derive its asymptotics including Scott, and Schwinger and Dirac corrections (depending on B≪ Z3). In the next versions we will consider also molecules and related topics: an excessive negative charge, ionization energy and excessive positive charge when atoms can still bind into molecules.