H2 molecule in strong magnetic fields

TL;DR

This paper analyzes the behavior of the H2 molecule under extremely strong magnetic fields, deriving an effective Hamiltonian and proving the existence of a ground state while showing the inter-nuclear distance shrinks to zero.

Contribution

It introduces an asymptotic effective Hamiltonian for H2 in strong magnetic fields and proves the existence of a ground state with inter-nuclear distance tending to zero.

Findings

Existence of a ground state for the effective Hamiltonian.

Inter-nuclear distance approaches zero as magnetic field strength increases.

Effective Hamiltonian characterized by one-dimensional delta interactions.

Abstract

The Pauli-Hamiltonian of a molecule with fixed nuclei in a strong constant magnetic field is asymptotic, in norm-resolvent sense, to an effective Hamiltonian which has the form of a multi-particle Schr\"odinger operator with interactions given by one-dimensional \delta-potentials. We study this effective Hamiltonian in the case of the H2 -molecule and establish existence of the ground state. We also show that the inter-nuclear equilibrium distance tends to 0 as the field-strength tends to infinity.