A Nonlinear Schrödinger Equation Yielding the “Shape of Molecules” by Spontaneous Symmetry Breaking
Abstract
It is reviewed how a molecule with an almost-degenerate ground state, if modelled as two-level system, is structurally unstable as follows: If the difference between the lowest two energy levels is below a certain critical value (determined by the free-molecule Coulomb Hamiltonian), then the coupling of the molecule to the quantized radiation field yields two symmetry-broken effective ground states of the molecule (one is the mirror image of the other) which are separated by a superselection rule orginating from the infrared singularity of the electromagnetic field. If this energy difference exceeds the critical value, then the ground state of the free molecule is not altered by the interaction with the field. It is shown how these results can be recovered from a Schrödinger equation for the molecule which, in addition to the free-molecule part, contains a nonlinear term incorporating the interaction with the radiation field.
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