Adiabatic switching for degenerate ground states

Friday, May 22, 2009 - 1:00pm - 2:00pm
Lind 409
Gabriel Stoltz (École Nationale des Ponts-et-Chaussées (ENPC))
The Gell-Mann and Low switching allows to transform eigenstates of an unperturbed Hamiltonian H0 into eigenstates of the modified Hamiltonian H0 + V. This switching can be performed when the initial eigenstate is not degenerate, under some gap conditions with the remainder of the spectrum. We show here how to extend this approach to the case when the ground state of the unperturbed Hamiltonian is degenerate. More precisely, we prove that theswitching procedure can still be performed when the initial states are eigenstates of the finite rank self-adjoint operator
\cP0 V \cP0, where \cP0 is the projection onto the degenerate eigenspace of H0.