31 research outputs found
Hyperfine splitting of the dressed hydrogen atom ground state in non-relativistic QED
We consider a spin-1/2 electron and a spin-1/2 nucleus interacting with the
quantized electromagnetic field in the standard model of non-relativistic QED.
For a fixed total momentum sufficiently small, we study the multiplicity of the
ground state of the reduced Hamiltonian. We prove that the coupling between the
spins of the charged particles and the electromagnetic field splits the
degeneracy of the ground state.Comment: 22 page
On the theory of resonances in non-relativistic QED and related models
We study the mathematical theory of quantum resonances in the standard model
of non-relativistic QED and in Nelson's model. In particular, we estimate the
survival probability of metastable states corresponding to quantum resonances
and relate the resonances to poles of an analytic continuation of matrix
elements of the resolvent of the quantum Hamiltonian.Comment: 28 page
Hyperfine splitting in non-relativistic QED: uniqueness of the dressed hydrogen atom ground state
We consider a free hydrogen atom composed of a spin-1/2 nucleus and a
spin-1/2 electron in the standard model of non-relativistic QED. We study the
Pauli-Fierz Hamiltonian associated with this system at a fixed total momentum.
For small enough values of the fine-structure constant, we prove that the
ground state is unique. This result reflects the hyperfine structure of the
hydrogen atom ground state.Comment: 22 pages, 3 figure
Second order perturbation theory for embedded eigenvalues
We study second order perturbation theory for embedded eigenvalues of an
abstract class of self-adjoint operators. Using an extension of the Mourre
theory, under assumptions on the regularity of bound states with respect to a
conjugate operator, we prove upper semicontinuity of the point spectrum and
establish the Fermi Golden Rule criterion. Our results apply to massless
Pauli-Fierz Hamiltonians for arbitrary coupling.Comment: 30 pages, 2 figure
Spectral theory for a mathematical model of the weak interaction: The decay of the intermediate vector bosons W+/-, II
We do the spectral analysis of the Hamiltonian for the weak leptonic decay of
the gauge bosons W+/-. Using Mourre theory, it is shown that the spectrum
between the unique ground state and the first threshold is purely absolutely
continuous. Neither sharp neutrino high energy cutoff nor infrared
regularization are assumed.Comment: To appear in Ann. Henri Poincar\'
Ground State and Resonances in the Standard Model of Non-relativistic QED
We prove existence of a ground state and resonances in the standard model of
the non-relativistic quantum electro-dynamics (QED). To this end we introduce a
new canonical transformation of QED Hamiltonians and use the spectral
renormalization group technique with a new choice of Banach spaces.Comment: 50 pages change
Resonances in Models of Spin Dependent Point Interactions
In dimension we define a family of two-channel Hamiltonians
obtained as point perturbations of the generator of the free decoupled
dynamics. Within the family we choose two Hamiltonians, and \hat
H_\ve, giving rise respectively to the unperturbed and to the perturbed
evolution. The Hamiltonian does not couple the channels and has an
eigenvalue embedded in the continuous spectrum. The Hamiltonian \hat H_\ve is
a small perturbation, in resolvent sense, of and exhibits a small
coupling between the channels.
We take advantage of the complete solvability of our model to prove with
simple arguments that the embedded eigenvalue of shifts into a
resonance for \hat H_\ve. In dimension three we analyze details of the time
behavior of the projection onto the region of the spectrum close to the
resonance.Comment: Changes in the proof of theorem 3, few misprints corrected, 21 page