6,754 research outputs found
Ground States in the Spin Boson Model
We prove that the Hamiltonian of the model describing a spin which is
linearly coupled to a field of relativistic and massless bosons, also known as
the spin-boson model, admits a ground state for small values of the coupling
constant lambda. We show that the ground state energy is an analytic function
of lambda and that the corresponding ground state can also be chosen to be an
analytic function of lambda. No infrared regularization is imposed. Our proof
is based on a modified version of the BFS operator theoretic renormalization
analysis. Moreover, using a positivity argument we prove that the ground state
of the spin-boson model is unique. We show that the expansion coefficients of
the ground state and the ground state energy can be calculated using regular
analytic perturbation theory
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
Exponential localization of hydrogen-like atoms in relativistic quantum electrodynamics
We consider two different models of a hydrogenic atom in a quantized
electromagnetic field that treat the electron relativistically. The first one
is a no-pair model in the free picture, the second one is given by the
semi-relativistic Pauli-Fierz Hamiltonian. We prove that the no-pair operator
is semi-bounded below and that its spectral subspaces corresponding to energies
below the ionization threshold are exponentially localized. Both results hold
true, for arbitrary values of the fine-structure constant, , and the
ultra-violet cut-off, , and for all nuclear charges less than the
critical charge without radiation field, . We obtain
similar results for the semi-relativistic Pauli-Fierz operator, again for all
values of and and for nuclear charges less than .Comment: 37 page
Uniqueness of the ground state in the Feshbach renormalization analysis
In the operator theoretic renormalization analysis introduced by Bach,
Froehlich, and Sigal we prove uniqueness of the ground state.Comment: 10 page
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
A vanishing theorem for operators in Fock space
We consider the bosonic Fock space over the Hilbert space of transversal
vector fields in three dimensions. This space carries a canonical
representation of the group of rotations. For a certain class of operators in
Fock space we show that rotation invariance implies the absence of terms which
either create or annihilate only a single particle. We outline an application
of this result in an operator theoretic renormalization analysis of Hamilton
operators, which occur in non-relativistic qed.Comment: 14 page
Kramers degeneracy theorem in nonrelativistic QED
Degeneracy of the eigenvalues of the Pauli-Fierz Hamiltonian with spin 1/2 is
proven by the Kramers degeneracy theorem. The Pauli-Fierz Hamiltonian at fixed
total momentum is also investigated.Comment: LaTex, 11 page
Renormalized Electron Mass in Nonrelativistic QED
Within the framework of nonrelativistic QED, we prove that, for small values
of the coupling constant, the energy function, E_|P|, of a dressed electron is
twice differentiable in the momentum P in a neighborhood of P = 0. Furthermore,
(E_|P|)" is bounded from below by a constant larger than zero. Our results are
proven with the help of iterative analytic perturbation theory
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