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We consider the ground state of an atom in the framework of non-relativistic qed. We show that the ground state as well as the ground state energy are analytic functions of the coupling constant which couples to the vector potential, under…
We consider the ground state of an atom in the framework of non-relativistic qed. We assume that the ultraviolet cutoff is of the order of the Rydberg energy and that the atomic Hamiltonian has a non-degenerate ground state. We show that…
We consider atoms or molecules coupled to the quantized electromagnetic radiation field in a dipole approximation. We show the existence of ground states and resonance states in situations where the eigenvalues are degenerate and protected…
We discuss recent results concerning the ground state of non-relativistic quantum electrodynamics as a function of a magnetic coupling constant or the fine structure constant, obtained by the authors in [12,13,14].
For a large class of quantum mechanical models of matter and radiation we develop an analytic perturbation theory for non-degenerate ground states. This theory is applicable, for example, to models of matter with static nuclei and…
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…
We derive the ground state energy up to the fourth order in the fine structure constant $\alpha$ for the translation invariant Pauli-Fierz Hamiltonian for a spinless electron coupled to the quantized radiation field. As a consequence, we…
We consider a non-relativistic electron bound by an external potential and coupled to the quantized electromagnetic field in the standard model of non-relativistic QED. We compute the energy functional of product states of the form…
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…
The excited states of a charged particle interacting with the quantized electromagnetic field and an external potential all decay, but such a particle should have a true ground state--one that minimizes the energy and satisfies the…
For a model of atoms and molecules made from static nuclei and non-relativistic electrons coupled to the quantized radiation field (the standard model of non-relativistic QED), we prove a Mourre estimate and a limiting absorption principle…
We consider the semi-relativistic Pauli-Fierz Hamiltonian and a no-pair model of a hydrogen-like atom interacting with a quantized photon field at the respective critical values of the Coulomb coupling constant. For arbitrary values of the…
We consider an atom interacting with the quantized electromagnetic field in the standard model of non-relativistic QED. The nucleus is supposed to be fixed. We prove smoothness of the resolvent and local decay of the photon dynamics for…
Within the framework of nonrelativisitic quantum electrodynamics we consider a single nucleus and $N$ electrons coupled to the radiation field. Since the total momentum $P$ is conserved, the Hamiltonian $H$ admits a fiber decomposition with…
Kato's well known distributional inequality for the magnetic Laplacian holds equally in the more general setting of non-relativistic quantum electrodynamics (QED), where the wave function is vector-valued and the vector potential is…
We present a large deviation analysis of a recently proposed probabilistic approach to the study of the ground-state properties of lattice quantum systems. The ground-state energy, as well as the correlation functions in the ground state,…
We consider a Hamilton operator which describes a finite dimensional quantum mechanical system with degenerate eigenvalues coupled to a field of relativistic bosons. We show that the ground state projection and the ground state energy are…
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…
Using the Pauli-Fierz model of non-relativistic quantum electrodynamics, we calculate the binding energy of an electron in the field of a nucleus of charge $Z$ and in presence of the quantized radiation field. We consider the case of small…
We investigate the ground-state energy and spin of disordered quantum dots using spin-density-functional theory. Fluctuations of addition energies (Coulomb-blockade peak spacings) do not scale with average addition energy but remain…