相关论文: Exponential localization of hydrogen-like atoms in…
In this review 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…
We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of the semi-relativistic Pauli-Fierz operator and prove that the infimum of the spectrum of the latter operator is an eigenvalue. In particular,…
We consider a hydrogen-like atom in a quantized electromagnetic field which is modeled by means of a no-pair operator acting in the positive spectral subspace of the free Dirac operator minimally coupled to the quantized vector potential.…
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…
A semi-relativistic Pauli-Fierz model is defined by the sum of the free Hamiltonian $H_{\rm f}$ of a Boson Fock space, an nuclear potential $V$ and a relativistic kinetic energy: $$ H=\sqrt{[\sigma\cdot(\mathbf{p}+e\mathbf{A})]^2+M^2} - M +…
HVZ type theorem for semi-relativistic Pauli-Fierz Hamiltonian, $$\HHH=\sqrt{(p\otimes \one -A)^2+M^2}+V\otimes \one +\one\otimes \hf,\quad M\geq 0,$$ in quantum electrodynamics is studied. Here $H$ is a self-adjoint operator in Hilbert…
Spatial localization of the electrons of an atom or molecule is studied in models of non-relativistic matter coupled to quantized radiation. We give two definitions of the ionization threshold. One in terms of spectral data of cluster…
We consider the Pauli--Fierz model, which describes a particle (an electron) coupled to the quantized electromagnetic field and limit the number of photons to less than 2. By computing \red{the resolvent explicitly}, we located the spectrum…
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 relativistic no-pair model of a hydrogenic atom in a classical, exterior magnetic field. First, we prove that the corresponding Hamiltonian is semi-bounded below, for all coupling constants less than or equal to the critical…
We investigate the ground state energy of an electron coupled to a photon field. First, we regard the self-energy of a free electron, which we describe by the Pauli-Fierz Hamiltonian. We show that, in the case of small values of the…
We consider a (semi-)relativistic spin-1/2 particle interacting with quantized radiation. The Hamiltonian has the form $\hat{H}_c^V:=\{c^2[(\mathbf{p}+{\bf A})^2+{\bf \sigma}\cdot{\bf B}]+(mc^2)^2\}^{1/2}-mc^2+V+H_f$. Assuming that the…
We present a semi-relativistic model for the description of the ionization process of atomic hydrogen by electron impact in the first Born approximation by using the Darwin wave function to describe the bound state of atomic hydrogen and…
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…
The spinless semi-relativistic Pauli-Fierz Hamiltonian $H$ in quantum electrodynamics is considered. The self-adjointness and essential self-adjointness of $H$ are shown. It is emphasized that it includes the massless case. Furthermore, the…
We discuss the possibility of exponential quantum localization in systems of ultracold bosonic atoms with repulsive interactions in open optical lattices without disorder. We show that exponential localization occurs in the maximally…
We examine the dipole approximated Pauli-Fierz Hamiltonians of the nonrelativistic QED. We assume that the Coulomb potential of the nuclei together with the Coulomb interaction between the electrons can be approximated by harmonic…
We consider the semi-relativistic Pauli-Fierz model for a single free electron interacting with the quantized radiation field. Employing a variant of Pizzo's iterative analytic perturbation theory we construct a sequence of ground state…
We consider the polaron of the spinless semi-relativistic Pauli-Fierz model. The Hamiltonian of the model is defined by $H(\mathbf{P}) = \sqrt{(\mathbf{P}-d\Gamma(\mathbf{k}) + e\bA)^2 + M^2} + d\Gamma(\omega_m)$, where…
We investigate the role of relativity in photo ionization of hydrogen-like ions by a laser pulse. For hydrogen, the wavelengths of the laser resides in the weakly ultra violet region. For higher nuclear charges, the laser parameters are…