Non-analyticity of the ground state energy of the hydrogen atom in non-relativistic QED

@article{Barbaroux2010NonanalyticityOT,
  title={Non-analyticity of the ground state energy of the hydrogen atom in non-relativistic QED},
  author={J. M. Barbaroux and Simeon A. Vugalter},
  journal={Journal of Physics A: Mathematical and Theoretical},
  year={2010},
  volume={43},
  pages={474004}
}
We derive the ground state energy up to the fourth order in the fine-structure constant α for the translation-invariant Pauli–Fierz Hamiltonian for a spinless electron coupled to the quantized radiation field. As a consequence, we obtain the non-analyticity of the ground state energy of the Pauli–Fierz operator for a single particle in the Coulomb field of a nucleus. 
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Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED

In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli–Fierz model up to the order α5 log α−1, where α denotes the fine structure constant, and prove rigorous…

Scale dependence of the retarded van der Waals potential

We study the ground state energy for a system of two hydrogen atoms coupled to the quantized Maxwell field in the limit α → 0 together with the relative distance between the atoms increasing as α−γR,…

On the ground state energy of the translation invariant Pauli-Fierz model. II.

In this note, we determine the ground state energy of the translation invariant Pauli-Fierz model to subleading order $O(\alpha^3)$ with respect to powers of the finestructure constant $\alpha$, and…

Renormalization Group and Problem of Radiation

The standard model of non-relativistic quantum electrodynamics describes non-relativistic quantum matter, such as atoms and molecules, coupled to the quantized electromagnetic field. Within this…

References

SHOWING 1-10 OF 22 REFERENCES

Ground states in non-relativistic quantum electrodynamics

Abstract.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…

Convergent expansions in non-relativistic QED: Analyticity of the ground state

Quantitative Estimates on the Binding Energy for Hydrogen in Non-Relativistic QED

In this paper, we determine the exact expression for the hydrogen binding energy in the Pauli–Fierz model up to the order α5 log α−1, where α denotes the fine structure constant, and prove rigorous…

The increase of binding energy and enhanced binding in nonrelativistic QED

We consider a Pauli–Fierz Hamiltonian for a particle coupled to a photon field. We discuss the effects of the increase of the binding energy and enhanced binding through coupling to a photon field,…

Enhanced Binding in Non-Relativistic QED

Abstract: We consider a spinless particle coupled to a photon field and prove that even if the Schrödinger operator p2+V does not have eigenvalues the system can have a ground state. We describe the…

Existence of Atoms and Molecules in Non-Relativistic Quantum Electrodynamics

We show that the Hamiltonian describing N nonrelativistic electrons with spin, interacting with the quantized radiation field and several fixed nuclei with total charge Z, has a ground state when N <…

Binding Conditions for Atomic N-electron Systems in Non-Relativistic QED

Abstract. We examine the binding conditions for atoms in non-relativistic QED, and prove that removing one electron from an atom requires a positive energy. As an application, we establish the…

Analytic Perturbation Theory and Renormalization Analysis of Matter Coupled to Quantized Radiation

Abstract.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…

The renormalized electron mass in non-relativistic quantum electrodynamics

QUANTUM ELECTRODYNAMICS OF CONFINED NONRELATIVISTIC PARTICLES

Abstract We consider a system of finitely many nonrelativistic, quantum mechanical electrons bound to static nuclei. The electrons are minimally coupled to the quantized electromagnetic field; but we…