Stability of Atoms in the Brown–Ravenhall Model

We consider the Brown–Ravenhall model of a relativistic atom with N electrons and a nucleus of charge Z and prove the existence of an infinite number of discrete eigenvalues for N⩽ Z. As an intermediate result we prove a HVZ-type theorem for these systems. Communicated by Rafael D. Benguria Submitted: 9/11/2005 Accepted: 15/12/2005     

Enhanced Binding in Non-Relativistic QED

 We consider a spinless particle coupled to a photon field and prove that even if the Schr?dinger operator p ² +V does not have eigenvalues the system can have a ground state. We describe the coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant α is small. Received: 7 January 2002 / Accepted: 8 November 2002 Published online: 13 January 2003     

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 α ⁵ log α ⁻¹, where α denotes the fine structure constant, and prove rigorous bounds on the remainder term of the order o(α ⁵ log α ⁻¹). As a consequence, we prove that the binding energy is not a real analytic function of α, and verify the existence of logarithmic corrections to the expansion of the ground state energy in powers of α, as conjectured in the recent literature.     

Binding Threshold for the Pauli–Fierz Operator

For the Pauli–Fierz operator with a short range potential we study the binding threshold ₁() as a function of the fine structure constant and show that it converges to the binding threshold for the Schrödinger operator in the limit 0.This work was supported in part by Fondecyt (Chile), Project #102-0844. Work partially supported by HPRN-CT-2002-00277, and the Volkswagen Stiftung through a cooperation grant.     

Ionization in a quantized electromagnetic field

An analytical expression for a matrix element of the transition from a bound state of an electron in an atom to continuum states is obtained by solving the problem of interaction of the electron with a quantized electromagnetic field. This expression is used to derive formulas for the photoelectron spectrum and the rate of ionization of the simplest model atomic system upon absorption of an arbitrary number of photons. The expressions derived are analyzed and compared with the corresponding relationships obtained via other approaches. It is demonstrated that there are differences as compared to the case of the classical field. In particular, the photoelectron spectrum exhibits dips due to the destructive interference of the transition amplitudes in the quantized electromagnetic field.     

Electromagnetically induced transparency of magnetic nanoclusters under the action of a two-frequency pump field

The effect of electromagnetically induced transparency arising in a crystal of Fe₈ magnetic molecules under the action of a two-frequency pump field is investigated theoretically. The problem of selecting the polarizations of resonance magnetic fields acting on the crystal is discussed. The results of numerical calculation of the magnetic susceptibility are presented.     

Weakly coupled bound states of Pauli operators

We consider the two-dimensional Pauli operator perturbed by a weakly coupled, attractive potential. We show that besides the eigenvalues arising from the Aharonov?CCasher zero modes there are two or one (depending on whether the flux of the magnetic field is integer or not) additional eigenvalues for arbitrarily small coupling and we calculate their asymptotics in the weak coupling limit.     

Absence of the efimov effect in a homogeneous magnetic field

A system of three identical particles in a homogeneous magnetic field is studied. It is shown that the Hamiltonian of this system with short-range potentials after the separation of the center of mass motion has a finite discrete spectrum for each fixed type m of the rotational (SO(2)) symmetry.Supported by the Erwin Schrödinger Institute, Austria, International Science Foundation Grant No. 9400 and Russian Grant of the State Committee for High Education RF-94-27-1022.     

Discrete Spectrum of a Three-Particle Schrodinger Operator with a Homogeneous Magnetic Field

The discrete spectrum of the Schrödinger operator is studiedfor a system of three identical particles with short-range interactionsin a homogeneous magnetic field. All the two-particle subsystemsare supposed to be unstable. Finiteness of the discrete spectrumis established under some assumptions about the solutions ofthe corresponding two-particle Schrödinger equation.