Semjon Vugalter

Enhanced Binding in Non-Relativistic QED

Abstract:u2002We 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 coupling by means of the Pauli-Fierz Hamiltonian and our result holds in the case where the coupling constant α is small.

Two-Dimensional Berezin-Li-Yau Inequalities with a Correction Term

We improve the Berezin-Li-Yau inequality in dimension two by adding a positive correction term to its right-hand side. It is also shown that the asymptotical behaviour of the correction term is almost optimal. This improves a previous result by Melas, [11].

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, and prove that both effects are the results of the existence of the ground state of the self-energy operator with total momentum P=0.

Stability of Atoms in the Brown–Ravenhall Model

Abstract.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

Spectral Estimates for Two-Dimensional Schrödinger Operators with Application to Quantum Layers

A logarithmic type Lieb-Thirring inequality for two-dimensional Schrödinger operators is established. The result is applied to prove spectral estimates on trapped modes in quantum layers.

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–Casher 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.

Binding Threshold for the Pauli–Fierz Operator

For the Pauli–Fierz operator with a short range potential we study the binding threshold λ1(α) as a function of the fine structure constant α and show that it converges to the binding threshold for the Schrödinger operator in the limit α → 0.

Estimates on trapped modes in deformed quantum layers

Abstract We use the logarithmic Lieb–Thirring inequality for two-dimensional Schrodinger operators and establish estimates on trapped modes in geometrically deformed quantum layers.