Enhanced Binding in non-relativistic QED

We consider a spinless particle coupled to a photon field and prove that even if the Schr\"odinger 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 $\alpha$ is small.Comment: simplified versio

Solvability Conditions for Some non Fredholm Operators

We obtain solvability conditions for some elliptic equations involving non Fredholm operators with the methods of spectral theory and scattering theory for Schrodinger type operators. Though the Fredholm property is not satisfied, the solvability conditions are formulated in terms of orthogonality of the right-hand side to solutions of the homogeneous adjoint equation

SOLVABILITY OF SOME INTEGRO-DIFFERENTIAL EQUATIONS WITH DRIFT

We prove the existence in the sense of sequences of solutions for some integro-differential type equations involving the drift term in the appropriate H² spaces using the fixed point technique when the elliptic problems contain second order differential operators with and without Fredholm property. It is shown that, under the reasonable technical conditions, the convergence in L¹ of the integral kernels yields the existence and convergence in H² of solutions

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

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 prove rigorous error bounds of order $O(\alpha^{4})$. A main objective of our argument is its brevity.Comment: AMS Latex, 8 page

On the existence of stationary solutions for some non-Fredholm integro-differential equations

We show the existence of stationary solutions for some reaction-diffusion type equations in the appropriate H2 spaces using the fixed point technique when the elliptic problem contains second order differential operators with and without Fredholm property