Weakly coupled bound states of Pauli operators

Nonlinear Bound States on Weakly Homogeneous Spaces

We prove the existence of ground state solutions for a class of nonlinear elliptic equations, arising in the production of standing wave solutions to an associated family of nonlinear Schrödinger equations. We examine two constrained minimization problems, which give rise to such solutions. One yields what we call Fλ-minimizers, the other energy minimizers. We produce such ground state solution...

Bound states in weakly disordered spin ladders

We study the appearance of bound states in the spin gap of spin-1/2 ladders induced by weak bond disorder. Starting from the strong-coupling limit, i.e., the limit of weakly coupled dimers, we perform a projection on the single-triplet subspace and derive the position of bound states for the single impurity problem of one modified coupling as well as for small impurity clusters. The case of a f...

A Perturbative Expansion for Weakly Bound States ∗

We describe a perturbation expansion for the energy and wave function of a weakly bound particle in a short-range potential in one space dimension. ∗Research supported in part by the National Science Foundation under Grant #PHY-9218167.

On Bound States for Systems of Weakly Coupled Schr Odinger Equations in One Space Dimension

Weakly coupled states on branching graphs

of N links joined at a single point. Each link supports a real locally integrable potential Vj ; the self–adjointness is ensured by the δ type boundary condition at the vertex. If all the links are semiinfinite and ideally coupled, the potential decays as x−1−ǫ along each of them, is non–repulsive in the mean and weak enough, the corresponding Schrödinger operator has a single negative eigenval...