Colloquia

The polaron is a mathematical model for a “dressed” particle consisting of an electron together with its entourage of local excitations of a quantized phonon field. We will give a brief historical review of the polaron, including the analysis of its ground state by a Brownian motion functional integral and by a related variational expression.
For the case of two or more electrons, the interaction of the electrons with the phonon field gives rise to an effective attraction between electrons that causes the particles to bind together. For N electrons, N → ∞, the systems are unstable in the sense that the binding energy grows faster than linearly in N. We will discuss recent work with Frank, Lieb, and Seiringer which shows that sufficiently strong Coulomb repulsion between electrons can compensate for this binding and provide stability for polaron systems for large N.