A Mean-field Calculation for the Three-Dimensional Holstein Model

A path integral representation appropriate for further Monte Carlo simulations is derived for the electron-phonon Holstein model in three spatial dimensions. The model is studied within mean-field theory. Charge density wave and superconducting phase transitions are discussed.Comment: Latex file typeset using elsart.cls, 16 pages, 2 figures, submitted to Journal of Physics: Condensed Matte

Multiple normalized solutions for quasi-linear Schr\"odinger equations

In this paper we prove the existence of two solutions having a prescribed $L^2$-norm for a quasi-linear Schr\"odinger equation. One of these solutions is a mountain pass solution relative to a constraint and the other one a minimum either local or global. To overcome the lack of differentiability of the associated functional, we rely on a perturbation method developed in [27]