Quantum theory of electric polarization nonlinearity in metal nanofilms
  We develop a quantum theory of electron confinement in metal nanofilms. The theory is used to compute the nonlinear response of the film to a static or low-frequency external electric field and to investigate the role of boundary conditions imposed on the metal surface. We find that the sign and magnitude of the nonlinear polarizability depends dramatically on the type of boundary condition used. 
George Y. Panasyuk, John C. Schotland and Vadim A. Markel
cond-mat.mes-hall physics.optics quant-ph