  Dynamic Hubbard models describe the fact that the wavefunction of an electron
in an atomic orbital expands when a second electron occupies the orbital. These
models give rise to superconductivity driven by lowering of kinetic energy when
the electronic energy band is almost full, with higher transition temperatures
resulting when the ions are negatively charged. We show that the charge
distribution in dynamic Hubbard models can be highly inhomogeneous in the
presence of disorder, and that a finite system will expel {\it negative charge}
from the interior to the surface, and that these tendencies are largest in the
parameter regime where the models give rise to highest superconducting
transition temperatures. High $T_c$ cuprate materials exhibit charge
inhomogeneity and they exhibit tunneling asymmetry, a larger tendency to emit
electrons rather than holes in NIS tunnel junctions. We propose that these
properties, as well as their high $T_c$'s, are evidence that they are governed
by the physics described by dynamic Hubbard models. Below the superconducting
transition temperature the models considered here describe a negatively charged
superfluid and positively charged quasiparticles, unlike the situation in
conventional BCS superconductors where quasiparticles are charge neutral on
average. We examine the temperature dependence of the superfluid and
quasiparticle charges and conclude that spontaneous electric fields should be
observable in the interior and in the vicinity of superconducting materials
described by these models at sufficiently low temperatures. We furthermore
suggest that the dynamics of the negatively charged superfluid and positively
charged quasiparticles in dynamic Hubbard models can provide an explanation for
the Meissner effect observed in superconducting materials.
