Density-potential mapping in time-dependent density-functional theory

The key questions of uniqueness and existence in time-dependent density-functional theory are usually formulated only for potentials and densities that are analytic in time. Simple examples, standard in quantum mechanics, lead, however, to nonanalyticities. We reformulate these questions in terms of a nonlinear Schrödinger equation with a potential that depends nonlocally on the wave function.

Figure 1

Density of an initial exponential dispersing under free-particle evolution.

Figure 2

The initial state of the example in Sec. 3a3 (taking $C=1$) and the potential at which it is the ground state.