Current-density-functional theory for time-dependent systems

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Abstract
It is proved that the mapping, time-dependent potential → time-dependent density, is not invertible, in general, over the class of all potentials expandable in a Taylor series with respect to time coordinates. However, an invertible mapping does exist between the time-dependent potential and time-dependent current density. To explore this in detail, a one-body time-dependent problem is examined in an attempt to seek a time-dependent current-density-functional formalism.

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