# Properties of the time-dependent xc potential

# Properties of the time-dependent xc potential

This chapter reviews the properties of the time-dependent exchange-correlation (xc) potential. It starts with a discussion of the meaning of the universal xc functional, and then covers a number of exact conditions: the adiabatic limit, the zero-force theorem, freedom of self-interaction, sum rules, and various scaling properties. Next, Galiean invariance of the xc potential and the harmonic potential theorem are discussed. The xc potential has the intriguing property that it has a memory of the previous history of the system. The ramifications of this memory dependence are discussed, as well as causality properties. Another property is the dependence on the initial state of the system. Then, a time-dependent variational principle is presented which yields the xc potential, provided that one pays attention to certain boundary conditions. Finally, it is shown that the time-dependent xc potential has a discontinuity upon change of particle number.

*Keywords:*
exchange-correlation potential, variational principle, harmonic potential theorem, Galiean invariance, derivative discontinuity, zero-force theorem, scaling properties

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