Complex systems time-dependent electric field

Below we first offer some brief remarks on SDFT, and then turn to the more complex problems posed by orbital currents, described by CDFT. Both, SDFT and CDFT also have a relativistic version, on which we make some brief comments in Sect. V11.2. Next, we briefly consider the simpler (but still not trivial) case of external electric fields. Finally, we describe the peculiar problems arising in the calculation of the electric polarization and the orbital magnetization of extended systems. We do not address, in this chapter, time-dependent electromagnetic fields, for which we refer the reader to reviews of the large and flourishing field of TD-DFT. ... 

Due to the nature of the dynamical system, chaotic advection requires either time-dependent flow in simple 2-D geometries or complex 3-D geometries [9, 12]. T q)ically, active chaotic micro-mixers which are actuated externally by time-dependent energy sources (i.e., pressure, electric and/or magnetic fields) use time-dependent 2-D flow to achieve chaotic advection for mixing enhancement. 

Let the electric field vary harmonically, i.e. in the complex notation let it be given by E (t) = E exp(icot), where E is the amplitude and co the angular frequency of variation. For an isotropic system, the time dependence of the electric displacement is also harmonic D (t) = DSexp(icot- eo), although and the phase difference are frequency dependent. Equation (4.3) now becomes... 

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