Four-wave mixing nonlinear response function

Banerjee and Harbola [69] have worked out a variation perturbation method within the hydrodynamic approach to the time-dependent density functional theory (TDDFT) in order to evaluate the linear and nonlinear responses of alkali metal clusters. They employed the spherical jellium background model to determine the static and degenerate four-wave mixing (DFWM) y and showed that y evolves almost linearly with the number of atoms in the cluster. 

II. The Nonlinear Response Function for Four-Wave Mixing... 

II. THE NONLINEAR RESPONSE FUNCTION FOR FOUR-WAVE MIXING... 

The essential quantity in the present formulation is a three-time correlation funetion, Cjltj, T2, T3), whieh is similar to the nonlinear response funetion investigated in the context of four wave mixing processes [62]. The three-time correlation function contains all the microscopic information relevant for the calculation of the line shape fluctuations described by Q. It has appeared as well in a recent paper of Plakhotnik [66] in the context of intensity-time-frequency-correlation technique. In the present work, important time-ordering properties of this function are fully investigated, and an analytical expression for Q is found. The relation between T2, tj)... 

Due to the stationarity of the process, T2, T3) does not depend on the time elapsing between start of observation t = 0 and tj. It has a similar mathematical structure to that of the nonlinear response function used to describe four-wave mixing spectroscopies such as photon echo or hole burning [62]. 

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