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Correlations, highly important in low--dimensional systems, are known todecrease the plasmon dispersion of two-dimensional electron liquids. Here wecalculate the plasmon properties, applying the 'Dynamic Many-Body Theory',accounting for correlated two-particle--two-hole fluctuations. These dynamiccorrelations are found to significantly lower the plasmon's energy. For thedata obtained numerically, we provide an analytic expression that is validacross a wide range both of densities and of wave vectors. Finally, wedemonstrate how this can be invoked in determining the actual electrondensities from measurements on an AlGaAs quantum well.

Dynamic correlations in the highly dilute 2D electron liquid: loss function, critical wave vector and analytic plasmon dispersion