Corrigendum: Self-consistent description of local density dynamics in simple liquids. The case of molten lithium (2018 J. Phys.: Condens. Matter 30 085102)

We wish to report the following corrections to the paper [1].

First, equation (25e) should be written as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq: Delta5} \Delta_5^2(k) &= \frac{1}{\Delta_{1}^{2}(k)\Delta_{2}^{2}(k)\Delta_{3}^{2}(k)\Delta_{4}^{2}(k)}\Bigg\{\langle \omega^{(10)}(k)\rangle \nonumber \\ & - 2\omega^{(8)}(k) \Big[\Delta_{1}^{2}(k)+\Delta_{2}^{2}(k)+ \Delta_{3}^{2}(k)+\Delta_{4}^{2}(k)\Big] \nonumber \\ & +\omega^{(6)}(k)\Big[\Delta_{1}^{4}(k)+2\Delta_{1}^{2}(k)\Delta_{2}^{2}(k)+\Delta_{2}^{4}(k)+4\Delta_{1}^{2}(k)\Delta_{3}^{2}(k) \nonumber \\& +2\Delta_{2}^{2}(k)\Delta_{3}^{2}(k)+\Delta_{3}^{4}(k)+4\Delta_{1}^{2}(k)\Delta_{4}^{2}(k) \Big]\Biggl\}+\Delta_{4}^{2}(k). \nonumber \end{align} \tag{ 1 }$$

Namely, the tenth frequency moment $\langle \omega^{(10)}(k)\rangle$ should be be written in angle brackets $\langle \ldots \rangle$.

Second, the factor $\Delta_3^2(k)$ is omitted in the third contribution of dispersion equation (45), and this dispersion equation should have the following form:

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq: dispersion_equation} s^3 &+ \frac{2 \Delta_3^2(k) \sqrt{\Delta_4^2(k)}}{2\Delta_4^2(k) - \Delta_3^2(k)}s^2+ \left [\Delta_1^2(k) + \Delta_2^2(k) + \frac{\Delta_2^2(k)\Delta_3^2(k)}{2\Delta_4^2(k)-\Delta_3^2(k)} \right] s \nonumber \\ & + \frac{2\Delta_1^2(k)\Delta_3^2(k)\sqrt{\Delta_4^2(k)}}{2\Delta_4^2(k) - \Delta_3^2(k)} = 0. \nonumber \end{align} \tag{ 2 }$$

Third, the subscript j  of the parameter $\Delta_{j+1}^2(k)$ in relation (A.8) in the appendix takes integer values including zero, and, therefore, this relation should be written as

$$\begin{align} \newcommand{\e}{{\rm e}} \displaystyle \label{eq_appendix_1} &\Delta_{j+1}^{2}(k)=\frac{\left\langle\left\{\mathrm{Re} [A_{j+1}(k,t)] \right \}^{2}+\left\{\mathrm{Im} [A_{j+1}(k,t)]\right \}^{2}\right\rangle}{\left\langle\left \{\mathrm{Re} [A_{j}(k,t)] \right \}^{2}+\left \{\mathrm{Im} [A_{j}(k,t)] \right \}^{2}\right\rangle}, \nonumber \\ &j=0,\;1,\;2,\;3,\; \ldots . \nonumber \end{align} \tag{ 3 }$$