\noindentwhere
the notation
is used. The properties of \(n^{\prime(y)}(\mathbf{r},\tau_{y})\) are also similar with to those of \(n^{\prime(x)}(\mathbf{r},\tau_{x})\). At \({V_{0}=0}\), the frequency branches coincide; therefore, in order to derive \(n^{\prime(y)}(\mathbf{r},\tau_{y})\) from \(n^{\prime(x)}(\mathbf{r},\tau_{x}),\) the substitution \({X\leftrightarrow Y}\) should be made. The same concerns Fig. 4 as well. In contrast to \(n^{\prime(x)}(\mathbf{r},\tau_{x})\), \(n^{\prime(y)}(\mathbf{r},\tau_{y})\) is an odd function of the coordinate \(y\) for an arbitrary \(V_{0}\), which is connected with a constant orientation of the dipole in parallel to the \(OY\) axis. Figure 8 illustrates the coordinate (panel \(a\)) and coordinate-time (panel \(b\)) dependences of the electron concentration perturbation, which corresponds to the \(y\)-branch at the electron drift. At \({Y=0}\), the integrand in the integral \(J_{y}(\mathbf{r})\) is an odd function, so that \({n^{\prime(y)}(x,y=0,\tau_{y})=0}\). Therefore, Fig. 8 was plotted for \(y=0.5\). It can be interpreted like Fig. 7,\(b\): perturbations are blown down the electron streams; however, in this case, perturbation minima transform into maxima and vice versa.
Hence, in this section, we determined the behavior of perturbations in the two-dimensional electron gas in the hybrid system for various types of solutions, which takes into account whether or not the electrons drift.