Semiclassical Coulomb field

The contribution of different modes of the Coulomb field to decoherence and to the dynamical breakdown of the time reversal invariance is calculated in the one-loop approximation for nonrelativistic electron gas. The dominant contribution was found to come from the usual collective modes in the plasma, namely, the zero-sound and the plasmon oscillations. The length scale of the quantum-classical transition is found to be close to the Thomas-Fermi screening length. It is argued that the extension of these modes to the whole Fock space yields optimal pointer states.

Figure 1

The frequency-wave vector plane of Coulomb photons.

Figure 2

${\mathit{q}}^2-L_{|\omega |,\mathit{q}}$ plotted on the segment $0.1<q,z<0.3$ of the frequency-wave vector plane for $r_s=0.05$. The function has a valley stretching from the origin along the line $z=q$. The function is increasing in the valley as we move away from the origin and the minimum of the valley reaches zero at $z\approx q=0.1875$.

Figure 3

$1/({\mathit{q}}^2-L_{|\omega |,\mathit{q}})$ as the function of $z$ and $q$ for $r_s=0.05$. The function diverges along the zero-sound/plasmon line but its value is cut at 100 for easier visualization.

Figure 4

The classicality, Eq. (27), as the function of $z$ and $q$ for $r_s=0.05$. The shape of this function is qualitatively similar to that shown in Fig. 3 except the part with vanishing $r_{\omega ,\mathit{q}}$ is replaced by zero. The value of the function is cut at 1.5 for easier visualization.

Figure 5

The ratios ${\omega }_{\mathrm{cl}}/{\omega }_{\mathrm{pl}}$ and $k_{\mathrm{cl}}/k_{\mathrm{TF}}$ as the functions of $r_s$. The straight lines correspond to the fit (31, 32).