Electric current in a translation invariant environment

The master equation for the reduced density matrix of a charged particle interacting with a translation invariant weakly coupled environment is considered. The electric current is renormalized by the system-environment interaction, leading to a direct signature of the environment in the bremsstrahlung. The general solution is given in the absence of the external electromagnetic field, and the spread and the decoherence of a wave packet are followed. The increased complexity and importance of the boundary conditions for the density matrix are pointed out.

Figure 1

The discontinuity of the potential on the plane $(x,x_d)$. The density matrix in the regions with an index $P$ or a star can be obtained by spatial inversion, $x\to -x$, $x_d\to -x_d$, or complex conjugation, respectively.