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Radiation fields for nanoscale systems

For a group of charged particles obeying quantum mechanics interacting with an electromagnetic field, the charge and current density in a pure state of the system are expressed with the many-body wave function of the state. Using these as sources, the microscopic Maxwell equations can be written down for any given pure state of a many-body system. By employing semi-classical radiation theory with these sources, the microscopic Maxwell equations can be used to compute the strong radiation fields produced by interacting charged quantal particles. For a charged quantal particle, three radiation fields involve only the vector potential $\mathbf{A}$. This is another example demonstrating the observability of vector potential. Five radiation fields are perpendicular to the canonical momentum of a single charged particle. For a group of charged particles, a new type of radiation field is predicted to be perpendicular to $\mathbf{A}(\mathbf{x}_{j},t)\times \lbrack\nabla\times(\nabla_{j}Ψ^{\prime})]$, where $Ψ^{'}$ is the many-body wave function. This kind of radiation does not exist for a single charged particle. The macroscopic Maxwell equations are derived from the corresponding microscopic equations for a pure state by the Russakoff-Robinson procedure which requires only a spatial coarse graining. Because the sources of fields are also the responses of a system to an external field, one also has to give up the temporal coarse graining of the current density which is often supposed to be critical in the kinetic approach of conductivity.