The Relationship Between the Exact Exchange Potential and Dephasing Induced by Coulomb Interaction in Quantum Plasmonics

The Coulomb exchange interaction can not only provide an exchange potential (real part), but also can generate optical polarization dephasing (imaginary part). Based on the density matrix as well as the electron scattering theory, in this paper, we reveal the relationship between the exact exchange potential and the exchange-induced dephasing time in quantum plasmonics. Our results indicate that the linewidth of the nanoplasmonics is mainly determined by a first-order Coulomb interaction in the Hartree-Fock approximation rather than a second-order (or high-order) interaction. Meanwhile, the exact exchange potential, a long-term problem to use this nonlocal functional in practical system for huge computation, can be calculated from the corresponding simple damping factor with great efficiency. In addition, since the Coulomb screening effect is automatically included, this relation provides a new thought to detect and test how the nonlocal exchange functions are related to the density-dependent screening Coulomb effect, hence the development of the density functional theory in chemistry and condensed matter physics. Finally, numerical simulations demonstrate that our model can reveal more quantum phenomena than traditional methods in nanoplasmonics, and these quantum features are consistent with the results obtained from the first principles.