Density Matrix Formalism: Hamilton and Current Density Operators – Gauge Invariance

  • Ole KellerEmail author
Part of the Nano-Optics and Nanophotonics book series (NON, volume 2)


In Chap. 10, we discussed the microscopic linear response theory from a general point of view paying special attention to spatial nonlocality. The response tensors \(\vec{\Sigma }(\vec{r},\vec{r}\prime;\omega )\) and \(\vec{R}(\vec{r},\vec{r}\prime;\omega )\), describing the microscopic current density (\(\vec{J}(\vec{r};\omega )\)) induced by the transverse part (\(\vec{{E}}_{\mathrm{T}}(\vec{r};\omega )\)) of the local electric field and the longitudinal part (\(\vec{{E}}_{\mathrm{L}}^{\mathrm{ext}}(\vec{r};\omega )\)) of the external field, respectively, played a central role in our discussion but no attempts were made to carry out an explicit calculation of these quantities.

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  1. 1.Institut for FysikAalborg UniversitetAalborgDenmark

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