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Classically the interaction between light and matter is given by the Maxwell relations. These are briefly reviewed and will be used as a basis to discuss several techniques that are used in optical spectroscopy. We then discuss the quantum mechanical description of the optical conductivity based on the Kubo formalism. This is used as a basis to understand how strong correlation effects can be observed using optical techniques. We will discuss the use of sum rules in the interpretation of optical experiments. Finally, we describe the effect of including interactions between electronic and collective degrees of freedom on optical spectra.
An essential ingredient in many model Hamiltonians, such as the Hubbard model, is the effective electron-electron interaction $U$, which enters as matrix elements in some localized basis. These matrix elements provide the necessary information in the
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We study the physics of cold polar molecules loaded into an optical lattice in the regime of strong three-body interactions, as put forward recently by Buchler [Nature Phys. 3, 726 (2007)]. To this end quantum Monte Carlo simulations, exact diagonali
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