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The Dicke model of cavity quantum electrodynamics is approximately realized in condensed matter when the cyclotron transition of a two-dimensional electron gas is nearly resonant with a cavity photon mode.
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In the ultrastrong limit the strength of the radiation-induced coupling between two consecutive LLs is of the same order as the bare cyclotron transition energy
Cited in the paper.
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Strictly speaking this derivative yields the current operator Fourier component with wavevector 𝒒 {\bm{q}} equal to the lateral wavevector of the privileged photon mode. In practice 𝒒 = 𝟎 {\bm{q}}={\bm{0}}
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In a crystal the momentum-space response functions χ μ ν \chi^{\mu\nu} and K μ ν K^{\mu\nu} are matrices
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Note that in a homogeneous and isotropic liquid Ξ μ ν ( q ) \Xi^{\mu\nu}(q) can be decomposed into a longitudinal and a transverse part: Ξ μ ν ( q ) = ( q μ q ν / q 2 ) Ξ L ( q ) + ( δ μ ν − q μ q ν / q 2 ) Ξ T ( q ) \Xi^{\mu\nu}(q)=(q_{\mu}q_{\nu}/q^{2})\Xi_{\rm L}(q)+(\delta_{\mu\nu}-q_{\mu}q_{\nu}/q^{2})\Xi_{\rm T}(q) . The following properties hold true [ 13 , 14 ] : Ξ L ( q ) = 0 \Xi_{\rm L}(q)=0 for every q q and lim q → 0 Ξ T ( q ) = 0 \lim_{q\to 0}\Xi_{\rm T}(q)=0 (diamagnetic sum rule)
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