We investigate the relation between the canonical model of quantum optics, the Jaynes-Cummings Hamiltonian and Dirac fermions in quantizing magnetic field. We demonstrate that Rabi oscillations are observable in the optical response of graphene, prov
iding us with a transparent picture about the structure of optical transitions. While the longitudinal conductivity reveals chaotic Rabi oscillations, the Hall component measures coherent ones. This opens up the possibility of investigating a microscopic model of a few quantum objects in a macroscopic experiment with tunable parameters.
The scattering of conduction electrons by crystalline electric field (CEF) excitations may enhance their effective quasiparticle mass similar to scattering from phonons. A wellknown example is Pr metal where the isotropic exchange scattering from ine
lastic singlet-singlet excitations causes the mass enhancement. An analogous mechanism may be at work in the skutterudite compounds Pr_{1-x}La_xOs_4Sb_12 where close to x=1 the compound develops heavy quasiparticles with a large linear specific heat coefficient. There the low lying CEF states are singlet ground state and a triplet at 8 K. Due to the tetrahedral CEF the main scattering mechanism must be the aspherical Coulomb scattering. We derive the expression for mass enhancement in this model including also the case of dispersive excitations. We show that for small to moderate dispersion there is a strongly field dependent mass enhancement due to the field induced triplet splitting. It is suggested that this effect may be seen in Pr_{1-x}La_xOs_4Sb_12 with suitably large x when the dispersion is small.
A phenomenological description for the dynamical spin susceptibility $chi({bf q},omega;T)$ observed in inelastic neutron scattering measurements on powder samples of LiV$_2$O$_4$ is developed in terms of the parametrized self-consistent renormalizati
on (SCR) theory of spin fluctuations. Compatible with previous studies at $Tto 0$, a peculiar distribution in ${bf q}$-space of strongly enhanced and slow spin fluctuations at $q sim Q_c simeq$ 0.6 $AA^{-1}$ in LiV$_2$O$_4$ is involved to derive the mode-mode coupling term entering the basic equation of the SCR theory. The equation is solved self-consistently with the parameter values found from a fit of theoretical results to experimental data. For low temperatures, $T lesssim 30$K, where the SCR theory is more reliable, the observed temperature variations of the static spin susceptibility $chi(Q_c;T)$ and the relaxation rate $Gamma_Q(T)$ at $qsim Q_c$ are well reproduced by those suggested by the theory. For $Tgtrsim 30$K, the present SCR is capable in predicting only main trends in $T$-dependences of $chi(Q_c;T)$ and $Gamma_Q(T)$. The discussion is focused on a marked evolution (from $q sim Q_c$ at $Tto 0$ towards low $q$ values at higher temperatures) of the dominant low-$omega$ integrated neutron scattering intensity $I(q; T)$.
The effect of weak potential and bond disorder on the density of states of graphene is studied. By comparing the self-consistent non-crossing approximation on the honeycomb lattice with perturbation theory on the Dirac fermions, we conclude, that the
linear density of states of pure graphene changes to a non-universal power-law, whose exponent depends on the strength of disorder like 1-4g/sqrt{3}t^2pi, with g the variance of the Gaussian disorder, t the hopping integral. This can result in a significant suppression of the exponent of the density of states in the weak-disorder limit. We argue, that even a non-linear density of states can result in a conductivity being proportional to the number of charge carriers, in accordance with experimental findings.
