We study Faraday rotation in the quantum relativistic limit. Starting from the photon self-energy in the presence of a constant magnetic field the rotation of the polarization vector of a plane electromagnetic wave which travel along the fermion-antifermion gas is studied. The connection between Faraday Effect and Quantum Hall Effect (QHE) is discussed. The Faraday Effect is also investigated for a massless relativistic (2D+1)-dimensional fermion system which is derived by using the compactification along the dimension parallel to the magnetic field. The Faraday angle shows a quantized behavior as Hall conductivity in two and three dimensions.
We study the (2+1)-dimensional Dirac oscillator in the presence of an external uniform magnetic field ($B$). We show how the change of the strength of $B$ leads to the existence of a quantum phase transition in the chirality of the system. A critical
value of the strength of the external magnetic field ($B_c$) can be naturally defined in terms of physical parameters of the system. While for $B=B_c$ the fermion can be considered as a free particle without defined chirality, for $B<B_c$ ($B>B_c$) the chirality is left (right) and there exist a net potential acting on the fermion. For the three regimes defined in the quantum phase transition of chirality, we observe that the energy spectra for each regime is drastically different. Then, we consider the $z$-component of the orbital angular momentum as an order parameter that characterizes the quantum phase transition.
We proposed an action of neutral fermions interacting with external electromagnetic fields to construct a 3+1 dimensional topological field theory as the effective action attained by integrating out the fermionic fields in the related path integral.
These neutral quasiparticles are assumed to emerge from the collective behavior of the original physical particles and holes (antiparticles). Although our construction is general it is particularly useful to formulate effective actions of the time reversal invariant topological insulators.
We show that the mixing effect of the neutral gauge bosons in the 3-3-1-1 model comes from two sources. The first one is due to the 3-3-1-1 gauge symmetry breaking as usual, whereas the second one results from the kinetic mixing between the gauge bos
ons of U(1)_X and U(1)_N groups, which are used to determine the electric charge and baryon minus lepton numbers, respectively. Such mixings modify the rho-parameter and the known couplings of Z with fermions. The constraints that arise from flavor-changing neutral currents due to the gauge boson mixings and non-universal fermion generations are also given.
The possibility that particle production in high-energy collisions is a result of two asymmetric hydrodynamic flows is investigated, using the Khalatnikov form of the 1+1-dimensional approximation of hydrodynamic equations. The general solution is di
scussed and applied to the physically appealing generalized in-out cascade where the space-time and energy-momentum rapidities are equal at initial temperature but boost-invariance is not imposed. It is demonstrated that the two-bump structure of the entropy density, characteristic of the asymmetric input, changes easily into a single broad maximum compatible with data on particle production in symmetric processes. A possible microscopic QCD interpretation of asymmetric hydrodynamics is proposed.
Two-dimensional electron or hole systems in semiconductors offer the unique opportunity to investigate the physics of strongly interacting fermions. We have measured the 1/f resistance noise of two-dimensional hole systems in high mobility GaAs quant
um wells, at densities below that of the metal-insulator transition (MIT) at zero magnetic field. Two techniques voltage and current fluctuations were used. The normalized noise power SR/R2 increases strongly when the hole density or the temperature are decreased. The temperature dependence is steeper at the lowest densities. This contradicts the predictions of the modulation approach in the strong localization hopping transport regime. The hypothesis of a second order phase transition or percolation transition at a density below that of the MIT is thus reinforced.