Abstract:
The low flux infrared imaging needs performant high wavelength detectors. Quantum Well Infrared Photodetectors (QWIP), thanks to the maturity of GaAs, the possibility to adjust the detected wavelength on a large range and to realize large uniform matrix are good candidate for such applications. In order to validate this interest, we have performed an electro-optic characterization of a 15{\mu}m sample. These measurements have been used to simulate the performance of a camera based on this QWIP and used in a low infrared photons flux scenario. We predict that this QWIP would succeed. Nevertheless these simulations also underline the detrimental role of the dark current. Thus we have developed a simulation tool based on a hoping approach between localized states, which provide us a better understanding of the transport in these heterostructures. The code has in particular underlines the role plays by the electron -ionized impurities interaction, which make the dark current very sensitive to the doping profile. Using this tool we have designed new structures, with optimized doping profile, in which the scattering rate has been decreased by a factor two. Moreover we have identified a quantum origin to the plateau shape of the I(V) curve. This code is more generally a useful simulation tool for the transport in h\'et\'erostructures. The influence of growth defects (non ideal interface and disorder) has been quantized and we have performed the first evaluation of The R0A in a THz QCD. Finally non local transport effects have been investigated. Saw teeth observation on the I(V) curves have been modeled and their influence on the detectivty estimated.

Abstract:
A description of different phases of two dimensional magnetic insulators is given. The first chapters are devoted to the understanding of the symmetry breaking mechanism in the semi-classical Neel phases. Order by disorder selection is illustrated. All these phases break SU(2) symmetry and are gapless phases with magnon excitations. Different gapful quantum phases exist in two dimensions: the Valence Bond Crystal phases (VBC) which have long range order in local S=0 objects (either dimers in the usual Valence Bond acception or quadrumers..), but also Resonating Valence Bond Spin Liquids (RVBSL), which have no long range order in any local order parameter and an absence of susceptibility to any local probe. VBC have gapful S = 0, or 1 excitations, RVBSL on the contrary have deconfined spin-1/2 excitations. Examples of these two kinds of quantum phases are given in chapters 4 and 5. A special class of magnets (on the kagome or pyrochlore lattices) has an infinite local degeneracy in the classical limit: they give birth in the quantum limit to different behaviors which are illustrated and questionned in the last lecture.

Abstract:
The QED radiative corrections to virtual Compton scattering (reaction $e p \to e p \gamma$) are calculated to first order in $\alpha_{em} \equiv e^2 / 4 \pi$. A detailed study is presented for the one-loop virtual corrections and for the first order soft-photon emission contributions. Furthermore, a full numerical calculation is given for the radiative tail, corresponding with photon emission processes, where the photon energy is not very small compared with the lepton momenta. We compare our results with existing works on elastic electron-proton scattering, and show for the $e p \to e p \gamma$ reaction how the observables are modified due to these first order QED radiative corrections. We show results for both unpolarized and polarized observables of the virtual Compton scattering in the low energy region (where one is sensitive to the generalized polarizabilities of the nucleon), as well as for the deeply virtual Compton scattering.

Abstract:
Recently new reactor antineutrino spectra have been provided for 235U, 239Pu, 241Pu and 238U, increasing the mean flux by about 3 percent. To good approximation, this reevaluation applies to all reactor neutrino experiments. The synthesis of published experiments at reactor-detector distances <100 m leads to a ratio of observed event rate to predicted rate of 0.976(0.024). With our new flux evaluation, this ratio shifts to 0.943(0.023), leading to a deviation from unity at 98.6% C.L. which we call the reactor antineutrino anomaly. The compatibility of our results with the existence of a fourth non-standard neutrino state driving neutrino oscillations at short distances is discussed. The combined analysis of reactor data, gallium solar neutrino calibration experiments, and MiniBooNE-neutrino data disfavors the no-oscillation hypothesis at 99.8% C.L. The oscillation parameters are such that |Delta m_{new}^2|>1.5 eV^2 (95%) and sin^2(2\theta_{new})=0.14(0.08) (95%). Constraints on the theta13 neutrino mixing angle are revised.

Abstract:
In this paper we report the latest results of exact diagonalizations of SU(2) invariant models on various lattices (square, triangular, hexagonal, checkerboard and kagome lattices). We focus on the low lying levels in each S sector. The differences in behavior between gapless systems and gapped ones are exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on the kagome lattice is discussed. A rough estimate of the spin susceptibility in such an hypothesis is given.The evolution of the intra-S channel spectra under the effect of a small perturbation is consistent with the proximity of a quantum critical point. We emphasize that the very small intra-S channel energy scale observed in exact spectra is a very interesting information to understand the low T dynamics of this model.

Abstract:
We determine dynamical response functions of the S=1/2 Heisenberg quantum antiferromagnet on the kagome lattice based on large-scale exact diagonalizations combined with a continued fraction technique. The dynamical spin structure factor has important spectral weight predominantly along the boundary of the extended Brillouin zone and energy scans reveal broad response extending over a range of 2 \sim 3J concomitant with pronounced intensity at lowest available energies. Dispersive features are largely absent. Dynamical singlet correlations -- which are relevant for inelastic light probes -- reveal a similar broad response, with a high intensity at low frequencies omega/J \lesssim 0.2J. These low energy singlet excitations do however not seem to favor a specific valence bond crystal, but instead spread over many symmetry allowed eigenstates.

Abstract:
The properties of the groundstate and first excitations of 2dimensionnal quantum antiferromagnets are rapidly sketched. A special emphasis is put on the gapped phases: Valence Bond Crystals and the two types of Spin Liquids. New results on the spin susceptibility of small samples of the Heisenberg antiferromagnet on a kagom\'e lattice are displayed for comparison with Kagemaya {\it et al.} experimental result (this conference).

Abstract:
The extension of the Lieb-Schultz-Mattis theorem to dimensions larger than one is discussed. It is explained why the variational wave-function built by the previous authors is of no help to prove the theorem in dimension larger than one. The short range R.V.B. picture of Sutherland, Rokhsar and Kivelson, Read and Chakraborty gives a strong support to the assertion that the theorem is indeed valid in any dimension. Some illustrations of the general ideas are displayed on exact spectra.

Abstract:
We present a method to compute the magnetic susceptibility of spin systems at all temperatures in one and two dimensions. It relies on an approximation of the entropy versus energy (microcanonical potential function) on the whole range of energies. The intrinsic constraints on the entropy function and a careful treatment of boundary behaviors allow to extend the standard high temperature series expansions (HTE) towards zero temperature, overcoming the divergence of truncated HTE. This method is benchmarked against two one-dimensional solvable models: the Ising model in longitudinal field and the XY model in a transverse field. With ten terms in the HTE, we find a spin susceptibility within a few \% of the exact results in the whole range of temperature. The method is then applied to two two-dimensional models: the supposed-to-be gapped Heisenberg model and the $J_1$-$J_2$-$J_d$ model on the kagome lattice.

Abstract:
In these lectures we sketch a rapid survey of recent theoretical advances in the study of frustrated quantum magnets with a special emphasis on two dimensional magnets.