Nonperturbative model for optical response under intense periodic fields with application to graphene in a strong perpendicular magnetic field

Graphene exhibits extremely strong optical nonlinearity when a strong perpendicular magnetic field is applied, the response current shows strong field dependence even for moderate light intensity, and the perturbation theory fails. We nonperturbatively calculate full optical conductivities induced by a periodic field in an equation-of-motion framework based on the Floquet theorem, with the scattering described phenomenologically. The nonlinear response at high fields is understood in terms of the dressed electronic states, or Floquet states, which is further characterized by the optical conductivity for a weak probe light field. This approach is illustrated for a magnetic field at $5$ T and a driving field with photon energy $0.05$ eV. Our results show that the perturbation theory works only for weak fields $<3$ kV/cm, confirming the extremely strong light matter interaction for Landau levels of graphene. This approach can be easily extended to the calculation of optical conductivities in other systems

Analytical smoothing effect of solution for the boussinesq equations

In this paper, we study the analytical smoothing effect of Cauchy problem for the incompressible Boussinesq equations. Precisely, we use the Fourier method to prove that the Sobolev H 1-solution to the incompressible Boussinesq equations in periodic domain is analytic for any positive time. So the incompressible Boussinesq equation admet exactly same smoothing effect properties of incompressible Navier-Stokes equations

Nonlinear magneto-optic effects in doped graphene and gapped graphene: a perturbative treatment

The nonlinear magneto-optic responses are investigated for gapped graphene and doped graphene in a perpendicular magnetic field. The electronic states are described by Landau levels, and the electron dynamics in an optical field is obtained by solving the density matrix in the equation of motion. In the linear dispersion approximation around the Dirac points, both linear conductivity and third order nonlinear conductivities are numerically evaluated for infrared frequencies. The nonlinear phenomena, including third harmonic generation, Kerr effects and two photon absorption, and four wave mixing, are studied. All optical conductivities show strong dependence on the magnetic field. At weak magnetic fields, our results for doped graphene agree with those in the literature. We also present the spectra of the conductivities of gapped graphene. At strong magnetic fields, the third order conductivities show peaks with varying the magnetic field and the photon energy. These peaks are induced by the resonant transitions between different Landau levels. The resonant channels, the positions, and the divergences of peaks are analyzed. The conductivities can be greatly modified, up to orders of magnitude. The dependence of the conductivities on the gap parameter and the chemical potential is studied.Comment: 18 pages, 8 figure

A Morphological Approach to the Pulsed Emission from Soft Gamma Repeaters

We present a geometrical methodology to interpret the periodical light curves of Soft Gamma Repeaters based on the magnetar model and the numerical arithmetic of the three-dimensional magnetosphere model for the young pulsars. The hot plasma released by the star quake is trapped in the magnetosphere and photons are emitted tangent to the local magnetic field lines. The variety of radiation morphologies in the burst tails and the persistent stages could be well explained by the trapped fireballs on different sites inside the closed field lines. Furthermore, our numerical results suggests that the pulse profile evolution of SGR 1806-20 during the 27 December 2004 giant flare is due to a lateral drift of the emitting region in the magnetosphere.Comment: 7 figures, accepted by Ap

Physical modelling of amorphous thermoplastic polymer and numerical simulation of micro hot embossing process

Micro hot embossing process is considered as one of the most promising micro replication processes for manufacturing of polymeric components, especially for the high aspect ratio components and large surface structural components. A large number of hot embossing experimental results have been published, the material modelling and processes simulation to improve the quality of micro replication by hot embossing process are still lacking. This paper consists to 3D modelling of micro hot embossing process with amorphous thermoplastic polymers, including the mechanical characterisation of polymers properties, identification of the viscoelastic behaviour law of the polymers, numerical simulation and experimental investigation of micro hot embossing process. Static compression creep tests have been carried out to investigate the selected polymers’ viscoelastic properties. The Generalized Maxwell model has been proposed to describe the relaxation modulus of the polymers and good agreement has been observed. The numerical simulation of the hot embossing process in 3D has been achieved by taking into account the viscoelastic behaviour of the polymers. The microfluidic devices with the thickness of 2 mm have been elaborated by hot embossing process. The hot embossing process has been carried out using horizontal injection/compression moulding equipment, especially developed for this study. A complete compression mould tool, equipped with the heating system, the cooling system, the ejection system and the vacuum system, has been designed and elaborated in our research. Polymer-based microfluidic devices have been successfully replicated by the hot embossing process using the compression system developed. Proper agreement between the numerical simulation and the experimental elaboration has been observed. It shows strong possibility for the development of the 3D numerical model to optimize the micro hot embossing process in the future

Collective Quartics and Dangerous Singlets in Little Higgs

Any extension of the standard model that aims to describe TeV-scale physics without fine-tuning must have a radiatively-stable Higgs potential. In little Higgs theories, radiative stability is achieved through so-called collective symmetry breaking. In this letter, we focus on the necessary conditions for a little Higgs to have a collective Higgs quartic coupling. In one-Higgs doublet models, a collective quartic requires an electroweak triplet scalar. In two-Higgs doublet models, a collective quartic requires a triplet or singlet scalar. As a corollary of this study, we show that some little Higgs theories have dangerous singlets, a pathology where collective symmetry breaking does not suppress quadratically-divergent corrections to the Higgs mass.Comment: 4 pages; v2: clarified the existing literature; v3: version to appear in JHE