Floquet analysis of pulsed Dirac systems: A way to simulate rippled graphene

The low energy continuum limit of graphene is effectively known to be modeled using Dirac equation in (2+1) dimensions. We consider the possibility of using modulated high frequency periodic driving of a two-dimension system (optical lattice) to simulate properties of rippled graphene. We suggest that the Dirac Hamiltonian in a curved background space can also be effectively simulated by a suitable driving scheme in optical lattice. The time dependent system yields, in the approximate limit of high frequency pulsing, an effective time independent Hamiltonian that governs the time evolution, except for an initial and a final kick. We use a specific form of 4-phase pulsed forcing with suitably tuned choice of modulating operators to mimic the effects of curvature. The extent of curvature is found to be directly related to $\omega^{-1}$ the time period of the driving field at the leading order. We apply the method to engineer the effects of curved background space. We find that the imprint of curvilinear geometry modifies the electronic properties, such as LDOS, significantly. We suggest that this method shall be useful in studying the response of various properties of such systems to non-trivial geometry without requiring any actual physical deformations.Comment: 16 pages, 1 figure. Suggestions and comments are welcom

Primordial Non-Gaussianity in the Forest: 3D Bispectrum of Ly-alpha Flux Spectra Along Multiple Lines of Sight

We investigate the possibility of constraining primordial non-Gaussianity using the 3D bispectrum of Ly-alpha forest. The strength of the quadratic non-Gaussian correction to an otherwise Gaussian primordial gravitational field is assumed to be dictated by a single parameter fnl. We present the first prediction for bounds on fnl using Ly-alpha flux spectra along multiple lines of sight. The 3D Ly-$\alpha$ transmitted flux field is modeled as a biased tracer of the underlying matter distribution sampled along 1D skewers corresponding to quasars sight lines. The precision to which fnl can be constrained depends on the survey volume, pixel noise and aliasing noise (arising from discrete sampling of the density field). We consider various combinations of these factors to predict bounds on fnl. We find that in an idealized situation of full sky survey and negligible Poisson noise one may constrain fnl ~ 23 in the equilateral limit. Assuming a Ly-alpha survey covering large parts of the sky (k_{min} = 8 * 10^{-4} Mpc^{-1}) and with a quasar density of \bar n = 5 * 10^{-3} Mpc^{-2} it is possible to constrain fnl ~ 100 for equilateral configurations. The possibility of measuring fnl at a precision comparable to LSS studies maybe useful for joint constraining of inflationary scenarios using different data sets.Comment: 4 pages, 1 figure, 1 table. Accepted for publication in Physical Review Letter