A concise proof of the Multiplicative Ergodic Theorem on Banach spaces

We give a streamlined proof of the multiplicative ergodic theorem for quasi-compact operators on Banach spaces with a separable dual.Comment: 18 page

Effects of Foreign Exchange Intervention Under Public Information: the Chilean Case

This paper studies the effects of exchange rate interventions using daily and intraday data for Chile, from 1998 to 2003. Its main contribution is the recognition of the role played by transparency and public announcements in the success of the intervention policy, through the existence of an expectations mechanism which directly impacts the exchange rate. Three foreign exchange policy instruments are distinguished –spot, dollar denominated papers (BCD´s) and announcements- and treated as independent interventions. Time series estimations are used to capture the effect of the traditionally studied spot interventions, as well as the effects associated to the announcement channel that we propose as potentially relevant. Results show that the impact of individual interventions (spot and BCD) are extremely small and, in most cases, non-significant. Also, the importance of the hypothesized announcement mechanism is confirmed. The impact of Central Bank actions on the exchange rate’s level and trend seem to be channeled through the public announcements made by the monetary authority. The market adjusts its expectations to the information revealed through them, with the exchange rate responding accordingly. These effects occur on longer time spans than the ones suggested by the traditional literature. The negligible effect of individual interventions is also found, for the year 2001, with the use of intraday data.

Continuous wave lasing between Landau levels in graphene

We predict the general feasibility and demonstrate the specific design of the THz laser operating between Landau levels in graphene placed on a polar substrate in a magnetic field of order 1 T. Steady state operation under a continuous wave optical pumping is possible due to an interplay between Auger and surface-phonon mediated relaxation of carriers. The scheme is scalable to other materials with massless Dirac fermions, for example surface states in 3D topological insulators such as Bi$_2$Se$_3$ or Bi$_2$Te$_3$.Comment: 12 pages, 5 figure

Second-order nonlinear optical response of graphene

Although massless Dirac fermions in graphene constitute a centrosymmetric medium for in-plane excitations, their second-order nonlinear optical response is nonzero if the effects of spatial dispersion are taken into account. Here we present a rigorous quantum-mechanical theory of the second-order nonlinear response of graphene beyond the electric dipole approximation, which includes both intraband and interband transitions. The resulting nonlinear susceptibility tensor satisfies all symmetry and permutation properties, and can be applied to all three-wave mixing processes. We obtain useful analytic expressions in the limit of a degenerate electron distribution, which reveal quite strong second-order nonlinearity at long wavelengths, Fermi-edge resonances, and unusual polarization properties.Comment: The new version makes the bold font vector notation uniform throughout the paper and corrects a misprint in Eq. (34): replaces v_F^2 with v_F^3 in the common facto

Generation of entangled photons in graphene in a strong magnetic field

Entangled photon states attract tremendous interest as the most vivid manifestation of nonlocality of quantum mechanics and also for emerging applications in quantum information. Here we propose a mechanism of generation of polarization-entangled photons, which is based on the nonlinear optical interaction (four-wave mixing) in graphene placed in a magnetic field. Unique properties of quantized electron states in a magnetized graphene and optical selection rules near the Dirac point give rise to a giant optical nonlinearity and a high rate of photon production in the mid/far-infrared range.Comment: 5 pages, 4 figure

Efficient nonlinear generation of THz plasmons in graphene and topological insulators

Surface plasmons in graphene may provide an attractive alternative to noble-metal plasmons due to their tighter confinement, peculiar dispersion, and longer propagation distance. We present theoretical studies of the nonlinear difference frequency generation of terahertz surface plasmon modes supported by two-dimensional layers of massless Dirac electrons, which includes graphene and surface states in topological insulators. Our results demonstrate strong enhancement of the DFG efficiency near the plasmon resonance and the feasibility of phase-matched nonlinear generation of plasmons over a broad range of frequencies.Comment: 5 pages, 4 figure