Modulation of the dephasing time for a magnetoplasma in a quantum well

We investigate the femtosecond kinetics of optically excited 2D magneto-plasma. We calculate the femtosecond dephasing and relaxation kinetics of the laser pulse excited magneto-plasma due to bare Coulomb potential scattering, because screening is under these conditions of minor importance. By taking into account four Landau subbands in both the conduction band and the valence band, we are now able to extend our earlier study [Phys. Rev. B {\bf 58}, 1998,in print (see also cond-mat/9808073] to lower magnetic fields. We can also fix the magnetic field and change the detuning to further investigate the carrier density-dependence of the dephasing time. For both cases, we predict strong modulation in the dephasing time.Comment: RevTex, 3 figures, to be published in Solid. Stat. Commu

Riemann zeros, prime numbers and fractal potentials

Using two distinct inversion techniques, the local one-dimensional potentials for the Riemann zeros and prime number sequence are reconstructed. We establish that both inversion techniques, when applied to the same set of levels, lead to the same fractal potential. This provides numerical evidence that the potential obtained by inversion of a set of energy levels is unique in one-dimension. We also investigate the fractal properties of the reconstructed potentials and estimate the fractal dimensions to be $D=1.5$ for the Riemann zeros and $D = 1.8$ for the prime numbers. This result is somewhat surprising since the nearest-neighbour spacings of the Riemann zeros are known to be chaotically distributed whereas the primes obey almost poisson-like statistics. Our findings show that the fractal dimension is dependent on both the level-statistics and spectral rigidity, $\Delta_3$, of the energy levels.Comment: Five postscript figures included in the text. To appear in Phys. Rev.

Strongly modulated transmissions in gapped armchair graphene nanoribbons with sidearm or on-site gate voltage

We propose two schemes of field-effect transistor based on gapped armchair graphene nanoribbons connected to metal leads, by introducing sidearms or on-site gate voltages. We make use of the band gap to reach excellent switch-off character. By introducing one sidearm or on-site gate to the graphene nanoribbon, conduction peaks appear inside the gap regime. By further applying two sidearms or on-site gates, these peaks are broadened to conduction plateaus with a wide energy window, thanks to the resonance from the dual structure. The position of the conduction windows inside the gap can be fully controlled by the length of the sidearms or the on-site gate voltages, which allows "on" and "off" operations for a specific energy window inside the gap regime. The high robustness of both the switch-off character and the conduction windows is demonstrated and shows the feasibility of the proposed dual structures for real applications.Comment: 6 pages, 6 figure

Comment on "Photon energy and carrier density dependence of spin dynamics in bulk CdTe crystal at room temperature"

We comment on the conclusion by Ma et al. [Appl. Phys. Lett. {\bf 94}, 241112 (2009)] that the Elliott-Yafet mechanism is more important than the D'yakonov-Perel' mechanism at high carrier density in intrinsic bulk CdTe at room temperature. We point out that the spin relaxation is solely from the D'yakonov-Perel' mechanism. The observed peak in the density dependence of spin relaxation time is exactly what we predicted in a recent work [Phys. Rev. B {\bf 79}, 125206 (2009)].Comment: 2 page

SOS-convex Semi-algebraic Programs and its Applications to Robust Optimization: A Tractable Class of Nonsmooth Convex Optimization

In this paper, we introduce a new class of nonsmooth convex functions called SOS-convex semialgebraic functions extending the recently proposed notion of SOS-convex polynomials. This class of nonsmooth convex functions covers many common nonsmooth functions arising in the applications such as the Euclidean norm, the maximum eigenvalue function and the least squares functions with $\ell_1$-regularization or elastic net regularization used in statistics and compressed sensing. We show that, under commonly used strict feasibility conditions, the optimal value and an optimal solution of SOS-convex semi-algebraic programs can be found by solving a single semi-definite programming problem (SDP). We achieve the results by using tools from semi-algebraic geometry, convex-concave minimax theorem and a recently established Jensen inequality type result for SOS-convex polynomials. As an application, we outline how the derived results can be applied to show that robust SOS-convex optimization problems under restricted spectrahedron data uncertainty enjoy exact SDP relaxations. This extends the existing exact SDP relaxation result for restricted ellipsoidal data uncertainty and answers the open questions left in [Optimization Letters 9, 1-18(2015)] on how to recover a robust solution from the semi-definite programming relaxation in this broader setting