Quantum-beat Auger spectroscopy

The concept of nonlinear quantum-beat pump-probe Auger spectroscopy is introduced by discussing a relatively simple four-level model system. We consider a coherent wave packet involving two low-lying states that was prepared by an appropriate pump pulse. This wave packet is subsequently probed by a weak, time-delayed probe pulse with nearly resonant coupling to a core-excited state of the atomic or molecular system. The resonant Auger spectra are then studied as a function of the duration of the probe pulse and the time delay. With a bandwidth of the probe pulse approaching the energy spread of the wave packet, the Auger yields and spectra show quantum beats as a function of pump-probe delay. An analytic theory for the quantum-beat Auger spectroscopy will be presented, which allows for the reconstruction of the wave packet by analyzing the delaydependent Auger spectra. The possibility of extending this method to a more complex manifold of electronic and vibrational energy levels is also discussed.Comment: 13 papees,6 figure

Tests for High Dimensional Generalized Linear Models

We consider testing regression coefficients in high dimensional generalized linear models. An investigation of the test of Goeman et al. (2011) is conducted, which reveals that if the inverse of the link function is unbounded, the high dimensionality in the covariates can impose adverse impacts on the power of the test. We propose a test formation which can avoid the adverse impact of the high dimensionality. When the inverse of the link function is bounded such as the logistic or probit regression, the proposed test is as good as Goeman et al. (2011)'s test. The proposed tests provide p-values for testing significance for gene-sets as demonstrated in a case study on an acute lymphoblastic leukemia dataset.Comment: The research paper was stole by someone last November and illegally submitted to arXiv by a person named gong zi jiang nan. We have asked arXiv to withdraw the unfinished paper [arXiv:1311.4043] and it was removed last December. We have collected enough evidences to identify the person and Peking University has begun to investigate the plagiarize

Cone spherical metrics and stable vector bundles

Cone spherical metrics are conformal metrics with constant curvature one and finitely many conical singularities on compact Riemann surfaces. A cone spherical metric is called irreducible if each developing map of the metric does not have monodromy lying in ${\rm U(1)}$. We establish on compact Riemann surfaces of positive genera a correspondence between irreducible cone spherical metrics with cone angles being integral multiples of $2\pi$ and line subbundles of rank two stable vector bundles. Then we are motivated by it to prove a theorem of Lange-type that there always exists a stable extension of $L^*$ by $L$, for $L$ being a line bundle of negative degree on each compact Riemann surface of genus greater than one. At last, as an application of these two results, we obtain a new class of irreducible spherical metrics with cone angles being integral multiples of $2\pi$ on each compact Riemann surface of genus greater than oneComment: 22 pages, Submitte

1.55 µm AlGaInAs/InP sampled grating laser diodes for mode-locking at THz frequencies

We report mode locking in lasers integrated with semiconductor optical amplifiers, using either conventional or phase shifted sampled grating distributed Bragg reflectors(DBRs). For a conventional sampled grating with a continuous grating coupling coefficient of ~80 cm-1, mode-locking was observed at a fundamental frequency of 628 GHz and second harmonic of 1.20 THz. The peak output power was up to 142 mW. In the phase shifted sampled grating design, the grating is present along the entire length of the reflector with π-phase shift steps within each sampled section. The effective coupling coefficient is therefore increased substantially. Although the continuous grating coupling coefficient for the phase shifted gratings was reduced to ~23 cm-1 because of a different fabrication technology, the lasers demonstrated mode locking at fundamental repetition frequencies of 620 GHz and 1 THz, with a much lower level of amplified spontaneous emission seen in the output spectra than from conventional sampled grating devices. Although high pulse reproducibility and controllability over a wide operation range was seen for both types of grating, the π-phase-shifted gratings already demonstrate fundamental mode-locking to 1 THz. The integrated semiconductor optical amplifier makes sampled grating DBR lasers ideal pump sources for generating THz signals through photomixing