A Recursion Formula for Moments of Derivatives of Random Matrix Polynomials

We give asymptotic formulae for random matrix averages of derivatives of characteristic polynomials over the groups USp(2N), SO(2N) and O^-(2N). These averages are used to predict the asymptotic formulae for moments of derivatives of L-functions which arise in number theory. Each formula gives the leading constant of the asymptotic in terms of determinants of hypergeometric functions. We find a differential recurrence relation between these determinants which allows the rapid computation of the (k+1)-st constant in terms of the k-th and (k-1)-st. This recurrence is reminiscent of a Toda lattice equation arising in the theory of \tau-functions associated with Painlev\'e differential equations

Transient chirp in high speed photonic crystal quantum dots lasers with controlled spontaneous emission

We report on a series of experiments on the dynamics of spontaneous emission controlled nanolasers. The laser cavity is a photonic crystal slab cavity, embedding self-assembled quantum dots as gain material. The implementation of cavity electrodynamics effects increases significantly the large signal modulation bandwidth, with measured modulation speeds of the order of 10 GHz while keeping an extinction ratio of 19 dB. A linear transient wavelength shift is reported, corresponding to a chirp of less than 100 pm for a 35-ps laser pulse. We observe that the chirp characteristics are independent of the repetition rate of the laser up to 10 GHz

Coupled-resonator optical waveguides: Q-factor and disorder influence

Coupled resonator optical waveguides (CROW) can significantly reduce light propagation pulse velocity due to pronounced dispersion properties. A number of interesting applications have been proposed to benefit from such slow-light propagation. Unfortunately, the inevitable presence of disorder, imperfections, and a finite Q value may heavily affect the otherwise attractive properties of CROWs. We show how finite a Q factor limits the maximum attainable group delay time; the group index is limited by Q, but equally important the feasible device length is itself also limited by damping resulting from a finite Q. Adding the additional effects of disorder to this picture, limitations become even more severe due to destructive interference phenomena, eventually in the form of Anderson localization. Simple analytical considerations demonstrate that the maximum attainable delay time in CROWs is limited by the intrinsic photon lifetime of a single resonator.Comment: Accepted for Opt. Quant. Electro

Animal Models for Limbal Stem Cell Deficiency: A Critical Narrative Literature Review

\ua9 2024, The Author(s). This literature review will provide a critical narrative overview of the highlights and potential pitfalls of the reported animal models for limbal stem cell deficiency (LSCD) and will identify the neglected aspects of this research area. There exists significant heterogeneity in the literature regarding the methodology used to create the model and the predefined duration after the insult when the model is supposedly fully fit for evaluations and/or for testing various therapeutic interventions. The literature is also replete with examples wherein the implementation of a specific model varies significantly across different studies. For example, the concentration of the chemical, as well as its duration and technique of exposure in a chemically induced LSCD model, has a great impact not only on the validity of the model but also on the severity of the complications. Furthermore, while some models induce a full-blown clinical picture of total LSCD, some are hindered by their ability to yield only partial LSCD. Another aspect to consider is the nature of the damage induced by a specific method. As thermal methods cause more stromal scarring, they may be better suited for assessing the anti-fibrotic properties of a particular treatment. On the other hand, since chemical burns cause more neovascularisation, they provide the opportunity to tap into the potential treatments for anti-neovascularisation. The animal species (i.e., rats, mice, rabbits, etc.) is also a crucial factor in the validity of the model and its potential for clinical translation, with each animal having its unique set of advantages and disadvantages. This review will also elaborate on other overlooked aspects, such as the anaesthetic(s) used during experiments, the gender of the animals, care after LSCD induction, and model validation. The review will conclude by providing future perspectives and suggestions for further developments in this rather important area of research

Nanobeam photonic crystal cavity quantum dot laser

The lasing behavior of one dimensional GaAs nanobeam cavities with embedded InAs quantum dots is studied at room temperature. Lasing is observed throughout the quantum dot PL spectrum, and the wavelength dependence of the threshold is calculated. We study the cavity lasers under both 780 nm and 980 nm pump, finding thresholds as low as 0.3 uW and 19 uW for the two pump wavelengths, respectively. Finally, the nanobeam cavity laser wavelengths are tuned by up to 7 nm by employing a fiber taper in near proximity to the cavities. The fiber taper is used both to efficiently pump the cavity and collect the cavity emission.Comment: 8 pages; 6 figure

Q-ball formation in the wake of Hubble-induced radiative corrections

We discuss some interesting aspects of the $\rm Q$-ball formation during the early oscillations of the flat directions. These oscillations are triggered by the running of soft $({\rm mass})^2$ stemming from the nonzero energy density of the Universe. However, this is quite different from the standard $\rm Q$-ball formation. The running in presence of gauge and Yukawa couplings becomes strong if $m_{1/2}/m_0$ is sufficiently large. Moreover, the $\rm Q$-balls which are formed during the early oscillations constantly evolve, due to the redshift of the Hubble-induced soft mass, until the low-energy supersymmtery breaking becomes dominant. For smaller $m_{1/2}/m_0$, $\rm Q$-balls are not formed during early oscillations because of the shrinking of the instability band due to the Hubble expansion. In this case the $\rm Q$-balls are formed only at the weak scale, but typically carry smaller charges, as a result of their amplitude redshift. Therefore, the Hubble-induced corrections to the flat directions give rise to a successful $\rm Q$-ball cosmology.Comment: 7 revtex pages, few references corrected and added, final version to appear in Phys. Rev.

Lasing oscillation in a three-dimensional photonic crystal nanocavity with a complete bandgap

We demonstrate lasing oscillation in a three-dimensional photonic crystal nanocavity. The laser is realized by coupling a cavity mode, which is localized in a complete photonic bandgap and exhibits the highest quality factor of ~38,500, with high-quality semiconductor quantum dots. We show a systematic change in the laser characteristics, including the threshold and the spontaneous emission coupling factor by controlling the crystal size, which consequently changes the strength of photon confinement in the third dimension. This opens up many interesting possibilities for realizing future ultimate light sources and three-dimensional integrated photonic circuits and for more fundamental studies of physics in the field of cavity quantum electrodynamics.Comment: 14 pages, 4 figure