Self-consistent multi-mode lasing theory for complex or random lasing media

A semiclassical theory of single and multi-mode lasing is derived for open complex or random media using a self-consistent linear response formulation. Unlike standard approaches which use closed cavity solutions to describe the lasing modes, we introduce an appropriate discrete basis of functions which describe also the intensity and angular emission pattern outside the cavity. This constant flux (CF) basis is dictated by the Green function which arises when formulating the steady state Maxwell-Bloch equations as a self-consistent linear response problem. This basis is similar to the quasi-bound state basis which is familiar in resonator theory and it obeys biorthogonality relations with a set of dual functions. Within a single-pole approximation for the Green function the lasing modes are proportional to these CF states and their intensities and lasing frequencies are determined by a set of non-linear equations. When a near threshold approximation is made to these equations a generalized version of the Haken-Sauermann equations for multi-mode lasing is obtained, appropriate for open cavities. Illustrative results from these equations are given for single and few mode lasing states, for the case of dielectric cavity lasers. The standard near threshold approximation is found to be unreliable. Applications to wave-chaotic cavities and random lasers are discussed.Comment: 18 pages, 9 figure

Weak-Localization and Integrability in Ballistic Cavities

We demonstrate the existence of an interference contribution to the average magnetoconductance, G(B), of ballistic cavities and use it to test the semiclassical theory of quantum billiards. G(B) is qualitatively different for chaotic and regular cavities, an effect explained semiclassically by the differing classical distribution of areas. The magnitude of G(B) is poorly explained by the semiclassical theory of coherent backscattering (elastic enhancement factor)-- correlations beyond time-reversed pairs of trajectories must be included-- but is in agreement with random matrix theory.Comment: 12 pages + 3 figures, revtex, hub-92-w

Quantum Mechanics Another Way

Deformation quantization (sometimes called phase-space quantization) is a formulation of quantum mechanics that is not usually taught to undergraduates. It is formally quite similar to classical mechanics: ordinary functions on phase space take the place of operators, but the functions are multiplied in an exotic way, using the star product. Here we attempt a brief, pedagogical discussion of deformation quantization, that is suitable for inclusion in an undergraduate course.Comment: 14 pages, 3 figures, to be published in Eur. J. Phy

Quantum chaos in a deformable billiard: Applications to quantum dots

We perform a detailed numerical study of energy-level and wavefunction statistics of a deformable quantum billiard focusing on properties relevant to semiconductor quantum dots. We consider the family of Robnik billiards generated by simple conformal maps of the unit disk; the shape of this family of billiards may be varied continuously at fixed area by tuning the parameters of the map. The classical dynamics of these billiards is well-understood and this allows us to study the quantum properties of subfamilies which span the transition from integrability to chaos as well as families at approximately constant degree of chaoticity (Kolmogorov entropy). In the regime of hard chaos we find that the statistical properties of interest are well-described by random-matrix theory and completely insensitive to the particular shape of the dot. However in the nearly-integrable regime non-universal behavior is found. Specifically, the level-width distribution is well-described by the predicted $\chi^2$ distribution both in the presence and absence of magnetic flux when the system is fully chaotic; however it departs substantially from this behavior in the mixed regime. The chaotic behavior corroborates the previously predicted behavior of the peak-height distribution for deformed quantum dots. We also investigate the energy-level correlation functions which are found to agree well with the behavior calculated for quasi-zero-dimensional disordered systems.Comment: 25 pages (revtex 3.0). 16 figures are available by mail or fax upon request at [email protected]

Semiclassical theory of magnetotransport through a chaotic quantum well

We develop a quantitative semiclassical formula for the resonant tunneling current through a quantum well in a tilted magnetic field. It is shown that the current depends only on periodic orbits within the quantum well. The theory explains the puzzling evolution of the tunneling spectra near a tilt angle of $30^{\circ}$ as arising from an exchange bifurcation of the relevant periodic orbits.Comment: 4 pages, RevTeX, epsf, 2 PostScript Figures (1 with color

Toda Lattice Hierarchy and Generalized String Equations

String equations of the $p$-th generalized Kontsevich model and the compactified $c = 1$ string theory are re-examined in the language of the Toda lattice hierarchy. As opposed to a hypothesis postulated in the literature, the generalized Kontsevich model at $p = -1$ does not coincide with the $c = 1$ string theory at self-dual radius. A broader family of solutions of the Toda lattice hierarchy including these models are constructed, and shown to satisfy generalized string equations. The status of a variety of $c \le 1$ string models is discussed in this new framework.Comment: 35pages, LaTeX Errors are corrected in Eqs. (2.21), (2.36), (2.33), (3.3), (5.10), (6.1), sentences after (3.19) and theorem 5. A few references are update

Origin of strong scarring of wavefunctions in quantum wells in a tilted magnetic field

The anomalously strong scarring of wavefunctions found in numerical studies of quantum wells in a tilted magnetic field is shown to be due to special properties of the classical dynamics of this system. A certain subset of periodic orbits are identified which are nearly stable over a very large interval of variation of the classical dynamics; only this subset are found to exhibit strong scarring. Semiclassical arguments shed further light on why these orbits dominate the experimentally observed tunneling spectra.Comment: RevTeX, 5 page

Open-label add-on treatment trial of minocycline in fragile X syndrome

<p>Abstract</p> <p>Background</p> <p>Fragile X syndrome (FXS) is a disorder characterized by a variety of disabilities, including cognitive deficits, attention-deficit/hyperactivity disorder, autism, and other socio-emotional problems. It is hypothesized that the absence of the fragile X mental retardation protein (FMRP) leads to higher levels of matrix metallo-proteinase-9 activity (MMP-9) in the brain. Minocycline inhibits MMP-9 activity, and alleviates behavioural and synapse abnormalities in <it>fmr1 </it>knockout mice, an established model for FXS. This open-label add-on pilot trial was conducted to evaluate safety and efficacy of minocycline in treating behavioural abnormalities that occur in humans with FXS.</p> <p>Methods</p> <p>Twenty individuals with FXS, ages 13-32, were randomly assigned to receive 100 mg or 200 mg of minocycline daily. Behavioural evaluations were made prior to treatment (baseline) and again 8 weeks after daily minocycline treatment. The primary outcome measure was the Aberrant Behaviour Checklist-Community Edition (ABC-C) Irritability Subscale, and the secondary outcome measures were the other ABC-C subscales, clinical global improvement scale (CGI), and the visual analog scale for behaviour (VAS). Side effects were assessed using an adverse events checklist, a complete blood count (CBC), hepatic and renal function tests, and antinuclear antibody screen (ANA), done at baseline and at 8 weeks.</p> <p>Results</p> <p>The ABC-C Irritability Subscale scores showed significant improvement (p < 0.001), as did the VAS (p = 0.003) and the CGI (p < 0.001). The only significant treatment-related side effects were minor diarrhea (n = 3) and seroconversion to a positive ANA (n = 2).</p> <p>Conclusions</p> <p>Results from this study demonstrate that minocycline provides significant functional benefits to FXS patients and that it is well-tolerated. These findings are consistent with the <it>fmr1 </it>knockout mouse model results, suggesting that minocycline modifies underlying neural defects that account for behavioural abnormalities. A placebo-controlled trial of minocycline in FXS is warranted.</p> <p>Trial registration</p> <p>ClinicalTrials.gov Open-Label Trial NCT00858689.</p