Normal mode splitting in a coupled system of nanomechanical oscillator and parametric amplifier cavity

We study how an optical parametric amplifier inside the cavity can affect the normal mode splitting behavior of the coupled movable mirror and the cavity field. We work in the resolved sideband regime. The spectra exhibit a double-peak structure as the parametric gain is increased. Moreover, for a fixed parametric gain, the double-peak structure of the spectrum is more pronounced with increasing the input laser power. We give results for mode splitting. The widths of the split lines are sensitive to parametric gain.Comment: 7 pages,9 figure

Distribution of Interference in the Presence of Decoherence

We study the statistics of quantum interference for completely positive maps. We calculate analytically the mean interference and its second moment for finite dimensional quantum systems interacting with a simple environment consisting of one or several spins (qudits). The joint propagation of the entire system is taken as unitary with an evolution operator drawn from the Circular Unitary Ensemble (CUE). We show that the mean interference decays with a power law as function of the dimension of the Hilbert space of the environment, with a power that depends on the temperature of the environment.Comment: 28 pages of pd

The development of tape recorded discussions and check lists for evaluating progression in grades one through four.

Thesis (Ed.M.)--Boston Universit

Species Trees from Highly Incongruent Gene Trees in Rice

Several methods have recently been developed to infer multilocus phylogenies by incorporating information from topological incongruence of the individual genes. In this study, we investigate 2 such methods, Bayesian concordance analysis and Bayesian estimation of species trees. Our test data are a collection of genes from cultivated rice (genus Oryza) and the most closely related wild species, generated using a high-throughput sequencing protocol and bioinformatics pipeline. Trees inferred from independent genes display levels of topological incongruence that far exceed that seen in previous data sets analyzed with these species tree methods. We identify differences in phylogenetic results between inference methods that incorporate gene tree incongruence. Finally, we discuss the challenges of scaling these analyses for data sets with thousands of gene trees and extensive levels of missing data

Enhancement of Cavity Cooling of a Micromechanical Mirror Using Parametric Interactions

It is shown that an optical parametric amplifier inside a cavity can considerably improve the cooling of the micromechanical mirror by radiation pressure. The micromechanical mirror can be cooled from room temperature 300 K to sub-Kelvin temperatures, which is much lower than what is achievable in the absence of the parametric amplifier. Further if in case of a precooled mirror one can reach millikelvin temperatures starting with about 1 K. Our work demonstrates the fundamental dependence of radiation pressure effects on photon statistics.Comment: 14 pages, 7 figure

The Lagrange and Markov spectra from the dynamical point of view

This text grew out of my lecture notes for a 4-hours minicourse delivered on October 17 \& 19, 2016 during the research school "Applications of Ergodic Theory in Number Theory" -- an activity related to the Jean-Molet Chair project of Mariusz Lema\'nczyk and S\'ebastien Ferenczi -- realized at CIRM, Marseille, France. The subject of this text is the same of my minicourse, namely, the structure of the so-called Lagrange and Markov spectra (with an special emphasis on a recent theorem of C. G. Moreira).Comment: 27 pages, 6 figures. Survey articl

Structured matrices, continued fractions, and root localization of polynomials

We give a detailed account of various connections between several classes of objects: Hankel, Hurwitz, Toeplitz, Vandermonde and other structured matrices, Stietjes and Jacobi-type continued fractions, Cauchy indices, moment problems, total positivity, and root localization of univariate polynomials. Along with a survey of many classical facts, we provide a number of new results.Comment: 79 pages; new material added to the Introductio

How to relate the oscillator and Coulomb systems on spheres and pseudospheres?

We show that the oscillators on a sphere and pseudosphere are related, by the so-called Bohlin transformation, with the Coulomb systems on the pseudosphere: the even states of an oscillator yields the conventional Coulomb system on pseudosphere, while the odd states yield the Coulomb system on pseudosphere in the presence of magnetic flux tube generating half spin. In the higher dimensions the oscillator and Coulomb(-like) systems are connected in the similar way. In particular, applying the Kustaanheimo-Stiefel transformation to the oscillators on sphere and pseudosphere, we obtained the preudospherical generalization of MIC-Kepler problem describing three-dimensional charge-dyon system.Comment: 12 pages, Based on talk given at XXIII Colloquium on Group Theoretical Methods in Physics (July 31-August 5, 2000, Dubna

Response of the Antarctic Stratosphere to Two Types of El Nino Events

This study is the first to identify a robust El Nino/Southern Oscillation (ENSO) signal in the Antarctic stratosphere. El Nino events are classified as either conventional "cold tongue" events (positive SST anomalies in the Nino 3 region) or "warm pool" events (positive SST anomalies in the Nino 4 region). The ERA-40, NCEP and MERRA meteorological reanalyses are used to show that the Southern Hemisphere stratosphere responds differently to these two types of El Nino events. Consistent with previous studies, "cold tongue" events do not impact temperatures in the Antarctic stratosphere. During "warm pool" El Nino events, the poleward extension and increased strength of the South Pacific Convergence Zone (SPCZ) favor an enhancement of planetary wave activity during the SON season. On average, these conditions lead to higher polar stratospheric temperatures and a weakening of the Antarctic polar jet in November and December, as compared with neutral ENSO years. The phase of the quasi-biennial oscillation (QBO) modulates the stratospheric response to "warm pool" El Nino events: the strongest planetary wave driving events are coincident with the easterly phase of the QBO