Unitary relation between a harmonic oscillator of time-dependent frequency and a simple harmonic oscillator with and without an inverse-square potential

The unitary operator which transforms a harmonic oscillator system of time-dependent frequency into that of a simple harmonic oscillator of different time-scale is found, with and without an inverse-square potential. It is shown that for both cases, this operator can be used in finding complete sets of wave functions of a generalized harmonic oscillator system from the well-known sets of the simple harmonic oscillator. Exact invariants of the time-dependent systems can also be obtained from the constant Hamiltonians of unit mass and frequency by making use of this unitary transformation. The geometric phases for the wave functions of a generalized harmonic oscillator with an inverse-square potential are given.Comment: Phys. Rev. A (Brief Report), in pres

Geometric Phase, Hannay's Angle, and an Exact Action Variable

Canonical structure of a generalized time-periodic harmonic oscillator is studied by finding the exact action variable (invariant). Hannay's angle is defined if closed curves of constant action variables return to the same curves in phase space after a time evolution. The condition for the existence of Hannay's angle turns out to be identical to that for the existence of a complete set of (quasi)periodic wave functions. Hannay's angle is calculated, and it is shown that Berry's relation of semiclassical origin on geometric phase and Hannay's angle is exact for the cases considered.Comment: Submitted to Phys. Rev. Lett. (revised version

On Horizontal and Vertical Separation in Hierarchical Text Classification

Hierarchy is a common and effective way of organizing data and representing their relationships at different levels of abstraction. However, hierarchical data dependencies cause difficulties in the estimation of "separable" models that can distinguish between the entities in the hierarchy. Extracting separable models of hierarchical entities requires us to take their relative position into account and to consider the different types of dependencies in the hierarchy. In this paper, we present an investigation of the effect of separability in text-based entity classification and argue that in hierarchical classification, a separation property should be established between entities not only in the same layer, but also in different layers. Our main findings are the followings. First, we analyse the importance of separability on the data representation in the task of classification and based on that, we introduce a "Strong Separation Principle" for optimizing expected effectiveness of classifiers decision based on separation property. Second, we present Hierarchical Significant Words Language Models (HSWLM) which capture all, and only, the essential features of hierarchical entities according to their relative position in the hierarchy resulting in horizontally and vertically separable models. Third, we validate our claims on real-world data and demonstrate that how HSWLM improves the accuracy of classification and how it provides transferable models over time. Although discussions in this paper focus on the classification problem, the models are applicable to any information access tasks on data that has, or can be mapped to, a hierarchical structure.Comment: Full paper (10 pages) accepted for publication in proceedings of ACM SIGIR International Conference on the Theory of Information Retrieval (ICTIR'16

Probing and modelling the localized self-mixing in a GaN/AlGaN field-effect terahertz detector

In a GaN/AlGaN field-effect terahertz detector, the directional photocurrent is mapped in the two-dimensional space of the gate voltage and the drain/source bias. It is found that not only the magnitude, but also the polarity, of the photocurrent can be tuned. A quasistatic self-mixing model taking into account the localized terahertz field provides a quantitative description of the detector characteristics. Strongly localized self-mixing is confirmed. It is therefore important to engineer the spatial distribution of the terahertz field and its coupling to the field-effect channel on the sub-micron scale.Comment: 12 pages, 4 figures, submitted to AP

Stable fourfold configurations for small vacancy clusters in silicon from ab initio calculations

Using density-functional-theory calculations, we have identified new stable configurations for tri-, tetra-, and penta-vacancies in silicon. These new configurations consist of combinations of a ring-hexavacancy with three, two, or one interstitial atoms, respectively, such that all atoms remain fourfold. As a result, their formation energies are lower by 0.6, 1.0, and 0.6 eV, respectively, than the ``part of a hexagonal ring'' configurations, believed up to now to be the lowest-energy states

Exact quantum states of a general time-dependent quadratic system from classical action

A generalization of driven harmonic oscillator with time-dependent mass and frequency, by adding total time-derivative terms to the Lagrangian, is considered. The generalization which gives a general quadratic Hamiltonian system does not change the classical equation of motion. Based on the observation by Feynman and Hibbs, the propagators (kernels) of the systems are calculated from the classical action, in terms of solutions of the classical equation of motion: two homogeneous and one particular solutions. The kernels are then used to find wave functions which satisfy the Schr\"{o}dinger equation. One of the wave functions is shown to be that of a Gaussian pure state. In every case considered, we prove that the kernel does not depend on the way of choosing the classical solutions, while the wave functions depend on the choice. The generalization which gives a rather complicated quadratic Hamiltonian is simply interpreted as acting an unitary transformation to the driven harmonic oscillator system in the Hamiltonian formulation.Comment: Submitted to Phys. Rev.

Characterizing Earth Analogs in Reflected Light: Atmospheric Retrieval Studies for Future Space Telescopes

Space-based high contrast imaging mission concepts for studying rocky exoplanets in reflected light are currently under community study. We develop an inverse modeling framework to estimate the science return of such missions given different instrument design considerations. By combining an exoplanet albedo model, an instrument noise model, and an ensemble Markov chain Monte Carlo sampler, we explore retrievals of atmospheric and planetary properties for Earth twins as a function of signal-to-noise ratio (SNR) and resolution ($R$). Our forward model includes Rayleigh scattering, single-layer water clouds with patchy coverage, and pressure-dependent absorption due to water vapor, oxygen, and ozone. We simulate data at $R = 70$ and $R = 140$ from 0.4-1.0 $\mu$m with SNR $= 5, 10, 15, 20$ at 550 nm (i.e., for HabEx/LUVOIR-type instruments). At these same SNR, we simulate data for WFIRST paired with a starshade, which includes two photometric points between 0.48-0.6 $\mu$m and $R = 50$ spectroscopy from 0.6-0.97 $\mu$m. Given our noise model for WFIRST-type detectors, we find that weak detections of water vapor, ozone, and oxygen can be achieved with observations with at least $R = 70$ / SNR$\ = 15$, or $R = 140$ / SNR$\ = 10$ for improved detections. Meaningful constraints are only achieved with $R = 140$ / SNR$\ = 20$ data. The WFIRST data offer limited diagnostic information, needing at least SNR = 20 to weakly detect gases. Most scenarios place limits on planetary radius, but cannot constrain surface gravity and, thus, planetary mass.Comment: Resubmitted to AAS Journals after incorporating reviewer feedback. 26 pages, 18 figure, 9 table

Commensurability oscillations in the rf conductivity of unidirectional lateral superlattices: measurement of anisotropic conductivity by coplanar waveguide

We have measured the rf magnetoconductivity of unidirectional lateral superlattices (ULSLs) by detecting the attenuation of microwave through a coplanar waveguide placed on the surface. ULSL samples with the principal axis of the modulation perpendicular (S_perp) and parallel (S_||) to the microwave electric field are examined. For low microwave power, we observe expected anisotropic behavior of the commensurability oscillations (CO), with CO in samples S_perp and S_|| dominated by the diffusion and the collisional contributions, respectively. Amplitude modulation of the Shubnikov-de Haas oscillations is observed to be more prominent in sample S_||. The difference between the two samples is washed out with the increase of the microwave power, letting the diffusion contribution govern the CO in both samples. The failure of the intended directional selectivity in the conductivity measured with high microwave power is interpreted in terms of large-angle electron-phonon scattering.Comment: 8 pages, 5 figure

Observation of pinning mode of stripe phases of 2D systems in high Landau levels

We study the radio-frequency diagonal conductivities of the anisotropic stripe phases of higher Landau levels near half integer fillings. In the hard direction, in which larger dc resistivity occurs, the spectrum exhibits a striking resonance, while in the orthogonal, easy direction, no resonance is discernable. The resonance is interpreted as a pinning mode of the stripe phase