Percentile residual life orders

In this paper we study a family of stochastic orders of random variables defined via the comparison of their percentile residual life functions. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are also studied. Finally, some applications in reliability theory and finance are described

The percentile residual life up to time t0: ordering and aging properties

Motivated by practical issues, a new stochastic order for random variables is introduced by comparing all their percentile residual life functions until a certain instant. Some interpretations of these stochastic orders are given, and various properties of them are derived. The relationships to other stochastic orders are studied, and also an application in Reliability Theory is described. Finally, we present some characterization results of the decreasing percentile residual life up to time t0 aging notion.Aging notion, Hazard rate, Mean residual life, Percentile residual life, Reliability, Stochastic ordering

Direct Imaging in Reflected Light: Characterization of Older, Temperate Exoplanets With 30-m Telescopes

Direct detection, also known as direct imaging, is a method for discovering and characterizing the atmospheres of planets at intermediate and wide separations. It is the only means of obtaining spectra of non-transiting exoplanets. Characterizing the atmospheres of planets in the <5 AU regime, where RV surveys have revealed an abundance of other worlds, requires a 30-m-class aperture in combination with an advanced adaptive optics system, coronagraph, and suite of spectrometers and imagers - this concept underlies planned instruments for both TMT (the Planetary Systems Imager, or PSI) and the GMT (GMagAO-X). These instruments could provide astrometry, photometry, and spectroscopy of an unprecedented sample of rocky planets, ice giants, and gas giants. For the first time habitable zone exoplanets will become accessible to direct imaging, and these instruments have the potential to detect and characterize the innermost regions of nearby M-dwarf planetary systems in reflected light. High-resolution spectroscopy will not only illuminate the physics and chemistry of exo-atmospheres, but may also probe rocky, temperate worlds for signs of life in the form of atmospheric biomarkers (combinations of water, oxygen and other molecular species). By completing the census of non-transiting worlds at a range of separations from their host stars, these instruments will provide the final pieces to the puzzle of planetary demographics. This whitepaper explores the science goals of direct imaging on 30-m telescopes and the technology development needed to achieve them.Comment: (March 2018) Submitted to the Exoplanet Science Strategy committee of the NA

Observation of coherent backscattering of light by cold atoms

Coherent backscattering (CBS) of light waves by a random medium is a signature of interference effects in multiple scattering. This effect has been studied in many systems ranging from white paint to biological tissues. Recently, we have observed CBS from a sample of laser-cooled atoms, a scattering medium with interesting new properties. In this paper we discuss various effects, which have to be taken into account for a quantitative study of coherent backscattering of light by cold atoms.Comment: 25 pages LaTex2e, 17 figures, submitted to J. Opt. B: Quant. Semicl. Op

Quantum and classical dynamics of a three-mode absorption refrigerator

We study the quantum and classical evolution of a system of three harmonic modes interacting via a trilinear Hamiltonian. With the modes prepared in thermal states of different temperatures, this model describes the working principle of an absorption refrigerator that transfers energy from a cold to a hot environment at the expense of free energy provided by a high-temperature work reservoir. Inspired by a recent experimental realization with trapped ions, we elucidate key features of the coupling Hamiltonian that are relevant for the refrigerator performance. The coherent system dynamics exhibits rapid effective equilibration of the mode energies and correlations, as well as a transient enhancement of the cooling performance at short times. We find that these features can be fully reproduced in a classical framework.Comment: 11 pages, 8 figures; additions and corrections; accepted in Quantum on 2017-12-0

A temperature behavior of the frustrated translational mode of adsorbate and the nature of the "adsorbate-substrate" interaction

A temperature behavior of the frustrated translational mode (T-mode) of a light particle, coupled by different regimes of ohmicity to the surface, is studied within a formalism of the generalized diffusion coefficients. The memory effects of the adsorbate motion are considered to be the main reason of the T-mode origin. Numerical calculations yield a thermally induced shift and broadening of the T-mode, which is found to be linear in temperature for Ohmic and super-Ohmic systems and nonlinear for strongly sub-Ohmic ones. We obtain analytical expressions for the T-mode shift and width at weak coupling for the systems with integer "ohmicity" indexes n=0-2 in zero temperature and high temperature limits. We provide an explanation of the experimentally observed blue- or red-shifts of the T-mode on the basis of a comparative analysis of two typical times of the system evolution: a time of decay of the "velocity-velocity" autocorrelation function, and a correlation time of the thermal bath random forces. A relation of the T-mode to the multiple jumps of the adsorbate is discussed, and generalization of conditions of the multiple hopping to the case of quantum surface diffusion is performed.Comment: 12 pages, 4 figure