Probability of Reflection by a Random Laser

A theory is presented (and supported by numerical simulations) for phase-coherent reflection of light by a disordered medium which either absorbs or amplifies radiation. The distribution of reflection eigenvalues is shown to be the Laguerre ensemble of random-matrix theory. The statistical fluctuations of the albedo (the ratio of reflected and incident power) are computed for arbitrary ratio of sample thickness, mean free path, and absorption or amplification length. On approaching the laser threshold all moments of the distribution of the albedo diverge. Its modal value remains finite, however, and acquires an anomalous dependence on the illuminated surface area.Comment: 8 pages (revtex), 3 figures, to appear in Phys.Rev.Let

Time-delay matrix, midgap spectral peak, and thermopower of an Andreev billiard

We derive the statistics of the time-delay matrix (energy derivative of the scattering matrix) in an ensemble of superconducting quantum dots with chaotic scattering (Andreev billiards), coupled ballistically to $M$ conducting modes (electron-hole modes in a normal metal or Majorana edge modes in a superconductor). As a first application we calculate the density of states $\rho_0$ at the Fermi level. The ensemble average $\langle\rho_0\rangle=\delta_0^{-1}M[\max(0,M+2\alpha/\beta)]^{-1}$ deviates from the bulk value $1/\delta_0$ by an amount depending on the Altland-Zirnbauer symmetry indices $\alpha,\beta$. The divergent average for $M=1,2$ in symmetry class D ($\alpha=-1$, $\beta=1$) originates from the mid-gap spectral peak of a closed quantum dot, but now no longer depends on the presence or absence of a Majorana zero-mode. As a second application we calculate the probability distribution of the thermopower, contrasting the difference for paired and unpaired Majorana edge modes.Comment: 13 pages, 6 figure

Fluctuating "order parameter" for a quantum chaotic system with partially broken time-reversal symmetry

The functional defined as the squared modulus of the spatial average of the wave function squared, plays the role of an ``order parameter'' for the transition between Hamiltonian ensembles with orthogonal and unitary symmetry. Upon breaking time-reversal symmetry, the order parameter crosses over from one to zero. We compute its distribution in the crossover regime and find that it has large fluctuations around the ensemble average. These fluctuations imply long-range spatial correlations in the eigenfunction and non-Gaussian perturbations of eigenvalues, in precise agreement with results by Fal'ko and Efetov and by Taniguchi, Hashimoto, Simons, and Altshuler. As a third implication of the order-parameter fluctuations we find correlations in the response of an eigenvalue to independent perturbations of the system.Comment: 4 pages, REVTeX-3.0, 1 figure. Reference added to Y. V. Fyodorov and A. D. Mirlin, Phys. Rev. B 51, 13403 (1995

Ehrenfest-time dependence of weak localization in open quantum dots

Semiclassical theory predicts that the weak localization correction to the conductance of a ballistic chaotic cavity is suppressed if the Ehrenfest time exceeds the dwell time in the cavity [I. L. Aleiner and A. I. Larkin, Phys. Rev. B {\bf 54}, 14424 (1996)]. We report numerical simulations of weak localization in the open quantum kicked rotator that confirm this prediction. Our results disagree with the `effective random matrix theory' of transport through ballistic chaotic cavities.Comment: 4 pages, 2 figure

Rectification of displacement currents in an adiabatic electron pump

Rectification of ac displacement currents generated by periodic variation of two independent gate voltages of a quantum dot can lead to a dc voltage linear in the frequency. The presence of this rectified displacement current could account for the magnetic field symmetry observed in a recent measurement on an adiabatic quantum electron pump by Switkes et al. [Science 283, 1905 (1999)].Comment: 2 pages, RevTeX; 1 figur

Crossover from weak localization to weak antilocalization in a disordered microbridge

We calculate the weak localization correction in the double crossover to broken time-reversal and spin-rotational symmetry for a disordered microbridge or a short disordered wire using a scattering-matrix approach. Whereas the correction has universal limiting values in the three basic symmetry classes, the functional form of the magnetoconductance is affected by eventual non-homogeneities in the microbridge.Comment: 5 pages, RevTeX; 2 figure

Finite size effects and localization properties of disordered quantum wires with chiral symmetry

Finite size effects in the localization properties of disordered quantum wires are analyzed through conductance calculations. Disorder is induced by introducing vacancies at random positions in the wire and thus preserving the chiral symmetry. For quasi one-dimensional geometries and low concentration of vacancies, an exponential decay of the mean conductance with the wire length is obtained even at the center of the energy band. For wide wires, finite size effects cause the conductance to decay following a non-pure exponential law. We propose an analytical formula for the mean conductance that reproduces accurately the numerical data for both geometries. However, when the concentration of vacancies increases above a critical value, a transition towards the suppression of the conductance occurs. This is a signature of the presence of ultra-localized states trapped in finite regions of the sample.Comment: 5 figures, revtex

Measuring the value of life: Exploring a new method for deriving the monetary value of a QALY

Economic evaluations of new health technologies now typically produce an incremental cost per Quality Adjusted Life Year (QALY) value. The QALY is a measure of health benefit that combines length of life with quality of life, where quality of life is assessed on a scale where zero represents a health state equivalent to being dead and one represents full health. The challenge for decision makers, such as the Treasury, is to determine the appropriate size of the healthcare budget. Bodies such as the National Institute for Health and Clinical Excellent (NICE) in the U.K. must then determine how much they can afford to pay for a gain of one QALY, while operating under this fixed budget. While there is no fixed cost-effectiveness threshold and each intervention is assessed on a case by case basis, under normal circumstances the threshold will not be below £20,000 and not above £30,000 per QALY. Recent research has sought to determine the monetary value individuals place on a QALY to inform the size of the healthcare budget and the level of the cost-effectiveness threshold. This research has predominantly used Willingness to Pay (WTP) approaches. However, WTP has a number of known problems, most notably its insensitivity to scope. In this paper we present an alternative approach to estimating the monetary value of a QALY (MVQ), which is based upon a Time Trade Off (TTO) exercise of income with health held constant at perfect health. We present the methods and theory underlying this experimental approach and some results from an online feasibility study in the Netherlands

The impact of losses in income due to ill health: does the EQ-5D reflect lost earnings?

Two key questions in the context of UK health policy are: do the published preference indices for EQ-5D reflect the impact of lost earnings? Are we currently implicitly including indirect costs in our analyses? It is crucial to investigate whether or not individuals take into account any possible impact of lost income in health state valuation exercises. If respondents do consider income effects, and these considerations change valuations, then these effects would need to be excluded both under the current NICE reference case, or where productivity costs are included in the numerator to avoid double counting. This study adapts the study design used to generate population value sets for EQ-5D, as first used in the Measurement and Valuation of Health (MVH) Study, and carries out valuations of hypothetical EQ-5D states using Time Trade Off (TTO) exercises through an online survey administered in the Netherlands. Furthermore, this study uses a number of different TTO questions to explore the impact of losses in income on the valuation of hypothetical health states, and to determine the relationship between income and health.EQ-5D; time trade-off; health-related loss of income