Mission: Impossible (Escape from the Lyman Limit)

We investigate the intrinsic opacity of high-redshift galaxies to outgoing ionising photons using high-quality photometry of a sample of 27 spectroscopically-identified galaxies of redshift 1.9<z<3.5 in the Hubble Deep Field. Our measurement is based on maximum-likelihood fitting of model galaxy spectral energy distributions-including the effects of intrinsic Lyman-limit absorption and random realizations of intervening Lyman-series and Lyman-limit absorption-to photometry of galaxies from space- and ground-based broad-band images. Our method provides several important advantages over the methods used by previous groups, including most importantly that two-dimensional sky subtraction of faint-galaxy images is more robust than one-dimensional sky subtraction of faint-galaxy spectra. We find at the 3sigma statistical confidence level that on average no more than 4% of the ionising photons escape galaxies of redshift 1.9<z<3.5. This result is consistent with observations of low- and moderate-redshift galaxies but is in direct contradiction to a recent result based on medium-resolution spectroscopy of high-redshift (z~3) galaxies. Dividing our sample in subsamples according to luminosity, intrinsic ultraviolet colour, and redshift, we find no evidence for selection effects that could explain such discrepancy. Even when all systematic effects are included, the data could not realistically accomodate any escape fraction value larger than ~15%.Comment: Accepted for publication in Monthly Notices of the Royal Astronomical Society. 8 pages, 4 b/w figures, MNRAS styl

Violation of action--reaction and self-forces induced by nonequilibrium fluctuations

We show that the extension of Casimir-like forces to fluctuating fluids driven out of equilibrium can exhibit two interrelated phenomena forbidden at equilibrium: self-forces can be induced on single asymmetric objects and the action--reaction principle between two objects can be violated. These effects originate in asymmetric restrictions imposed by the objects' boundaries on the fluid's fluctuations. They are not ruled out by the second law of thermodynamics since the fluid is in a nonequilibrium state. Considering a simple reaction--diffusion model for the fluid, we explicitly calculate the self-force induced on a deformed circle. We also show that the action--reaction principle does not apply for the internal Casimir forces exerting between a circle and a plate. Their sum, instead of vanishing, provides the self-force on the circle-plate assembly.Comment: 4 pages, 1 figure. V2: New title; Abstract partially rewritten; Largely enhanced introductory and concluding remarks (incl. new Refs.

The Unusual Spectral Energy Distribution of a Galaxy Previously Reported to be at Redshift 6.68

Observations of distant galaxies are important both for understanding how galaxies form and for probing the physical conditions of the universe at the earliest epochs. It is, however, extremely difficult to identify galaxies at redshift z>5, because these galaxies are faint and exhibit few spectral features. In a previous work, we presented observations that supported the identification of a galaxy at redshift z = 6.68 in a deep STIS field. Here we present new ground-based photometry of the galaxy. We find that the galaxy exhibits moderate detections of flux in the optical B and V images that are inconsistent with the expected absence of flux at wavelength shortward of the redshifted Lyman-alpha emission line of a galaxy at redshift z>5. In addition, the new broad-band imaging data not only show flux measurements of this galaxy that are incompatible with the previous STIS measurement, but also suggest a peculiar spectral energy distribution that cannot be fit with any galaxy spectral template at any redshift. We therefore conclude that the redshift identification of this galaxy remains undetermined.Comment: 9 pages, 2 figures; To appear in Nature (30 November 2000

Alternative analysis to perturbation theory

We develop an alternative approach to time independent perturbation theory in non-relativistic quantum mechanics. The method developed has the advantage to provide in one operation the correction to the energy and to the wave function, additionally we can analyze the time evolution of the system. To verify our results, we apply our method to the harmonic oscillator perturbed by a quadratic potential. An alternative form of the Dyson series, in matrix form instead of integral form, is also obtained.Comment: 12 pages, no figure

Lost and found: the radial quantum number of Laguerre-Gauss modes

We introduce an operator linked with the radial index in the Laguerre-Gauss modes of a two-dimensional harmonic oscillator in cylindrical coordinates. We discuss ladder operators for this variable, and confirm that they obey the commutation relations of the su(1,1) algebra. Using this fact, we examine how basic quantum optical concepts can be recast in terms of radial modes.Comment: Some minor typos fixed

On the structure of the sets of mutually unbiased bases for N qubits

For a system of N qubits, spanning a Hilbert space of dimension d=2^N, it is known that there exists d+1 mutually unbiased bases. Different construction algorithms exist, and it is remarkable that different methods lead to sets of bases with different properties as far as separability is concerned. Here we derive the four sets of nine bases for three qubits, and show how they are unitarily related. We also briefly discuss the four-qubit case, give the entanglement structure of sixteen sets of bases,and show some of them, and their interrelations, as examples. The extension of the method to the general case of N qubits is outlined.Comment: 16 pages, 10 tables, 1 figur