Functional Equations and the Generalised Elliptic Genus

We give a new derivation and characterisation of the generalised elliptic genus of Krichever-H\"ohn by means of a functional equation.Comment: To be published in the collection honouring Francesco Calogero's 70-th birthda

Testing the Unitarity of the CKM Matrix with a Space-Based Neutron Decay Experiment

If the Standard Model is correct, and fundamental fermions exist only in the three generations, then the CKM matrix should be unitary. However, there remains a question over a deviation from unitarity from the value of the neutron lifetime. We discuss a simple space-based experiment that, at an orbit height of 500 km above Earth, would measure the kinetic-energy, solid-angle, flux spectrum of gravitationally bound neutrons (kinetic energy K<0.606 eV at this altitude). The difference between the energy spectrum of neutrons that come up from the Earth's atmosphere and that of the undecayed neutrons that return back down to the Earth would yield a measurement of the neutron lifetime. This measurement would be free of the systematics of laboratory experiments. A package of mass $<25$ kg could provide a 10^{-3} precision in two years.Comment: 10 pages, 4 figures. Revised and updated for publicatio

Hubble Space Telescope Ultraviolet Imaging and High-Resolution Spectroscopy of Water Photodissociation Products in Comet Hyakutake (C/1996 B2)

Comet Hyakutake (C/1996 B2) provided a target of opportunity for performing a systematic study of water photodissociation products in which we obtained data from three instruments on the Hubble Space Telescope (HST). The HST Goddard High Resolution Spectrograph (GHRS) was used to measure the line profile of hydrogen Lyα (H Lyα) at six locations around the coma of the comet, ranging from the nucleus to a displacement of 100,000 km, and covering different directions compared with the comet-sun line. GHRS yielded line profiles with a spectral resolution (FWHM ~4 km s^(-1)) that was a factor of 2-3 better than any previous H Lyα or Hα ground-based measurements. The Wide Field Planetary Camera 2 (WFPC2) and the Woods filter were used to obtain H Lyα images of the inner coma. The faint object spectrograph (FOS) was used to determine the OH production rate and monitor its variation throughout the HST observing sequence. The GHRS H Lyα line profiles show the behavior of a line profile that is optically thick in the core for positions near the nucleus (<5000 km) and gradually becoming more optically thin at larger displacements and lower column abundances. A composite H Lyα image constructed from four separate WFPC2 exposures is consistent with the relative fluxes seen in GHRS observations and clearly shows the dayside enhancement of a solar illuminated optically thick coma. These data were analyzed self-consistently to test our understanding of the detailed physics and chemistry of the expanding coma and our ability to obtain accurate water production rates from remote observations of gaseous hydrogen (H) and hydroxyl (OH), the major water dissociation products. Our hybrid kinetic/hydrodynamic model of the coma combined with a spherical radiative transfer calculation is able to account for (1) the velocity distribution of H atoms, (2) the spatial distribution of the H Lyα emission in the inner coma, and (3) the absolute intensities of H and OH emissions, giving a water production rate of (2.6 ± 0.4) × 10^(29) s^(-1) on 1996 April 4

Spectral Function of 2D Fermi Liquids

We show that the spectral function for single-particle excitations in a two-dimensional Fermi liquid has Lorentzian shape in the low energy limit. Landau quasi-particles have a uniquely defined spectral weight and a decay rate which is much smaller than the quasi-particle energy. By contrast, perturbation theory and the T-matrix approximation yield spurious deviations from Fermi liquid behavior, which are particularly pronounced for a linearized dispersion relation.Comment: 6 pages, LaTeX2e, 5 EPS figure

On the Stability and Single-Particle Properties of Bosonized Fermi Liquids

We study the stability and single-particle properties of Fermi liquids in spatial dimensions greater than one via bosonization. For smooth non-singular Fermi liquid interactions we obtain Shankar's renormalization- group flows and reproduce well known results for quasi-particle lifetimes. We demonstrate by explicit calculation that spin-charge separation does not occur when the Fermi liquid interactions are regular. We also explore the relationship between quantized bosonic excitations and zero sound modes and present a concise derivation of both the spin and the charge collective mode equations. Finally we discuss some aspects of singular Fermi liquid interactions.Comment: 13 pages plus three postscript figures appended; RevTex 3.0; BUP-JBM-

THE WAIT-AND-SEE OPTION IN ASCENDING PRICE AUCTIONS

Cake-cutting protocols aim at dividing a ``cake'' (i.e., a divisible resource) and assigning the resulting portions to several players in a way that each of the players feels to have received a ``fair'' amount of the cake. An important notion of fairness is envy-freeness: No player wishes to switch the portion of the cake received with another player's portion. Despite intense efforts in the past, it is still an open question whether there is a \emph{finite bounded} envy-free cake-cutting protocol for an arbitrary number of players, and even for four players. We introduce the notion of degree of guaranteed envy-freeness (DGEF) as a measure of how good a cake-cutting protocol can approximate the ideal of envy-freeness while keeping the protocol finite bounded (trading being disregarded). We propose a new finite bounded proportional protocol for any number n \geq 3 of players, and show that this protocol has a DGEF of 1 + \lceil (n^2)/2 \rceil. This is the currently best DGEF among known finite bounded cake-cutting protocols for an arbitrary number of players. We will make the case that improving the DGEF even further is a tough challenge, and determine, for comparison, the DGEF of selected known finite bounded cake-cutting protocols.Comment: 37 pages, 4 figure

HUT observations of carbon monoxide in the coma of Comet Levy (1990c)

Observations of comet Levy (1990c) were made with the Hopkins Ultraviolet Telescope during the Astro-1 Space Shuttle mission on 10 Dec. 1990. The spectrum, covering the wavelength range 415 to 1850 A at a spectral emission of 3 A (in first order), shows the presence of carbon monoxide and atomic hydrogen, carbon, and sulfur in the coma. Aside from H I Lyman-beta, no cometary features are detected below 1200 A, although cometary O I and O II would be masked by the same emissions present in the day airglow spectrum. The 9.4 x 116 arcsec aperture corresponds to 12,000 x 148,000 km at the comet. The derived production rate of CO relative to water, 0.13 + or - 0.02, compared with the same ratio derived from IUE observations (made in Sep. 1990) which sample a much smaller region of the coma, 0.04 + or - 0.01, suggests the presence of an extended source of CO, as was found in comet Halley. Upper limits on Ne and Ar abundance are within an order of magnitude or solar abundances

Functional renormalization group approach to correlated fermion systems

Numerous correlated electron systems exhibit a strongly scale-dependent behavior. Upon lowering the energy scale, collective phenomena, bound states, and new effective degrees of freedom emerge. Typical examples include (i) competing magnetic, charge, and pairing instabilities in two-dimensional electron systems, (ii) the interplay of electronic excitations and order parameter fluctuations near thermal and quantum phase transitions in metals, (iii) correlation effects such as Luttinger liquid behavior and the Kondo effect showing up in linear and non-equilibrium transport through quantum wires and quantum dots. The functional renormalization group is a flexible and unbiased tool for dealing with such scale-dependent behavior. Its starting point is an exact functional flow equation, which yields the gradual evolution from a microscopic model action to the final effective action as a function of a continuously decreasing energy scale. Expanding in powers of the fields one obtains an exact hierarchy of flow equations for vertex functions. Truncations of this hierarchy have led to powerful new approximation schemes. This review is a comprehensive introduction to the functional renormalization group method for interacting Fermi systems. We present a self-contained derivation of the exact flow equations and describe frequently used truncation schemes. Reviewing selected applications we then show how approximations based on the functional renormalization group can be fruitfully used to improve our understanding of correlated fermion systems.Comment: Review article, final version, 59 pages, 28 figure

Drying Shrinkage Mechanisms in Portland Cement Paste

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/65426/1/j.1151-2916.1987.tb05002.x.pd