Ground State Entropy of the Potts Antiferromagnet on Cyclic Strip Graphs

We present exact calculations of the zero-temperature partition function (chromatic polynomial) and the (exponent of the) ground-state entropy $S_0$ for the $q$-state Potts antiferromagnet on families of cyclic and twisted cyclic (M\"obius) strip graphs composed of $p$-sided polygons. Our results suggest a general rule concerning the maximal region in the complex $q$ plane to which one can analytically continue from the physical interval where $S_0 > 0$. The chromatic zeros and their accumulation set ${\cal B}$ exhibit the rather unusual property of including support for $Re(q) < 0$ and provide further evidence for a relevant conjecture.Comment: 7 pages, Latex, 4 figs., J. Phys. A Lett., in pres

The missing metals problem. III How many metals are expelled from galaxies?

[Abridged] We revisit the metal budget at z~2. In the first two papers of this series, we already showed that ~30% (to <60% if extrapolating the LF) of the metals are observed in all z~2.5 galaxies detected in current surveys. Here, we extend our analysis to the metals outside galaxies, i.e. in intergalactic medium (IGM), using observational data and analytical calculations. Our results for the two are strikingly similar: (1) Observationally, we find that, besides the small (5%) contribution of DLAs, the forest and sub-DLAs contribute subtantially to make <30--45% of the metal budget, but neither of these appear to be sufficient to close the metal budget. The forest accounts for 15--30% depending on the UV background, and sub-DLAs for >2% to <17% depending on the ionization fraction. Together, the `missing metals' problem is substantially eased. (2) We perform analytical calculations based on the effective yield--mass relation. At z=2, we find that the method predicts that 2$--50% of the metals have been ejected from galaxies into the IGM, consistent with the observations. The metal ejection is predominantly by L<1/3L_B^*(z=2) galaxies, which are responsible for 90% the metal enrichment, while the 50 percentile is at L~1/10L^*_B(z=2). As a consequence, if indeed 50% of the metals have been ejected from galaxies, 3--5 bursts of star formation are required per galaxy prior to z=2. The ratio between the mass of metals outside galaxies to those in stars has changed from z=2 to z=0: it was 2:1 or 1:1 and is now 1:8 or 1:9. This evolution implies that a significant fraction of the IGM metals will cool and fall back into galaxies.Comment: 18pages, MNRAS, in press; small changes to match proofs; extended version with summary tabl

Stochastic polarization formation in exciton-polariton Bose-Einstein condensates

We demonstrate theoretically the spontaneous formation of a stochastic polarization in exciton-polariton Bose-Einstein condensates in planar microcavities under pulsed excitation. Below the threshold pumping intensity (dependent on the polariton life-time) the average polarization degree is close to zero, whilst above threshold the condensate acquires a polarization described by a (pseudospin) vector with random orientation, in general. We establish the link between second order coherence of the polariton condensate and the distribution function of its polarization. We examine also the mechanisms of polarization dephasing and relaxation.Comment: 4 pages, 3 figure

Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs

We present exact calculations of chromatic polynomials for families of cyclic graphs consisting of linked polygons, where the polygons may be adjacent or separated by a given number of bonds. From these we calculate the (exponential of the) ground state entropy, $W$, for the q-state Potts model on these graphs in the limit of infinitely many vertices. A number of properties are proved concerning the continuous locus, ${\cal B}$, of nonanalyticities in $W$. Our results provide further evidence for a general rule concerning the maximal region in the complex q plane to which one can analytically continue from the physical interval where $S_0 > 0$.Comment: 27 pages, Latex, 17 figs. J. Phys. A, in pres

Spin-Peierls states of quantum antiferromagnets on the CaV4O9Ca V_4 O_9 lattice

We discuss the quantum paramagnetic phases of Heisenberg antiferromagnets on the 1/5-depleted square lattice found in $Ca V_4 O_9$. The possible phases of the quantum dimer model on this lattice are obtained by a mapping to a quantum-mechanical height model. In addition to the ``decoupled'' phases found earlier, we find a possible intermediate spin-Peierls phase with spontaneously-broken lattice symmetry. Experimental signatures of the different quantum paramagnetic phases are discussed.Comment: 9 pages; 2 eps figure

Assimilation of TES data from the Mars Global Surveyor scientifc mapping phase

The Thermal Emission Spectrometer (TES)aboard Mars Global Surveyor has produced data which cover almost two Martian years so far (during its scientific mapping phase). Thermal profiles for the atmosphere below 40 km and total dust opacities can be retrieved from TES nadir spectra and assimilated into a Mars general circulation model (MGCM), by using the assimilation techniques described in detail by Lewis et al. (2002). This paper describes some preliminary results from assimilations of temperature data from the period Ls=141°- 270° corresponding to late northern summer until winter solstice on Mars. Work in progress is devoted to assimilate both temperature and total dust opacity data for the full period for which they are already available

Data assimilation for the Martian atmosphere using MGS Thermal Emission Spectrometer observations

From the introduction: Given the quantity of data expected from current and forthcoming spacecraft missions to Mars, it is now possible to use data assimilation as a means of atmospheric analysis for the first time for a planet other than the Earth. Several groups have described plans to develop assimilation schemes for Mars [Banfield et al., 1995; Houben, 1999; Lewis and Read, 1995; Lewis et al., 1996, 1997; Zhang et al., 2001]. Data assimilation is a technique for the analysis of atmospheric observations which combines currently valid information with prior knowledge from previous observations and dynamical and physical constraints, via the use of a numerical model. Despite the number of new missions, observations of the atmosphere of Mars in the near future are still likely to be sparse when compared to those of the Earth, perhaps comprising one orbiter and a few surface stations at best at any one time. Data assimilation is useful as a means to extract the maximum information from such observations, both by a form of interpolation in space and time using model constraints and by the combination of information from different observations, e.g. temperature profiles and surface pressure measurements which may be irregularly distributed. The procedure can produce a dynamically consistent set of meteorological fields and can be used directly to test and to refine an atmospheric model against observations

Andreev tunnelling in quantum dots: A slave-boson approach

We study a strongly interacting quantum dot connected to a normal and to a superconducting lead. By means of the slave-boson technique we investigate the low temperature regime and discuss electrical transport through the dot. We find that the zero bias anomaly in the current-voltage characteristics which is associated to the occurance of the Kondo resonance in the quantum dot, is enhanced in the presence of superconductivity, due to resonant Andreev scattering.Comment: 4 pages, 1 figur