Exactly-solvable coupled-channel potential models of atom-atom magnetic Feshbach resonances from supersymmetric quantum mechanics

Starting from a system of $N$ radial Schr\"odinger equations with a vanishing potential and finite threshold differences between the channels, a coupled $N \times N$ exactly-solvable potential model is obtained with the help of a single non-conservative supersymmetric transformation. The obtained potential matrix, which subsumes a result obtained in the literature, has a compact analytical form, as well as its Jost matrix. It depends on $N (N+1)/2$ unconstrained parameters and on one upper-bounded parameter, the factorization energy. A detailed study of the model is done for the $2\times 2$ case: a geometrical analysis of the zeros of the Jost-matrix determinant shows that the model has 0, 1 or 2 bound states, and 0 or 1 resonance; the potential parameters are explicitly expressed in terms of its bound-state energies, of its resonance energy and width, or of the open-channel scattering length, which solves schematic inverse problems. As a first physical application, exactly-solvable $2\times 2$ atom-atom interaction potentials are constructed, for cases where a magnetic Feshbach resonance interplays with a bound or virtual state close to threshold, which results in a large background scattering length.Comment: 19 pages, 15 figure

Restricted Wiedemann-Franz law and vanishing thermoelectric power in one-dimensional conductors

In one-dimensional (1D) conductors with linear E-k dispersion (Dirac systems) intrabranch thermalization is favored by elastic electron-electron interaction in contrast to electron systems with a nonlinear (parabolic) dispersion. We show that under external electric fields or thermal gradients the carrier populations of different branches, treated as Fermi gases, have different temperatures as a consequence of self-consistent carrier-heat transport. Specifically, in the presence of elastic phonon scattering, the Wiedemann-Franz law is restricted to each branch with its specific temperature and is characterized by twice the Lorenz number. In addition thermoelectric power vanishes due to electron-hole symmetry, which is validated by experiment.Comment: 10 pages, 2 figure

The Pattern of Correlated X-ray Timing and Spectral Behavior in GRS 1915+105

From data obtained from the PCA in the 2-11 keV and 11-30.5 keV energy range, GRS 1915+105 is seen during RXTE observations between 1996 May and October on two separate branches in a hardness intensity diagram. On the hard branch, GRS 1915+105 exhibits narrow quasi-periodic oscillations ranging from 0.5 to 6 Hz with ${\Delta \nu \over \nu} \sim 0.2$. The QPOs are observed over intensities ranging from about 6,000 to 20,000 counts s$^{-1}$ in the 2 - 12.5 keV energy band, indicating a strong dependence on source intensity. Strong harmonics are seen, especially, at lower frequencies. As the QPO frequency increases, the harmonic feature weakens and disappears. On the soft branch, narrow QPOs are absent and the low frequency component of the power density spectrum is approximated by a power-law, with index $\sim -1.25$ for low count rates and $\sim -1.5$ for high count rates (\gta 18000 cts/s). Occasionally, a broad peaked feature in the 1-6 Hz frequency range is also observed on this branch. The source was probably in the very high state similar to those of other black hole candidates. Thermal-viscous instabilities in accretion disk models do not predict the correlation of the narrow QPO frequency and luminosity unless the fraction of luminosity from the disk decreases with the total luminosity.Comment: ApJ Lett accepte

Statistical Curse of the Second Half Rank

In competitions involving many participants running many races the final rank is determined by the score of each participant, obtained by adding its ranks in each individual race. The "Statistical Curse of the Second Half Rank" is the observation that if the score of a participant is even modestly worse than the middle score, then its final rank will be much worse (that is, much further away from the middle rank) than might have been expected. We give an explanation of this effect for the case of a large number of races using the Central Limit Theorem. We present exact quantitative results in this limit and demonstrate that the score probability distribution will be gaussian with scores packing near the center. We also derive the final rank probability distribution for the case of two races and we present some exact formulae verified by numerical simulations for the case of three races. The variant in which the worst result of each boat is dropped from its final score is also analyzed and solved for the case of two races.Comment: 16 pages, 10 figure

Vibrational spectroscopy of H2+: precise evaluation of the Zeeman effect

We present an accurate computation of the g-factors of the hyperfine states of the hydrogen molecular ion H2+. The results are in good agreement with previous experiments, and can be tested further by rf spectroscopy. Their implication for high-precision two-photon vibrational spectroscopy of H2+ is also discussed. It is found that the most intense hyperfine components of two-photon lines benefit from a very small Zeeman splitting

Measuring Extinction Curves of Lensing Galaxies

We critique the method of constructing extinction curves of lensing galaxies using multiply imaged QSOs. If one of the two QSO images is lightly reddened or if the dust along both sightlines has the same properties then the method works well and produces an extinction curve for the lensing galaxy. These cases are likely rare and hard to confirm. However, if the dust along each sightline has different properties then the resulting curve is no longer a measurement of extinction. Instead, it is a measurement of the difference between two extinction curves. This "lens difference curve'' does contain information about the dust properties, but extracting a meaningful extinction curve is not possible without additional, currently unknown information. As a quantitative example, we show that the combination of two Cardelli, Clayton, & Mathis (CCM) type extinction curves having different values of R(V) will produce a CCM extinction curve with a value of R(V) which is dependent on the individual R(V) values and the ratio of V band extinctions. The resulting lens difference curve is not an average of the dust along the two sightlines. We find that lens difference curves with any value of R(V), even negative values, can be produced by a combination of two reddened sightlines with different CCM extinction curves with R(V) values consistent with Milky Way dust (2.1 < R(V) < 5.6). This may explain extreme values of R(V) inferred by this method in previous studies. But lens difference curves with more normal values of R(V) are just as likely to be composed of two dust extinction curves with R(V) values different than that of the lens difference curve. While it is not possible to determine the individual extinction curves making up a lens difference curve, there is information about a galaxy's dust contained in the lens difference curves.Comment: 15 pages, 4 figues, ApJ in pres

Joint density-functional theory for electronic structure of solvated systems

We introduce a new form of density functional theory for the {\em ab initio} description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of a solute with a classical density-functional theory for the liquid into a single variational principle for the free energy of the combined system. A simple approximate functional predicts, without any fitting of parameters to solvation data, solvation energies as well as state-of-the-art quantum-chemical cavity approaches, which require such fitting.Comment: Fixed typos and minor updates to tex