Schlesinger transformations for elliptic isomonodromic deformations

Schlesinger transformations are discrete monodromy preserving symmetry transformations of the classical Schlesinger system. Generalizing well-known results from the Riemann sphere we construct these transformations for isomonodromic deformations on genus one Riemann surfaces. Their action on the system's tau-function is computed and we obtain an explicit expression for the ratio of the old and the transformed tau-function.Comment: 19 pages, LaTeX2

Chemical compositions of six metal-poor stars in the ultra-faint dwarf spheroidal galaxy Bo\"otes I

Ultra-faint dwarf galaxies recently discovered around the Milky Way (MW) contain extremely metal-poor stars, and might represent the building blocks of low-metallicity components of the MW. Among them, the Bo\"otes I dwarf spheroidal galaxy is of particular interest because of its exclusively old stellar population. We determine chemical compositions of six red giant stars in Bo\"otes I, based on the high-resolution spectra obtained with the High Dispersion Spectrograph mounted on the Subaru Telescope. Abundances of 12 elements, including C, Na, alpha, Fe-peak, and neutron capture elements, were determined for the sample stars. The abundance results were compared to those in field MW halo stars previously obtained using an abundance analysis technique similar to the present study. We confirm the low metallicity of Boo-094 ([Fe/H]=-3.4). Except for this star, the abundance ratios ([X/Fe]) of elements lighter than zinc are generally homogeneous with small scatter around the mean values in the metallicities spanned by the other five stars (-2.7-2.7 show no significant enhancement of carbon. The [Mg/Fe] and [Ca/Fe] ratios are almost constant with a modest decreasing trend with increasing [Fe/H] and are slightly lower than the field halo stars. The [Sr/Fe] and [Sr/Ba] ratios also tend to be lower in the Bo\"otes I stars than in the halo stars. Our results of small scatter in the [X/Fe] ratios for elements lighter than zinc suggest that these abundances were homogeneous among the ejecta of prior generation(s) of stars in this galaxy.Comment: 16 pages, 12 figures. Accepted to A&A, language correcte

Stellar structures in the outer regions of M33

We present Subaru/Suprime-Cam deep V and I imaging of seven fields in the outer regions of M33. Our aim is to search for stellar structures corresponding to extended HI clouds found in a recent 21-cm survey of the galaxy. Three fields probe a large HI complex to the southeastern (SE) side of the galaxy. An additional three fields cover the northwestern (NW) side of the galaxy along the HI warp. A final target field was chosen further north, at a projected distance of approximately 25 kpc, to study part of the large stellar plume recently discovered around M33. We analyse the stellar population at R > 10 kpc by means of V, I colour magnitude diagrams reaching the red clump. Evolved stellar populations are found in all fields out to 120' (~ 30 kpc), while a diffuse population of young stars (~ 200 Myr) is detected out to a galactocentric radius of 15 kpc. The mean metallicity in the southern fields remains approximately constant at [M/H] = -0.7 beyond the edge of the optical disc, from 40' out to 80'. Along the northern fields probing the outer \hi disc, we also find a metallicity of [M/H] = -0.7 between 35' and 70' from the centre, which decreases to [M/H] = -1.0 at larger angular radii out to 120'. In the northernmost field, outside the disc extent, the stellar population of the large stellar feature possibly related to a M33-M31 interaction is on average more metal-poor ([M/H] = -1.3) and older (> 6 Gyr). An exponential disc with a large scale-length (~ 7 kpc) fits well the average distribution of stars detected in both the SE and NW regions from a galactocentric distance of 11 kpc out to 30 kpc. The stellar distribution at large radii is disturbed and, although there is no clear correlation between the stellar substructures and the location of the HI clouds, this gives evidence for tidal interaction or accretion events.Comment: 13 pages, 13 figures. Accepted for publications in Astronomy and Astrophysics; minor revisions of the tex

A remark on the Hankel determinant formula for solutions of the Toda equation

We consider the Hankel determinant formula of the $\tau$ functions of the Toda equation. We present a relationship between the determinant formula and the auxiliary linear problem, which is characterized by a compact formula for the $\tau$ functions in the framework of the KP theory. Similar phenomena that have been observed for the Painlev\'e II and IV equations are recovered. The case of finite lattice is also discussed.Comment: 14 pages, IOP styl

Fine structure and magneto-optics of exciton, trion, and charged biexciton states in single InAs quantum dots emitting at 1.3 um

We present a detailed investigation into the optical characteristics of individual InAs quantum dots (QDs) grown by metalorganic chemical vapor deposition, with low temperature emission in the telecoms window around 1300 nm. Using micro-photoluminescence (PL) spectroscopy we have identified neutral, positively charged, and negatively charged exciton and biexciton states. Temperature-dependent measurements reveal dot-charging effects due to differences in carrier diffusivity. We observe a pronounced linearly polarized splitting of the neutral exciton and biexciton lines (~250 ueV) resulting from asymmetry in the QD structure. This asymmetry also causes a mixing of the excited trion states which is manifested in the fine structure and polarization of the charged biexciton emission; from this data we obtain values for the ratio between the anisotropic and isotropic electron-hole exchange energies of (Delta1)/(Delta0)= 0.2--0.5. Magneto-PL spectroscopy has been used to investigate the diamagnetic response and Zeeman splitting of the various exciton complexes. We find a significant variation in g-factor between the exciton, the positive biexciton, and the negative biexciton; this is also attributed to anisotropy effects and the difference in lateral extent of the electron and hole wavefunctions.Comment: 7 pages, 6 figures, submitted to Phys. Rev.

Magnetic properties of the S=1/2S=1/2 distorted diamond chain at T=0

We explore, at T=0, the magnetic properties of the $S=1/2$ antiferromagnetic distorted diamond chain described by the Hamiltonian {\cal H} = \sum_{j=1}^{N/3}{J_1 ({\bi S}_{3j-1} \cdot {\bi S}_{3j} + {\bi S}_{3j} \cdot {\bi S}_{3j+1}) + J_2 {\bi S}_{3j+1} \cdot {\bi S}_{3j+2} + J_3 ({\bi S}_{3j-2} \cdot {\bi S}_{3j} + {\bi S}_{3j} \cdot {\bi S}_{3j+2})} \allowbreak - H \sum_{l=1}^{N} S_l^z with $J_1, J_2, J_3\ge0$, which well models ${\rm A_3 Cu_3 (PO_4)_4}$ with ${\rm A = Ca, Sr}$, ${\rm Bi_4 Cu_3 V_2 O_{14}}$ and azurite $\rm Cu_3(OH)_2(CO_3)_2$. We employ the physical consideration, the degenerate perturbation theory, the level spectroscopy analysis of the numerical diagonalization data obtained by the Lanczos method and also the density matrix renormalization group (DMRG) method. We investigate the mechanisms of the magnetization plateaux at $M=M_s/3$ and $M=(2/3)M_s$, and also show the precise phase diagrams on the $(J_2/J_1, J_3/J_1)$ plane concerning with these magnetization plateaux, where $M=\sum_{l=1}^{N} S_l^z$ and $M_s$ is the saturation magnetization. We also calculate the magnetization curves and the magnetization phase diagrams by means of the DMRG method.Comment: 21 pages, 29 figure

Field-Induced gap due to four-spin exchange in a spin ladder

The effect of the four-spin cyclic exchange interaction at each plaquette in the $S=1/2$ two-leg spin ladder is investigated at T=0, especially focusing on the field-induced gap. The strong rung coupling approximation suggests that it yields a plateau at half of the saturation moment ($m=1/2$) in the magnetization curve, which corresponds to a field-induced spin gap with a spontaneous breaking of the translational symmetry. A precise phase diagram at $m=1/2$ is also presented based on the level spectroscopy analysis of the numerical data obtained by Lanczos method. The boundary between the gapless and plateau phases is confirmed to be of the Kosterlitz-Thouless (KT) universality class.Comment: 10 pages, 3 eps figures (embedded), to be published in J. Phys.: Cond. Matte