The XX--model with boundaries. Part I: Diagonalization of the finite chain

This is the first of three papers dealing with the XX finite quantum chain with arbitrary, not necessarily hermitian, boundary terms. This extends previous work where the periodic or diagonal boundary terms were considered. In order to find the spectrum and wave-functions an auxiliary quantum chain is examined which is quadratic in fermionic creation and annihilation operators and hence diagonalizable. The secular equation is in general complicated but several cases were found when it can be solved analytically. For these cases the ground-state energies are given. The appearance of boundary states is also discussed and in view to the applications considered in the next papers, the one and two-point functions are expressed in terms of Pfaffians.Comment: 56 pages, LaTeX, some minor correction

Frustrated quantum Heisenberg ferrimagnetic chains

We study the ground-state properties of weakly frustrated Heisenberg ferrimagnetic chains with nearest and next-nearest neighbor antiferromagnetic exchange interactions and two types of alternating sublattice spins S_1 > S_2, using 1/S spin-wave expansions, density-matrix renormalization group, and exact- diagonalization techniques. It is argued that the zero-point spin fluctuations completely destroy the classical commensurate- incommensurate continuous transition. Instead, the long-range ferrimagnetic state disappears through a discontinuous transition to a singlet state at a larger value of the frustration parameter. In the ferrimagnetic phase we find a disorder point marking the onset of incommensurate real-space short-range spin-spin correlations.Comment: 16 pages (LaTex 2.09), 6 eps figure

Submillimeter Line Emission from LMC 30Dor: The Impact of a Starburst on a Low Metallicity Environment

(Abridged) The 30 Dor region in the Large Magellanic Cloud (LMC) is the most vigorous star-forming region in the Local Group. Star formation in this region is taking place in low-metallicity molecular gas that is exposed to an extreme far--ultraviolet (FUV) radiation field powered by the massive compact star cluster R136. We used the NANTEN2 telescope to obtain high-angular resolution observations of the 12CO 4-3, 7-6, and 13CO 4-3 rotational lines and [CI] 3P1-3P0 and 3P2-3P1 fine-structure submillimeter transitions in 30Dor-10, the brightest CO and FIR-emitting cloud at the center of the 30Dor region. We derived the properties of the low-metallicity molecular gas using an excitation/radiative transfer code and found a self-consistent solution of the chemistry and thermal balance of the gas in the framework of a clumpy cloud PDR model. We compared the derived properties with those in the N159W region, which is exposed to a more moderate far-ultraviolet radiation field compared with 30Dor-10, but has similar metallicity. We also combined our CO detections with previously observed low-J CO transitions to derive the CO spectral-line energy distribution in 30Dor-10 and N159W. The separate excitation analysis of the submm CO lines and the neutral carbon fine structure lines shows that the mid-J CO and [CI]-emitting gas in the 30Dor-10 region has a temperature of about 160 K and a H2 density of about 10^4 cm^-3. We find that the molecular gas in 30Dor-10 is warmer and has a lower beam filling factor compared to that of N159W, which might be a result of the effect of a strong FUV radiation field heating and disrupting the low--metallicity molecular gas. We use a clumpy PDR model (including the [CII] line intensity reported in the literature) to constrain the FUV intensity to about chi_0 ~ 3100 and an average total H density of the clump ensemble of about 10^5 cm^-3 in 30Dor-10.Comment: 11 pages, 8 figures. Accepted for publication in A&

SU(2)/Z2SU(2)/Z_2 symmetry of the BKT transition and twisted boundary conditio n

Berezinskii-Kosterlitz-Thouless (BKT) transition, the transition of the 2D sine-Gordon model, plays an important role in the low dimensional physics. We relate the operator content of the BKT transition to that of the SU(2) Wess-Zumino-Witten model, using twisted boundary conditions. With this method, in order to determine the BKT critical point, we can use the level crossing of the lower excitations than the periodic boundary case, thus the convergence to the transition point is highly improved. Then we verify the efficiency of this method by applying to the S=1,2 spin chains.Comment: LaTex2e,, 33 pages, 14 figures in eps file

Elementary Excitations of Heisenberg Ferrimagnetic Spin Chains

We numerically investigate elementary excitations of the Heisenberg alternating-spin chains with two kinds of spins 1 and 1/2 antiferromagnetically coupled to each other. Employing a recently developed efficient Monte Carlo technique as well as an exact diagonalization method, we verify the spin-wave argument that the model exhibits two distinct excitations from the ground state which are gapless and gapped. The gapless branch shows a quadratic dispersion in the small-momentum region, which is of ferromagnetic type. With the intention of elucidating the physical mechanism of both excitations, we make a perturbation approach from the decoupled-dimer limit. The gapless branch is directly related to spin 1's, while the gapped branch originates from cooperation of the two kinds of spins.Comment: 7 pages, 7 Postscript figures, RevTe

Photon Dominated Regions in NGC 3603

Aims: We aim at deriving the excitation conditions of the interstellar gas as well as the local FUV intensities in the molecular cloud surrounding NGC 3603 to get a coherent picture of how the gas is energized by the central stars. Methods: The NANTEN2-4m submillimeter antenna is used to map the [CI] 1-0, 2-1 and CO 4-3, 7-6 lines in a 2' x 2' region around the young OB cluster NGC 3603 YC. These data are combined with C18O 2-1 data, HIRES-processed IRAS 60 and 100 micron maps of the FIR continuum, and Spitzer/IRAC maps. Results: The NANTEN2 observations show the presence of two molecular clumps located south-east and south-west of the cluster and confirm the overall structure already found by previous CS and C18O observations. We find a slight position offset of the peak intensity of CO and [CI], and the atomic carbon appears to be further extended compared to the molecular material. We used the HIRES far-infrared dust data to derive a map of the FUV field heating the dust. We constrain the FUV field to values of \chi = 3 - 6 \times 10^3 in units of the Draine field across the clouds. Approximately 0.2 to 0.3 % of the total FUV energy is re-emitted in the [CII] 158 {\mu}m cooling line observed by ISO. Applying LTE and escape probability calculations, we derive temperatures (TMM1 = 43 K, TMM2 = 47 K), column densities (N(MM1) = 0.9 \times 10^22 cm^-2, N(MM2) = 2.5 \times 10^22 cm^-2) and densities (n(MM1) = 3 \times 10^3 cm^-3, n(MM2) = 10^3 -10^4 cm^-3) for the two observed molecular clumps MM1 and MM2. Conclusions: The cluster is strongly interacting with the ambient molecular cloud, governing its structure and physical conditions. A stability analysis shows the existence of gravitationally collapsing gas clumps which should lead to star formation. Embedded IR sources have already been observed in the outskirts of the molecular cloud and seem to support our conclusions.Comment: 13 pages, 10 figures, accepted for publication by A&

Variable Modified Chaplygin Gas in Anisotropic Universe with Kaluza-Klein Metric

In this work, we have consider Kaluza-Klein Cosmology for anisotropic universe where the universe is filled with variable modified chaplygin gas (VMCG). Here we find normal scalar field $\phi$ and the self interacting potential $V(\phi)$ to describe the VMCG Cosmology. Also we graphically analyzed the geometrical parameters named {\it statefinder parameters} in anisotropic Kaluza-Klein model. Next, we consider a Kaluza-Klein model of interacting VMCG with dark matter in the Einstein gravity framework. Here we construct the three dimensional autonomous dynamical system of equations for this interacting model with the assumption that the dark energy and the dark matter are interact between them and for that we also choose the interaction term. We convert that interaction terms to its dimensionless form and perform stability analysis and solve them numerically. We obtain a stable scaling solution of the equations in Kaluza-Klein model and graphically represent solutions.Comment: 11 pages, 13 figure

Spitzer Analysis of HII Region Complexes in the Magellanic Clouds: Determining a Suitable Monochromatic Obscured Star Formation Indicator

HII regions are the birth places of stars, and as such they provide the best measure of current star formation rates (SFRs) in galaxies. The close proximity of the Magellanic Clouds allows us to probe the nature of these star forming regions at small spatial scales. We aim to determine the monochromatic IR band that most accurately traces the bolometric IR flux (TIR), which can then be used to estimate an obscured SFR. We present the spatial analysis, via aperture/annulus photometry, of 16 LMC and 16 SMC HII region complexes using the Spitzer IRAC and MIPS bands. UV rocket data and SHASSA H-alpha data are also included. We find that nearly all of the LMC and SMC HII region SEDs peak around 70um, from ~10 to ~400 pc from the central sources. As a result, the sizes of HII regions as probed by 70um is approximately equal to the sizes as probed by TIR (about 70 pc in radius); the radial profile of the 70um flux, normalized by TIR, is constant at all radii (70um ~ 0.45 TIR); the 1-sigma standard deviation of the 70um fluxes, normalized by TIR, is a lower fraction of the mean (0.05 to 0.12 out to ~220 pc) than the normalized 8, 24, and 160um normalized fluxes (0.12 to 0.52); and these results are invariant between the LMC and SMC. From these results, we argue that 70um is the most suitable IR band to use as a monochromatic obscured star formation indicator because it most accurately reproduces the TIR of HII regions in the LMC and SMC and over large spatial scales. We also explore the general trends of the 8, 24, 70, and 160um bands in the LMC and SMC HII region SEDs, radial surface brightness profiles, sizes, and normalized (by TIR) radial flux profiles. We derive an obscured SFR equation that is modified from the literature to use 70um luminosity, SFR(Mo/yr) = 9.7(0.7)x10^{-44} L(70)(ergs/s), which is applicable from 10 to 300 pc distance from the center of an HII region.Comment: 21 pages, 12 figures, 4 tables. Will be published in ApJ

Determining the Physical Lens Parameters of the Binary Gravitational Microlensing Event MOA-2009-BLG-016

We report the result of the analysis of the light curve of the microlensing event MOA-2009-BLG-016. The light curve is characterized by a short-duration anomaly near the peak and an overall asymmetry. We find that the peak anomaly is due to a binary companion to the primary lens and the asymmetry of the light curve is explained by the parallax effect caused by the acceleration of the observer over the course of the event due to the orbital motion of the Earth around the Sun. In addition, we detect evidence for the effect of the finite size of the source near the peak of the event, which allows us to measure the angular Einstein radius of the lens system. The Einstein radius combined with the microlens parallax allows us to determine the total mass of the lens and the distance to the lens. We identify three distinct classes of degenerate solutions for the binary lens parameters, where two are manifestations of the previously identified degeneracies of close/wide binaries and positive/negative impact parameters, while the third class is caused by the symmetric cycloid shape of the caustic. We find that, for the best-fit solution, the estimated mass of the lower-mass component of the binary is (0.04 +- 0.01) M_sun, implying a brown-dwarf companion. However, there exists a solution that is worse only by \Delta\chi^2 ~ 3 for which the mass of the secondary is above the hydrogen-burning limit. Unfortunately, resolving these two degenerate solutions will be difficult as the relative lens-source proper motions for both are similar and small (~ 1 mas/yr) and thus the lens will remain blended with the source for the next several decades.Comment: 7 pages, 2 tables, and 5 figure

The First Neptune Analog or Super-Earth with Neptune-like Orbit: MOA-2013-BLG-605Lb

We present the discovery of the first Neptune analog exoplanet or super-Earth with Neptune-like orbit, MOA-2013-BLG-605Lb. This planet has a mass similar to that of Neptune or a super-Earth and it orbits at $9\sim 14$ times the expected position of the snow-line, $a_{\rm snow}$, which is similar to Neptune's separation of $11\,a_{\rm snow}$ from the Sun. The planet/host-star mass ratio is $q=(3.6\pm0.7)\times 10^{-4}$ and the projected separation normalized by the Einstein radius is $s=2.39\pm0.05$. There are three degenerate physical solutions and two of these are due to a new type of degeneracy in the microlensing parallax parameters, which we designate "the wide degeneracy". The three models have (i) a Neptune-mass planet with a mass of $M_{\rm p}=21_{-7}^{+6} M_{Earth}$ orbiting a low-mass M-dwarf with a mass of $M_{\rm h}=0.19_{-0.06}^{+0.05} M_\odot$, (ii) a mini-Neptune with $M_{\rm p}= 7.9_{-1.2}^{+1.8} M_{Earth}$ orbiting a brown dwarf host with $M_{\rm h}=0.068_{-0.011}^{+0.019} M_\odot$ and (iii) a super-Earth with $M_{\rm p}= 3.2_{-0.3}^{+0.5} M_{Earth}$ orbiting a low-mass brown dwarf host with $M_{\rm h}=0.025_{-0.004}^{+0.005} M_\odot$ which is slightly favored. The 3-D planet-host separations are 4.6$_{-1.2}^{+4.7}$ AU, 2.1$_{-0.2}^{+1.0}$ AU and 0.94$_{-0.02}^{+0.67}$ AU, which are $8.9_{-1.4}^{+10.5}$, $12_{-1}^{+7}$ or $14_{-1}^{+11}$ times larger than $a_{\rm snow}$ for these models, respectively. The Keck AO observation confirm that the lens is faint. This discovery suggests that low-mass planets with Neptune-like orbit are common. So processes similar to the one that formed Neptune in our own Solar System or cold super-Earth may be common in other solar systems.Comment: 54 pages, 10 figures, 13 tables, Accepted for publication in the Ap