Wave Chaos in Rotating Optical Cavities

It is shown that, even when the eigenmodes of an optical cavity are wave-chaotic, the frequency splitting due to the rotation of the cavity occurs and the frequency difference is proportional to the angular velocity although the splitting eigenmodes are still wave-chaotic and do not correspond to any unidirectionally-rotating waves.Comment: 4 pages, 6 figure

New detections of isotopic molecular absorption lines: a low ¹²C:¹³C ratio in nearby gas

Molecular absorption line observations towards the background source Sgr B2 `M' are presented. Previous observations have shown that there are ~9 foreground clouds of moderate density along this line of sight, which produce absorption lines that are well spaced in velocity. In two of these clouds, first detections have now been made of the rare isotopomers 12CS, HN13C, HC15N and HC18O+. For a feature at lsr velocities of -4 to +18km s-1, the isotopic ratio 12C:13C has been estimated, from the relative intensities of 12CS and 13CS J=1-0 lines, and also by comparing the strength of the 13CS line with that of C34S J=1-0 observed previously. A convergent solution for the two methods is found if 12CS is optically thick but the isotopomer lines are optically thin. In this case 12C:13C is 24±11, which is surprisingly low if the gas lies near the Sun, as indicated by its velocity. However, it has been suggested that parts of this feature may in fact arise in hot gas close to the Sgr B2 cloud, where a low isotope ratio is expected. If this region of the line is excluded, the 12C:13C ratio for the remaining lsr velocities of +11 to +18kms-1 is only slightly changed, with a value of 22±13. This is the true carbon isotope ratio in some nearby gas, if effects such as peculiar velocities and isotopic fractionation are unimportant. The value found here is well below the local average of ~60-70 in the solar neighbourhood, which suggests that some of the nearby absorbing gas has been recently isotopically enriched by stellar ejecta. This moderate density absorbing gas is then more likely to be material left over after star-formation, rather than a pre-star-for

NGC 7538 : Multiwavelength Study of Stellar Cluster Regions associated with IRS 1-3 and IRS 9 sources

We present deep and high-resolution (FWHM ~ 0.4 arcsec) near-infrared (NIR) imaging observations of the NGC 7538 IRS 1-3 region (in JHK bands), and IRS 9 region (in HK bands) using the 8.2m Subaru telescope. The NIR analysis is complemented with GMRT low-frequency observations at 325, 610, and 1280 MHz, molecular line observations of H13CO+ (J=1-0), and archival Chandra X-ray observations. Using the 'J-H/H-K' diagram, 144 Class II and 24 Class I young stellar object (YSO) candidates are identified in the IRS 1-3 region. Further analysis using 'K/H-K' diagram yields 145 and 96 red sources in the IRS 1-3 and IRS 9 regions, respectively. A total of 27 sources are found to have X-ray counterparts. The YSO mass function (MF), constructed using a theoretical mass-luminosity relation, shows peaks at substellar (~0.08-0.18 Msolar) and intermediate (~1-1.78 Msolar) mass ranges for the IRS 1-3 region. The MF can be fitted by a power law in the low mass regime with a slope of Gamma ~ 0.54-0.75, which is much shallower than the Salpeter value of 1.35. An upper limit of 10.2 is obtained for the star to brown dwarf ratio in the IRS 1-3 region. GMRT maps show a compact HII region associated with the IRS 1-3 sources, whose spectral index of 0.87+-0.11 suggests optical thickness. This compact region is resolved into three separate peaks in higher resolution 1280 MHz map, and the 'East' sub-peak coincides with the IRS 2 source. H13CO+ (J=1-0) emission reveals peaks in both IRS 1-3 and IRS 9 regions, none of which are coincident with visible nebular emission, suggesting the presence of dense cloud nearby. The virial masses are approximately of the order of 1000 Msolar and 500 Msolar for the clumps in IRS 1-3 and IRS 9 regions, respectively.Comment: 27 pages, 18 figures, 5 tables. Accepted for publication in MNRA

Hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices

We investigate the hydrodynamic limit for weakly asymmetric simple exclusion processes in crystal lattices. We construct a suitable scaling limit by using a discrete harmonic map. As we shall observe, the quasi-linear parabolic equation in the limit is defined on a flat torus and depends on both the local structure of the crystal lattice and the discrete harmonic map. We formulate the local ergodic theorem on the crystal lattice by introducing the notion of local function bundle, which is a family of local functions on the configuration space. The ideas and methods are taken from the discrete geometric analysis to these problems. Results we obtain are extensions of ones by Kipnis, Olla and Varadhan to crystal lattices.Comment: 41 pages, 7 figure

Observations of five molecular species in absorption towards Sagittarius B2

Seven diffuse molecular clouds have been detected in absorption, using the Sgr B2 star-formation region was used as a source of background continuum emission. Transitions were observed at frequencies around 49, 85 and 98 GHz, from CS, C34S, H13CN, H13CO+, SiO and C3H2. Clouds detected in absorption include the "nuclear disk", the 3 kpc expanding arm, spiral arms in the Galactic Plane, and two unidentified regions. The nuclear disk line profile was found to be inconsistent with homogeneous disk or bar models, instead suggesting irregular perturbations of the gas within a few hundred pc of the Galactic Centre. Absorption in CS was detected in two different rotational transitions, leading to reliable estimates of the physical parameters of the clouds. In particular, exitation temperaturers could be estimated, instead of assumed values being used, as was the case in previous studies. Results from an LTE analysis and from LVG modelling show that the absorption lines are mostly optically thin, with molecular column densities ~1012-14cm-2 per cloud. Excitation temperatures as high as 5K were found, inconsistent with heating by the 2.7K cosmic background radiation alone. Cloud densities were estimated at nH2~104cm-3, or less if the gas is highly subthermalised

Quantum graphs with singular two-particle interactions

We construct quantum models of two particles on a compact metric graph with singular two-particle interactions. The Hamiltonians are self-adjoint realisations of Laplacians acting on functions defined on pairs of edges in such a way that the interaction is provided by boundary conditions. In order to find such Hamiltonians closed and semi-bounded quadratic forms are constructed, from which the associated self-adjoint operators are extracted. We provide a general characterisation of such operators and, furthermore, produce certain classes of examples. We then consider identical particles and project to the bosonic and fermionic subspaces. Finally, we show that the operators possess purely discrete spectra and that the eigenvalues are distributed following an appropriate Weyl asymptotic law

New Maser Emission from Nonmetastable Ammonia in NGC 7538. II. Green Bank Telescope Observations Including Water Masers

We present new maser emission from ^{14}NH_3 (9,6) in NGC 7538. Our observations include the known spectral features near v_LSR = -60 km/s and -57 km/s and several more features extending to -46 km/s. In three epochs of observation spanning two months we do not detect any variability in the ammonia masers, in contrast to the >10-fold variability observed in other ^{14}NH_3 (9,6) masers in the Galaxy over comparable timescales. We also present observations of water masers in all three epochs for which emission is observed over the velocity range -105 km/s < v_LSR < -4 km/s, including the highest velocity water emission yet observed from NGC 7538. Of the remarkable number of maser species in IRS 1, H_2O and, now, ^{14}NH_3 are the only masers known to exhibit emission outside of the velocity range -62 km/s < v_LSR < -51 km/s. However, we find no significant intensity or velocity correlations between the water emission and ammonia emission. We also present a non-detection in the most sensitive search to date toward any source for emission from the CC^{32}S and CC^{34}S molecules, indicating an age greater than \approx 10^4 yr for IRS 1-3. We discuss these findings in the context of embedded stellar cores and recent models of the region.Comment: 7 pages, 4 figures, 3 tables; accepted to AJ; color figures only on arxiv; revised to include references and minor proof change

Universal behavior of quantum Green's functions

We consider a general one-particle Hamiltonian H = - \Delta_r + u(r) defined in a d-dimensional domain. The object of interest is the time-independent Green function G_z(r,r') = . Recently, in one dimension (1D), the Green's function problem was solved explicitly in inverse form, with diagonal elements of Green's function as prescribed variables. The first aim of this paper is to extract from the 1D inverse solution such information about Green's function which cannot be deduced directly from its definition. Among others, this information involves universal, i.e. u(r)-independent, behavior of Green's function close to the domain boundary. The second aim is to extend the inverse formalism to higher dimensions, especially to 3D, and to derive the universal form of Green's function for various shapes of the confining domain boundary.Comment: 46 pages, the shortened version submitted to J. Math. Phy

Finite geometries and diffractive orbits in isospectral billiards

Several examples of pairs of isospectral planar domains have been produced in the two-dimensional Euclidean space by various methods. We show that all these examples rely on the symmetry between points and blocks in finite projective spaces; from the properties of these spaces, one can derive a relation between Green functions as well as a relation between diffractive orbits in isospectral billiards.Comment: 10 page

Isospectral domains with mixed boundary conditions

We construct a series of examples of planar isospectral domains with mixed Dirichlet-Neumann boundary conditions. This is a modification of a classical problem proposed by M. Kac.Comment: 9 figures. Statement of Theorem 5.1 correcte