A Canonical Ensemble Approach to the Fermion/Boson Random Point Processes and its Applications

We introduce the boson and the fermion point processes from the elementary quantum mechanical point of view. That is, we consider quantum statistical mechanics of canonical ensemble for a fixed number of particles which obey Bose-Einstein, Fermi-Dirac statistics, respectively, in a finite volume. Focusing on the distribution of positions of the particles, we have point processes of the fixed number of points in a bounded domain. By taking the thermodynamic limit such that the particle density converges to a finite value, the boson/fermion processes are obtained. This argument is a realization of the equivalence of ensembles, since resulting processes are considered to describe a grand canonical ensemble of points. Random point processes corresponding to para-particles of order two are discussed as an application of the formulation. A statistics of a system of composite particles at zero temperature are also considered as a model of determinantal random point processes.Comment: 26pages, Some typos are corrected, to be published in Commun. Math. Phy

Tunable Exchange Interaction in Quantum Dot Devices

We theoretically discuss the Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction between semiconductor quantum dots (QDs). When each QD having a local spin is coupled to the conduction electrons in semiconductors, an indirect exchange interaction, i.e., the RKKY interaction, is induced between two local spins. The RKKY interaction between QDs, which is mediated by the Fermi sea in semiconductors, is modulated by changing the Fermi energy, and the magnitude or even the sign of the exchange interaction can be tuned, which leads to a tunable magnetic transition in QD devices. We estimate the magnitude of the RKKY interaction in QDs as a function of the electron density and the inter-dot distance

Star formation activity in the southern Galactic HII region G351.63-1.25

The southern Galactic high mass star-forming region, G351.6-1.3, is a HII region-molecular cloud complex with a luminosity of 2.0 x 10^5 L_sun, located at a distance of 2.4 kpc. In this paper, we focus on the investigation of the associated HII region, embedded cluster and the interstellar medium in the vicinity of G351.6-1.3. We address the identification of exciting source(s) as well as the census of stellar populations. The ionised gas distribution has been mapped using the Giant Metrewave Radio Telescope (GMRT), India at three continuum frequencies: 1280, 610 and 325 MHz. The HII region shows an elongated morphology and the 1280 MHz map comprises six resolved high density regions encompassed by diffuse emission spanning 1.4 pc x 1.0 pc. The zero age main-sequence (ZAMS) spectral type of the brightest radio core is O7.5. We have carried out near-infrared observations in the JHKs bands using the SIRIUS instrument on the 1.4 m Infrared Survey Facility (IRSF) telescope. The near-infrared images reveal the presence of a cluster embedded in nebulous fan-shaped emission. The log-normal slope of the K-band luminosity function of the embedded cluster is found to be 0.27 +- 0.03 and the fraction of the near-infrared excess stars is estimated to be 43%. These indicate that the age of the cluster is consistent with 1 Myr. The champagne flow model from a flat, thin molecular cloud is used to explain the morphology of radio emission with respect to the millimetre cloud and infrared brightness.Comment: 18 pages, 8 figures, To be published in MNRA

Bound states in two spatial dimensions in the non-central case

We derive a bound on the total number of negative energy bound states in a potential in two spatial dimensions by using an adaptation of the Schwinger method to derive the Birman-Schwinger bound in three dimensions. Specifically, counting the number of bound states in a potential gV for g=1 is replaced by counting the number of g_i's for which zero energy bound states exist, and then the kernel of the integral equation for the zero-energy wave functon is symmetrized. One of the keys of the solution is the replacement of an inhomogeneous integral equation by a homogeneous integral equation.Comment: Work supported in part by the U.S. Department of Energy under Grant No. DE-FG02-84-ER4015

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