Continuous measurement of canonical observables and limit stochastic Schrödinger equations

We derive the stochastic Schrodinger equation for the limit of continuous weak measurement where the observables monitored are canonical position and momentum. To this end we extend an argument due to Smolianov and Truman from the von Neumann model of indirect measurement of position to the Arthurs and Kelly model for simultaneous measurement of position and momentum. We only require unbiasedness of the detector states and an integrability condition sufficient to ensure a central limit effect. Despite taking a weak interaction, as opposed to weak measurement limit, the resulting stochastic wave equation is of the same form as that derived in a recent paper by Scott and Milburn for the specific case of joint Gaussian states.Comment: 15 pages, no figure

Positive Measure Spectrum for Schroedinger Operators with Periodic Magnetic Fields

We study Schroedinger operators with periodic magnetic field in Euclidean 2-space, in the case of irrational magnetic flux. Positive measure Cantor spectrum is generically expected in the presence of an electric potential. We show that, even without electric potential, the spectrum has positive measure if the magnetic field is a perturbation of a constant one.Comment: 17 page

Methanol in W3(H2O) and Surrounding Regions

We present the results of an interferometric study of 38 millimeter-wave lines of CH3OH in the region around the water maser source W3(H2O) and a region extending about 30" to the south and west of the hydroxyl maser source W3(OH). The methanol emitting region around W3(H2O) has an extent of 2.0" x 1.2" (4400 x 2600 AU). The density is of order 1.e7 cm-3, sufficient to thermalize most of the methanol lines. The kinetic temperature is approximately 140 K and the methanol fractional abundance greater than 1.e-6, indicative of a high degree of grain mantle evaporation. The W3(H2O) source contains sub-structure, with peaks corresponding to the TW source and Wyrowski's B/C, separated by 2500 AU in projection. The kinematics are consistent with these being distinct protostellar cores in a wide binary orbit and a dynamical mass for the region of a few tens of Mo. The extended methanol emission to the southwest of W3(OH) is seen strongly only from the lowest excitation lines and from lines known elsewhere to be class I methanol masers, namely the 84.5 GHz 5(-1)-4(0)E and 95.2 GHz 8(0)-7(1)A+ lines. Within this region there are two compact clumps, which we denote as swA and swB, each about 15" (0.16 pc projected distance) away from W3(OH). Excitation analysis of these clumps indicates the presence of lines with inverted populations but only weak amplification. The sources swA and swB appear to have kinetic temperatures of order 50-100 K and densities of order 1.e5 - 1.e6 cm-3. The methanol fractional abundance for the warmer clump is of order 1.e-7, suggestive of partial grain mantle evaporation. The clumping occurs on mass scales of order 1 Mo.Comment: 28 pages including 6 figures and 4 tables, accepted by Ap

A search for 85.5- and 86.6-GHz methanol maser emission

We have used the Australia Telescope National Facility Mopra 22m millimetre telescope to search for emission from the 85.5-GHz and 86.6-GHz transitions of methanol. The search was targeted towards 22 star formation regions which exhibit maser emission in the 107.0-GHz methanol transition, as well as in the 6.6-GHz transition characteristic of class II methanol maser sources. A total of 22 regions were searched at 85.5 GHz resulting in 5 detections, of which 1 appears to be a newly discovered maser. For the 86.6-GHz transition observations were made of 18 regions which yielded 2 detections, but no new maser sources. This search demonstrates that emission from the 85.5- and 86.6-GHz transitions is rare. Detection of maser emission from either of these transitions therefore indicates the presence of special conditions, different from those in the majority of methanol maser sources. We have observed temporal variability in the 86.6-GHz emission towards 345.010+1.792, which along with the very narrow line width, confirms that the emission is a maser in this source. We have combined our current observations with published data for the 6.6-, 12.1-, 85.5-, 86.6-, 107.0-, 108.8- and 156.6-GHz transitions for comparison with the maser model of Sobolev & Deguchi (1994). This has allowed us to estimate the likely ranges of dust temperature, gas density, and methanol column density, both for typical methanol maser sources and for those sources which also show 107.0-GHz emission.Comment: 11 pages, accepted for publication in MNRAS, Latex, mn2e.cl