Semiclassical Time Evolution and Trace Formula for Relativistic Spin-1/2 Particles

We investigate the Dirac equation in the semiclassical limit \hbar --> 0. A semiclassical propagator and a trace formula are derived and are shown to be determined by the classical orbits of a relativistic point particle. In addition, two phase factors enter, one of which can be calculated from the Thomas precession of a classical spin transported along the particle orbits. For the second factor we provide an interpretation in terms of dynamical and geometric phases.Comment: 8 pages, no figure

Low-frequency broadband sound source localization using an adaptive normal mode back-propagation approach in a shallow-water ocean

Author Posting. © Acoustical Society of America, 2012. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 131 (2012): 1798-1813, doi:10.1121/1.3672643.A variety of localization methods with normal mode theory have been established for localizing low frequency (below a few hundred Hz), broadband signals in a shallow water environment. Gauss-Markov inverse theory is employed in this paper to derive an adaptive normal mode back-propagation approach. Joining with the maximum a posteriori mode filter, this approach is capable of separating signals from noisy data so that the back-propagation will not have significant influence from the noise. Numerical simulations are presented to demonstrate the robustness and accuracy of the approach, along with comparisons to other methods. Applications to real data collected at the edge of the continental shelf off New Jersey, USA are presented, and the effects of water column fluctuations caused by nonlinear internal waves and shelfbreak front variability are discussed.The SW06 experiment was supported by the Office of Naval Research

Periodic-Orbit Bifurcations and Superdeformed Shell Structure

We have derived a semiclassical trace formula for the level density of the three-dimensional spheroidal cavity. To overcome the divergences occurring at bifurcations and in the spherical limit, the trace integrals over the action-angle variables were performed using an improved stationary phase method. The resulting semiclassical level density oscillations and shell-correction energies are in good agreement with quantum-mechanical results. We find that the bifurcations of some dominant short periodic orbits lead to an enhancement of the shell structure for "superdeformed" shapes related to those known from atomic nuclei.Comment: 4 pages including 3 figure

Isotopic ratios of H, C, N, O, and S in comets C/2012 F6 (Lemmon) and C/2014 Q2 (Lovejoy)

The apparition of bright comets C/2012 F6 (Lemmon) and C/2014 Q2 (Lovejoy) in March-April 2013 and January 2015, combined with the improved observational capabilities of submillimeter facilities, offered an opportunity to carry out sensitive compositional and isotopic studies of the volatiles in their coma. We observed comet Lovejoy with the IRAM 30m telescope between 13 and 26 January 2015, and with the Odin submillimeter space observatory on 29 January - 3 February 2015. We detected 22 molecules and several isotopologues. The H$_2^{16}$O and H$_2^{18}$O production rates measured with Odin follow a periodic pattern with a period of 0.94 days and an amplitude of ~25%. The inferred isotope ratios in comet Lovejoy are $^{16}$O/$^{18}$O = 499 $\pm$ 24 and D/H = 1.4 $\pm$ 0.4 $\times 10^{-4}$ in water, $^{32}$S/$^{34}$S = 24.7 $\pm$ 3.5 in CS, all compatible with terrestrial values. The ratio $^{12}$C/$^{13}$C = 109 $\pm$ 14 in HCN is marginally higher than terrestrial and $^{14}$N/$^{15}$N = 145 $\pm$ 12 in HCN is half the Earth ratio. Several upper limits for D/H or 12C/13C in other molecules are reported. From our observation of HDO in comet C/2014 Q2 (Lovejoy), we report the first D/H ratio in an Oort Cloud comet that is not larger than the terrestrial value. On the other hand, the observation of the same HDO line in the other Oort-cloud comet, C/2012 F6 (Lemmon), suggests a D/H value four times higher. Given the previous measurements of D/H in cometary water, this illustrates that a diversity in the D/H ratio and in the chemical composition, is present even within the same dynamical group of comets, suggesting that current dynamical groups contain comets formed at very different places or times in the early solar system.Comment: Accepted for publication in Astronomy and Astrophysic

Submillimeter Emission from Water in the W3 Region

We have mapped the submillimeter emission from the 1(10)-1(01) transition of ortho-water in the W3 star-forming region. A 5'x5' map of the W3 IRS4 and W3 IRS5 region reveals strong water lines at half the positions in the map. The relative strength of the Odin lines compared to previous observations by SWAS suggests that we are seeing water emission from an extended region. Across much of the map the lines are double-peaked, with an absorption feature at -39 km/s; however, some positions in the map show a single strong line at -43 km/s. We interpret the double-peaked lines as arising from optically thick, self-absorbed water emission near the W3 IRS5, while the narrower blue-shifted lines originate in emission near W3 IRS4. In this model, the unusual appearance of the spectral lines across the map results from a coincidental agreement in velocity between the emission near W3 IRS4 and the blue peak of the more complex lines near W3 IRS5. The strength of the water lines near W3 IRS4 suggests we may be seeing water emission enhanced in a photon-dominated region.Comment: Accepted to A&A Letters as part of the special Odin issue; 4 page

First detection of NH3 (1,0 - 0,0) from a low mass cloud core: On the low ammonia abundance of the rho Oph A core

Odin has successfully observed the molecular core rho Oph A in the 572.5 GHz rotational ground state line of ammonia, NH3 (J,K = 1,0 - 0,0). The interpretation of this result makes use of complementary molecular line data obtained from the ground (C17O and CH3OH) as part of the Odin preparatory work. Comparison of these observations with theoretical model calculations of line excitation and transfer yields a quite ordinary abundance of methanol, X(CH3OH) = 3e-9. Unless NH3 is not entirely segregated from C17O and CH3OH, ammonia is found to be significantly underabundant with respect to typical dense core values, viz. X(NH3) = 8e-10.Comment: 4 pages, 2 figures, 2 tables, to appear in Astron. Astrophys. Letter

Surface scattering and band gaps in rough waveguides and nanowires

The boundaries of waveguides and nanowires have drastic influence on their coherent scattering properties. Designing the boundary profile is thus a promising approach for transmission and band-gap engineering with many applications. By performing an experimental study of microwave transmission through rough waveguides we demonstrate that a recently proposed surface scattering theory can be employed to predict the measured transmission properties from the boundary profiles and vice versa. A new key ingredient of this theory is a scattering mechanism which depends on the squared gradient of the surface profiles. We demonstrate the non-trivial effects of this scattering mechanism by detailed mode-resolved microwave measurements and numerical simulations.Comment: 5 pages 4 figure

Semiclassical theory of spin-orbit interactions using spin coherent states

We formulate a semiclassical theory for systems with spin-orbit interactions. Using spin coherent states, we start from the path integral in an extended phase space, formulate the classical dynamics of the coupled orbital and spin degrees of freedom, and calculate the ingredients of Gutzwiller's trace formula for the density of states. For a two-dimensional quantum dot with a spin-orbit interaction of Rashba type, we obtain satisfactory agreement with fully quantum-mechanical calculations. The mode-conversion problem, which arose in an earlier semiclassical approach, has hereby been overcome.Comment: LaTeX (RevTeX), 4 pages, 2 figures, accepted for Physical Review Letters; final version (v2) for publication with minor editorial change

Semiclassical theory of spin-orbit interaction in the extended phase space

We consider the semiclassical theory in a joint phase space of spin and orbital degrees of freedom. The method is developed from the path integrals using the spin-coherent-state representation, and yields the trace formula for the density of states. We discuss special cases, such as weak and strong spin-orbit coupling, and relate the present theory to the earlier approaches.Comment: 36 pages, 8 figures. Version 2: revised Sec. 4.4 and Appendix B; minor corrections elsewher

Horizontal ducting of sound by curved nonlinear internal gravity waves in the continental shelf areas

Author Posting. © Acoustical Society of America, 2013. This article is posted here by permission of Acoustical Society of America for personal use, not for redistribution. The definitive version was published in Journal of the Acoustical Society of America 133 (2013): 37-49, doi:10.1121/1.4770240.The acoustic ducting effect by curved nonlinear gravity waves in shallow water is studied through idealized models in this paper. The internal wave ducts are three-dimensional, bounded vertically by the sea surface and bottom, and horizontally by aligned wavefronts. Both normal mode and parabolic equation methods are taken to analyze the ducted sound field. Two types of horizontal acoustic modes can be found in the curved internal wave duct. One is a whispering-gallery type formed by the sound energy trapped along the outer and concave boundary of the duct, and the other is a fully bouncing type due to continual reflections from boundaries in the duct. The ducting condition depends on both internal-wave and acoustic-source parameters, and a parametric study is conducted to derive a general pattern. The parabolic equation method provides full-field modeling of the sound field, so it includes other acoustic effects caused by internal waves, such as mode coupling/scattering and horizontal Lloyd's mirror interference. Two examples are provided to present internal wave ducts with constant curvature and meandering wavefronts.This work was sponsored by the Office of Naval Research under grants N00014-10-1-0040 and N00014-11- 1-0701