Group quantization of parametrized systems II. Pasting Hilbert spaces

The method of group quantization described in the preceeding paper I is extended so that it becomes applicable to some parametrized systems that do not admit a global transversal surface. A simple completely solvable toy system is studied that admits a pair of maximal transversal surfaces intersecting all orbits. The corresponding two quantum mechanics are constructed. The similarity of the canonical group actions in the classical phase spaces on the one hand and in the quantum Hilbert spaces on the other hand suggests how the two Hilbert spaces are to be pasted together. The resulting quantum theory is checked to be equivalent to that constructed directly by means of Dirac's operator constraint method. The complete system of partial Hamiltonians for any of the two transversal surfaces is chosen and the quantum Schr\"{o}dinger or Heisenberg pictures of time evolution are constructed.Comment: 35 pages, latex, no figure

Quantum corrections to the Larmor radiation formula in scalar electrodynamics

We use the semi-classical approximation in perturbative scalar quantum electrodynamics to calculate the quantum correction to the Larmor radiation formula to first order in Planck's constant in the non-relativistic approximation, choosing the initial state of the charged particle to be a momentum eigenstate. We calculate this correction in two cases: in the first case the charged particle is accelerated by a time-dependent but space-independent vector potential whereas in the second case it is accelerated by a time-independent vector potential which is a function of one spatial coordinate. We find that the corrections in these two cases are different even for a charged particle with the same classical motion. The correction in each case turns out to be non-local in time in contrast to the classical approximation.Comment: 19 page

Towards the re-verification of process tank calibrations

Re-verification is needed to ensure that the calibration (the relationship between measured level and measured volume) that is obtained during commissioning hasn’t changed over time. This can be achieved, in part, by metering in solution and correlating with marks identified a priori. Mark identification and correlation are discussed and possible error sources are outlined

Group Averaging for de Sitter free fields

Perturbative gravity about global de Sitter space is subject to linearization-stability constraints. Such constraints imply that quantum states of matter fields couple consistently to gravity {\it only} if the matter state has vanishing de Sitter charges; i.e., only if the state is invariant under the symmetries of de Sitter space. As noted by Higuchi, the usual Fock spaces for matter fields contain no de Sitter-invariant states except the vacuum, though a new Hilbert space of de Sitter invariant states can be constructed via so-called group-averaging techniques. We study this construction for free scalar fields of arbitrary positive mass in any dimension, and for linear vector and tensor gauge fields in any dimension. Our main result is to show in each case that group averaging converges for states containing a sufficient number of particles. We consider general $N$-particle states with smooth wavefunctions, though we obtain somewhat stronger results when the wavefunctions are finite linear combinations of de Sitter harmonics. Along the way we obtain explicit expressions for general boost matrix elements in a familiar basis.Comment: 33 pages, 2 figure

Arbitrary Choice of Basic Variables in Density Functional Theory. II. Illustrative Applications

Our recent theory (Ref. 1) enables us to choose arbitrary quantities as the basic variables of the density functional theory. In this paper we apply it to several cases. In the case where the occupation matrix of localized orbitals is chosen as a basic variable, we can obtain the single-particle equation which is equivalent to that of the LDA+U method. The theory also leads to the Hartree-Fock-Kohn-Sham equation by letting the exchange energy be a basic variable. Furthermore, if the quantity associated with the density of states near the Fermi level is chosen as a basic variable, the resulting single-particle equation includes the additional potential which could mainly modify the energy-band structures near the Fermi level.Comment: 27 page

Do static sources respond to massive scalar particles from the Hawking radiation as uniformly accelerated ones do in the inertial vacuum?

We revisit the recently found equivalence for the response of a static scalar source interacting with a {\em massless} Klein-Gordon field when the source is (i) static in Schwarzschild spacetime, in the Unruh vacuum associated with the Hawking radiation and (ii) uniformly accelerated in Minkowski spacetime, in the inertial vacuum, provided that the source's proper acceleration is the same in both cases. It is shown that this equivalence is broken when the massless Klein-Gordon field is replaced by a {\em massive} one.Comment: 4 pages, 2 figure

Satellite tracking in avian conservation: applications and results from Asia

Using satellite tracking, we have followed the movements of large wetland birds in Asia for more than 10 years. We have investigated the migration patterns of more than 10 species of birds, focusing on, but not limited to, cranes (Gruidae) and storks (Ciconiidae). To relay bird locations, we employed platform transmitter terminals in combination with ARGOS satellites. Location data were then utilized in a variety of applications, from determining migration routes, stopover patterns and wintering sites, through more advanced analyses including using various data overlays to examine habitat use, occupation of nature reserves, differential migration patterns between adults and juvenile birds, climatological effects on migration and the connectivity and network structure of migration pathways. Through this work, we have identified numerous important sites for migratory birds, especially cranes and storks. These include Bohai Bay and the Yellow River delta (China), the Korean Demilitarized Zone, Lake Khanka (Russia/China), and Poyang Lake, the Qiqihar Baicheng area, the Three Rivers Plain and Yangcheng Nature Reserve (all in China). We have also developed recommendations for spatial improvements to nature reserves, discovered different migration strategies in juvenile and adult birds, and a possible migration trigger involving temperature. We emphasize the importance of continued empirical research and development of analytical methodologies involving satellite location data. Further, we advocate the protection of habitats used by Gruidae and Ciconiidae over their entire migration routes

Optical control of magnetization of micron-size domains in antiferromagnetic NiO single crystals

We propose Raman-induced collinear difference-frequency generation (DFG) as a method to manipulate dynamical magnetization. When a fundamental beam propagates along a threefold rotational axis, this coherent second-order optical process is permitted by angular momentum conservation through the rotational analogue of the Umklapp process. As a demonstration, we experimentally obtained polarization properties of collinear magnetic DFG along a [111] axis of a single crystal of antiferromagnetic NiO with micro multidomain structure, which excellently agreed with the theoretical prediction.Comment: 11 pages, 3 figures, submitted to Physical Review Letter

Interaction of Hawking radiation with static sources in deSitter and Schwarzschild-deSitter spacetimes

We study and look for similarities between the response rates $R^{\rm dS}(a_0, \Lambda)$ and $R^{\rm SdS}(a_0, \Lambda, M)$ of a static scalar source with constant proper acceleration $a_0$ interacting with a massless, conformally coupled Klein-Gordon field in (i) deSitter spacetime, in the Euclidean vacuum, which describes a thermal flux of radiation emanating from the deSitter cosmological horizon, and in (ii) Schwarzschild-deSitter spacetime, in the Gibbons-Hawking vacuum, which describes thermal fluxes of radiation emanating from both the hole and the cosmological horizons, respectively, where $\Lambda$ is the cosmological constant and $M$ is the black hole mass. After performing the field quantization in each of the above spacetimes, we obtain the response rates at the tree level in terms of an infinite sum of zero-energy field modes possessing all possible angular momentum quantum numbers. In the case of deSitter spacetime, this formula is worked out and a closed, analytical form is obtained. In the case of Schwarzschild-deSitter spacetime such a closed formula could not be obtained, and a numerical analysis is performed. We conclude, in particular, that $R^{\rm dS}(a_0, \Lambda)$ and $R^{\rm SdS}(a_0, \Lambda, M)$ do not coincide in general, but tend to each other when $\Lambda \to 0$ or $a_0 \to \infty$. Our results are also contrasted and shown to agree (in the proper limits) with related ones in the literature.Comment: ReVTeX4 file, 9 pages, 5 figure