The single-particle density matrix and the momentum distribution of dark "solitons" in a Tonks-Girardeau gas

We study the reduced single-particle density matrix (RSPDM), the momentum distribution, natural orbitals and their occupancies, of dark "soliton" (DS) states in a Tonks-Girardeau gas. DS states are specially tailored excited many-body eigenstates, which have a dark solitonic notch in their single-particle density. The momentum distribution of DS states has a characteristic shape with two sharp spikes. We find that the two spikes arise due to the high degree of correlation observed within the RSPDM between the mirror points ($x$ and $-x$) with respect to the dark notch at $x=0$; the correlations oscillate rather than decay as the points $x$ and $-x$ are being separated.Comment: 9 pages, 8 figure

EU Peatlands: Current Carbon Stocks and Trace Gas Fluxes

Peatlands in Europe has formed a significant sink for atmospheric CO2 since the last glacial maximum. Currently they are estimated to hold ca. 42 Gt carbon in the form of peat and are therefore a considerable component in the European carbon budget. Due to the generally wet soil conditions in peatlands they are also significant emitters of the strong greenhouse gas (GHG) methane (CH4) and in some cases also of nitrous oxide (N2O). The EU funded CarboEurope-GHG Concerted Action attempts to develop a reliable and complete greenhouse gas budget for Europe and this report aims to provide a review and synthesis of the available information about GHG exchanges in European peatlands and their underlying processes. A best estimate for all the European countries shows that some are currently sinks for atmospheric CO2 while others are sources. In contrast, for CH4 and N2O, only the sources are relevant. Whilst some countries are CO2 sinks, all countries are net GHG emitters from peatlands. The results presented, however, carry large uncertainties, which cannot be adequately quantified yet. One outstanding uncertainty is the distribution of land use types, particular in Russia, the largest European peat nation. The synthesis of GHG exchange, nevertheless, indicates some interesting features. Russia hosts an estimated 41% of European peatlands and contributes most to all GHG exchanges (CO2: 25%, CH4: 52%, N2O: 26%, Total: 37%). Germany is the second-largest emitter (12% of European total) although it contains only 3.2% of European peatlands. The reason is the use of most of the peatland area for intensive cropland and grassland. The largest CO2 emitters are countries with large agricultural peatland areas (Russia, Germany, Belarus, Poland), the largest N2O emitters are those with large agricultural fen areas (Russia, Germany, Finland). In contrast, the largest CH4 emitters are concentrated in regions with large areas of intact mires, namely Russia and Scandinavia. High average emission densities above 3.5 t C-equiv. ha-1 are found in the Southeast Mediterranean, Germany and the Netherlands where agricultural use of peatlands is intense. Low average emission densities below 0.3 t C-equiv. ha-1 occur where mires and peatland forests dominate, e.g. Finland and the UK. This report concludes by pointing at key gaps in our knowledge about peatland carbon stocks and GHG exchanges which include insufficient basic information on areal distribution of peatlands, measurements of peat depth and also a lack of flux datasets providing full annual budgets of GHG exchanges

Hormander class of pseudo-differential operators on compact Lie groups and global hypoellipticity

In this paper we give several global characterisations of the Hormander class of pseudo-differential operators on compact Lie groups. The result is applied to give criteria for the ellipticity and the global hypoellipticity of pseudo-differential operators in terms of their matrix-valued full symbols. Several examples of the first and second order globally hypoelliptic differential operators are given. Where the global hypoelliptiticy fails, one can construct explicit examples based on the analysis of the global symbols.Comment: 20 page

A relativistic study of Bessel beams

We present a fully relativistic analysis of Bessel beams revealing some noteworthy features that are not explicit in the standard description. It is shown that there is a reference frame in which the field takes a particularly simple form, the wave appearing to rotate in circles. The concepts of polarization and angular momentum for Bessel beams is also reanalyzed.Comment: 11 pages, 2 fig

Interval valued (\in,\ivq)-fuzzy filters of pseudo BLBL-algebras

We introduce the concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set. By using this new idea, we introduce the notions of interval valued (\in,\ivq)-fuzzy filters of pseudo $BL$-algebras and investigate some of their related properties. Some characterization theorems of these generalized interval valued fuzzy filters are derived. The relationship among these generalized interval valued fuzzy filters of pseudo $BL$-algebras is considered. Finally, we consider the concept of implication-based interval valued fuzzy implicative filters of pseudo $BL$-algebras, in particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed

Energetic electron precipitation associated with pulsating aurora: EISCAT and Van Allen Probe observations

Pulsating auroras show quasi-periodic intensity modulations caused by the precipitation of energetic electrons of the order of tens of keV. It is expected theoretically that not only these electrons but also sub-relativistic/relativistic electrons precipitate simultaneously into the ionosphere owing to whistler-mode wave–particle interactions. The height-resolved electron density profile was observed with the European Incoherent Scatter (EISCAT) Tromsø VHF radar on 17 November 2012. Electron density enhancements were clearly identified at altitudes >68 km in association with the pulsating aurora, suggesting precipitation of electrons with a broadband energy range from ~10 keV up to at least 200 keV. The riometer and network of subionospheric radio wave observations also showed the energetic electron precipitations during this period. During this period, the footprint of the Van Allen Probe-A satellite was very close to Tromsø and the satellite observed rising tone emissions of the lower-band chorus (LBC) waves near the equatorial plane. Considering the observed LBC waves and electrons, we conducted a computer simulation of the wave–particle interactions. This showed simultaneous precipitation of electrons at both tens of keV and a few hundred keV, which is consistent with the energy spectrum estimated by the inversion method using the EISCAT observations. This result revealed that electrons with a wide energy range simultaneously precipitate into the ionosphere in association with the pulsating aurora, providing the evidence that pulsating auroras are caused by whistler chorus waves. We suggest that scattering by propagating whistler simultaneously causes both the precipitations of sub-relativistic electrons and the pulsating aurora

Optical dipole traps and atomic waveguides based on Bessel light beams

We theoretically investigate the use of Bessel light beams generated using axicons for creating optical dipole traps for cold atoms and atomic waveguiding. Zeroth-order Bessel beams can be used to produce highly elongated dipole traps allowing for the study of one-dimensional trapped gases and realization of a Tonks gas of impentrable bosons. First-order Bessel beams are shown to be able to produce tight confined atomic waveguides over centimeter distances.Comment: 20 pages, 5 figures, to appear in Phys. Rev.

Generation of nearly nondiffracting Bessel beams with a Fabry–Perot interferometer

A new concept for generating zero-order Bessel beams was studied theoretically. The spatial intensity distribution was calculated numerically using a wave optics model. Approximate analytical expressions were derived to describe the radial intensity distribution in planes perpendicular to the optical axis of an imaging lens.Texas InstrumentsNational Science FoundationOTKA Foundation of the Hungarian Academy of Science

Parameterisation of the chemical effects of sprites in the middle atmosphere

Transient luminous events, such as red sprites, occur in the middle atmosphere in the electric field above thunderstorms. We here address the question whether these processes may be a significant source of odd nitrogen and affect ozone or other important trace species. A well-established coupled ion-neutral chemical model has been extended for this purpose and applied together with estimated rates of ionisation, excitation and dissociation based on spectroscopic ratios from ISUAL on FORMOSAT-2. This approach is used to estimate the NO<sub>x</sub> and ozone changes for two type cases. <br><br> The NO<sub>x</sub> enhancements are at most one order of magnitude in the streamers, which means a production of at most 10 mol per event, or (given a global rate of occurrence of three events per minute) some 150–1500 kg per day. The present study therefore indicates that sprites are insignificant as a global source of NO<sub>x</sub>. Local effects on ozone are also negligible, but the local enhancement of NO<sub>x</sub> may be significant, up to 5 times the minimum background at 70 km in extraordinary cases

Broadband Meter-Wavelength Observations of Ionospheric Scintillation

Intensity scintillations of cosmic radio sources are used to study astrophysical plasmas like the ionosphere, the solar wind, and the interstellar medium. Normally these observations are relatively narrow band. With Low Frequency Array (LOFAR) technology at the Kilpisj\"arvi Atmospheric Imaging Receiver Array (KAIRA) station in northern Finland we have observed scintillations over a 3 octave bandwidth. ``Parabolic arcs'', which were discovered in interstellar scintillations of pulsars, can provide precise estimates of the distance and velocity of the scattering plasma. Here we report the first observations of such arcs in the ionosphere and the first broad-band observations of arcs anywhere, raising hopes that study of the phenomenon may similarly improve the analysis of ionospheric scintillations. These observations were made of the strong natural radio source Cygnus-A and covered the entire 30-250\,MHz band of KAIRA. Well-defined parabolic arcs were seen early in the observations, before transit, and disappeared after transit although scintillations continued to be obvious during the entire observation. We show that this can be attributed to the structure of Cygnus-A. Initial results from modeling these scintillation arcs are consistent with simultaneous ionospheric soundings taken with other instruments, and indicate that scattering is most likely to be associated more with the topside ionosphere than the F-region peak altitude. Further modeling and possible extension to interferometric observations, using international LOFAR stations, are discussed.Comment: 11 pages, 17 figure