Quantum pumping: Coherent Rings versus Open Conductors

We examine adiabatic quantum pumping generated by an oscillating scatterer embedded in a one-dimensional ballistic ring and compare it with pumping caused by the same scatterer connected to external reservoirs. The pumped current for an open conductor, paradoxically, is non-zero even in the limit of vanishing transmission. In contrast, for the ring geometry the pumped current vanishes in the limit of vanishing transmission. We explain this paradoxical result and demonstrate that the physics underlying adiabatic pumping is the same in open and in closed systems.Comment: 4 pages, 2 figure

Adiabatic quantum pump in the presence of external ac voltages

We investigate a quantum pump which in addition to its dynamic pump parameters is subject to oscillating external potentials applied to the contacts of the sample. Of interest is the rectification of the ac currents flowing through the mesoscopic scatterer and their interplay with the quantum pump effect. We calculate the adiabatic dc current arising under the simultaneous action of both the quantum pump effect and classical rectification. In addition to two known terms we find a third novel contribution which arises from the interference of the ac currents generated by the external potentials and the ac currents generated by the pump. The interference contribution renormalizes both the quantum pump effect and the ac rectification effect. Analysis of this interference effect requires a calculation of the Floquet scattering matrix beyond the adiabatic approximation based on the frozen scattering matrix alone. The results permit us to find the instantaneous current. In addition to the current generated by the oscillating potentials, and the ac current due to the variation of the charge of the frozen scatterer, there is a third contribution which represents the ac currents generated by an oscillating scatterer. We argue that the resulting pump effect can be viewed as a quantum rectification of the instantaneous ac currents generated by the oscillating scatterer. These instantaneous currents are an intrinsic property of a nonstationary scattering process.Comment: 11 pages, 1 figur

SPIDER: Probing the Early Universe with a Suborbital Polarimeter

We evaluate the ability of SPIDER, a balloon-borne polarimeter, to detect a divergence-free polarization pattern ("B-modes") in the Cosmic Microwave Background (CMB). In the inflationary scenario, the amplitude of this signal is proportional to that of the primordial scalar perturbations through the tensor-to-scalar ratio r. We show that the expected level of systematic error in the SPIDER instrument is significantly below the amplitude of an interesting cosmological signal with r=0.03. We present a scanning strategy that enables us to minimize uncertainty in the reconstruction of the Stokes parameters used to characterize the CMB, while accessing a relatively wide range of angular scales. Evaluating the amplitude of the polarized Galactic emission in the SPIDER field, we conclude that the polarized emission from interstellar dust is as bright or brighter than the cosmological signal at all SPIDER frequencies (90 GHz, 150 GHz, and 280 GHz), a situation similar to that found in the "Southern Hole." We show that two ~20-day flights of the SPIDER instrument can constrain the amplitude of the B-mode signal to r<0.03 (99% CL) even when foreground contamination is taken into account. In the absence of foregrounds, the same limit can be reached after one 20-day flight.Comment: 29 pages, 8 figures, 4 tables; v2: matches published version, flight schedule updated, two typos fixed in Table 2, references and minor clarifications added, results unchange

Planck 2015 results. XXVII. The Second Planck Catalogue of Sunyaev-Zeldovich Sources

We present the all-sky Planck catalogue of Sunyaev-Zeldovich (SZ) sources detected from the 29 month full-mission data. The catalogue (PSZ2) is the largest SZ-selected sample of galaxy clusters yet produced and the deepest all-sky catalogue of galaxy clusters. It contains 1653 detections, of which 1203 are confirmed clusters with identified counterparts in external data-sets, and is the first SZ-selected cluster survey containing > $10^3$ confirmed clusters. We present a detailed analysis of the survey selection function in terms of its completeness and statistical reliability, placing a lower limit of 83% on the purity. Using simulations, we find that the Y5R500 estimates are robust to pressure-profile variation and beam systematics, but accurate conversion to Y500 requires. the use of prior information on the cluster extent. We describe the multi-wavelength search for counterparts in ancillary data, which makes use of radio, microwave, infra-red, optical and X-ray data-sets, and which places emphasis on the robustness of the counterpart match. We discuss the physical properties of the new sample and identify a population of low-redshift X-ray under- luminous clusters revealed by SZ selection. These objects appear in optical and SZ surveys with consistent properties for their mass, but are almost absent from ROSAT X-ray selected samples

Planck 2018 results. IV. Diffuse component separation

We present full-sky maps of the cosmic microwave background (CMB) and polarized synchrotron and thermal dust emission, derived from the third set of Planck frequency maps. These products have significantly lower contamination from instrumental systematic effects than previous versions. The methodologies used to derive these maps follow closely those described in earlier papers, adopting four methods (Commander, NILC, SEVEM, and SMICA) to extract the CMB component, as well as three methods (Commander, GNILC, and SMICA) to extract astrophysical components. Our revised CMB temperature maps agree with corresponding products in the Planck 2015 delivery, whereas the polarization maps exhibit significantly lower large-scale power, reflecting the improved data processing described in companion papers; however, the noise properties of the resulting data products are complicated, and the best available end-to-end simulations exhibit relative biases with respect to the data at the few percent level. Using these maps, we are for the first time able to fit the spectral index of thermal dust independently over 3 degree regions. We derive a conservative estimate of the mean spectral index of polarized thermal dust emission of beta_d = 1.55 +/- 0.05, where the uncertainty marginalizes both over all known systematic uncertainties and different estimation techniques. For polarized synchrotron emission, we find a mean spectral index of beta_s = -3.1 +/- 0.1, consistent with previously reported measurements. We note that the current data processing does not allow for construction of unbiased single-bolometer maps, and this limits our ability to extract CO emission and correlated components. The foreground results for intensity derived in this paper therefore do not supersede corresponding Planck 2015 products. For polarization the new results supersede the corresponding 2015 products in all respects

Planck 2018 results. III. High Frequency Instrument data processing and frequency maps

This paper presents the High Frequency Instrument (HFI) data processing procedures for the Planck 2018 release. Major improvements in mapmaking have been achieved since the previous 2015 release. They enabled the first significant measurement of the reionization optical depth parameter using HFI data. This paper presents an extensive analysis of systematic effects, including the use of simulations to facilitate their removal and characterize the residuals. The polarized data, which presented a number of known problems in the 2015 Planck release, are very significantly improved. Calibration, based on the CMB dipole, is now extremely accurate and in the frequency range 100 to 353 GHz reduces intensity-to-polarization leakage caused by calibration mismatch. The Solar dipole direction has been determined in the three lowest HFI frequency channels to within one arc minute, and its amplitude has an absolute uncertainty smaller than $0.35\mu$K, an accuracy of order $10^{-4}$. This is a major legacy from the HFI for future CMB experiments. The removal of bandpass leakage has been improved by extracting the bandpass-mismatch coefficients for each detector as part of the mapmaking process; these values in turn improve the intensity maps. This is a major change in the philosophy of "frequency maps", which are now computed from single detector data, all adjusted to the same average bandpass response for the main foregrounds. Simulations reproduce very well the relative gain calibration of detectors, as well as drifts within a frequency induced by the residuals of the main systematic effect. Using these simulations, we measure and correct the small frequency calibration bias induced by this systematic effect at the $10^{-4}$ level. There is no detectable sign of a residual calibration bias between the first and second acoustic peaks in the CMB channels, at the $10^{-3}$ level

Planck 2018 results. XII. Galactic astrophysics using polarized dust emission

We present 353 GHz full-sky maps of the polarization fraction p, angle \u3c8, and dispersion of angles S of Galactic dust thermal emission produced from the 2018 release of Planck data. We confirm that the mean and maximum of p decrease with increasing NH. The uncertainty on the maximum polarization fraction, pmax=22.0% at 80 arcmin resolution, is dominated by the uncertainty on the zero level in total intensity. The observed inverse behaviour between p and S is interpreted with models of the polarized sky that include effects from only the topology of the turbulent Galactic magnetic field. Thus, the statistical properties of p, \u3c8, and S mostly reflect the structure of the magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map S 7p, looking for residual trends. While p decreases by a factor of 3--4 between NH=1020 cm 122 and NH=2 71022 cm 122, S 7p decreases by only about 25%, a systematic trend observed in both the diffuse ISM and molecular clouds. Second, we find no systematic trend of S 7p with the dust temperature, even though in the diffuse ISM lines of sight with high p and low S tend to have colder dust. We also compare Planck data with starlight polarization in the visible at high latitudes. The agreement in polarization angles is remarkable. Two polarization emission-to-extinction ratios that characterize dust optical properties depend only weakly on NH and converge towards the values previously determined for translucent lines of sight. We determine an upper limit for the polarization fraction in extinction of 13%, compatible with the pmax observed in emission. These results provide strong constraints for models of Galactic dust in diffuse gas

L. Evidence of spatial variation of the polarized thermal dust spectral energy distribution and implications for CMB B-mode analysis

Planck Collaboration.The characterization of the Galactic foregrounds has been shown to be the main obstacle in thechallenging quest to detect primordial B-modes in the polarized microwave sky. We make use of the Planck-HFI 2015 data release at high frequencies to place new constraints on the properties of the polarized thermal dust emission at high Galactic latitudes. Here, we specifically study the spatial variability of the dust polarized spectral energy distribution (SED), and its potential impact on the determination of the tensor-to-scalar ratio, r. We use the correlation ratio of the angular power spectra between the 217 and 353 GHz channels as a tracer of these potential variations, computed on different high Galactic latitude regions, ranging from 80% to 20% of the sky. The new insight from Planck data is a departure of the correlation ratio from unity that cannot be attributed to a spurious decorrelation due to the cosmic microwave background, instrumental noise, or instrumental systematics. The effect is marginally detected on each region, but the statistical combination of all the regions gives more than 99% confidence for this variation in polarized dust properties. In addition, we show that the decorrelation increases when there is a decrease in the mean column density of the region of the sky being considered, and we propose a simple power-law empirical model for this dependence, which matches what is seen in the Planck data. We explore the effect that this measured decorrelation has on simulations of the BICEP2-Keck Array/Planck analysis and show that the 2015 constraints from these data still allow a decorrelation between the dust at 150 and 353 GHz that is compatible with our measured value. Finally, using simplified models, we show that either spatial variation of the dust SED or of the dust polarization angle are able to produce decorrelations between 217 and 353 GHz data similar to the values we observe in the data.The Planck Collaboration acknowledges the support of: ESA; CNES, and CNRS/INSU-IN2P3-INP (France); ASI, CNR, and INAF (Italy); NASA and DoE (USA); STFC and UKSA (UK); CSIC, MINECO, J.A., and RES (Spain); Tekes, AoF, and CSC (Finland); DLR and MPG (Germany); CSA (Canada); DTU Space (Denmark); SER/SSO (Switzerland); RCN (Norway); SFI (Ireland); FCT/MCTES (Portugal); ERC and PRACE (EU). The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement No. 267934.Peer Reviewe

Planck 2018 results. XII. Galactic astrophysics using polarized dust emission

We present 353 GHz full-sky maps of the polarization fraction $p$, angle $\psi$, and dispersion of angles $S$ of Galactic dust thermal emission produced from the 2018 release of Planck data. We confirm that the mean and maximum of $p$ decrease with increasing $N_H$. The uncertainty on the maximum polarization fraction, $p_\mathrm{max}=22.0$% at 80 arcmin resolution, is dominated by the uncertainty on the zero level in total intensity. The observed inverse behaviour between $p$ and $S$ is interpreted with models of the polarized sky that include effects from only the topology of the turbulent Galactic magnetic field. Thus, the statistical properties of $p$, $\psi$, and $S$ mostly reflect the structure of the magnetic field. Nevertheless, we search for potential signatures of varying grain alignment and dust properties. First, we analyse the product map $S \times p$, looking for residual trends. While $p$ decreases by a factor of 3--4 between $N_H=10^{20}$ cm$^{-2}$ and $N_H=2\times 10^{22}$ cm$^{-2}$, $S \times p$ decreases by only about 25%, a systematic trend observed in both the diffuse ISM and molecular clouds. Second, we find no systematic trend of $S \times p$ with the dust temperature, even though in the diffuse ISM lines of sight with high $p$ and low $S$ tend to have colder dust. We also compare Planck data with starlight polarization in the visible at high latitudes. The agreement in polarization angles is remarkable. Two polarization emission-to-extinction ratios that characterize dust optical properties depend only weakly on $N_H$ and converge towards the values previously determined for translucent lines of sight. We determine an upper limit for the polarization fraction in extinction of 13%, compatible with the $p_\mathrm{max}$ observed in emission. These results provide strong constraints for models of Galactic dust in diffuse gas