分类： 数学 >> 计算数学 提交时间： 2023-12-25
摘要： This paper introduces a new kind of multigrid approach for semilinear elliptic problems, which is based on the symmetric interior penalty discontinuous Galerkin (SIPDG) method. We first give an optimal error estimate of the SIPDG method for the problem. Then, we design a type of multigrid method, which is called the multilevel correction method, and derive a-priori error estimates. The primary idea of this method is to take the solution of the semilinear problem and utilize it to establish a sequence of solutions for associated linear boundary value problem on discontinuous finite element spaces and a newly defined low dimensional augmented subspace. Lastly, numerical experiments are offered to confirm the suggested method's precision and effectiveness.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： The growth of large-scale structure, as revealed in the anisotropic of clustering of galaxies in the low redshift Universe, provides a stringent test of our cosmological model. The strongest current constraints come from the BOSS and eBOSS surveys, with uncertainties on the amplitude of clustering of less than 10 per cent. A number of different approaches have been taken to fitting this signal, leading to apparently discrepant conclusions about the amplitude of fluctuations at late times. We compare in some detail two of the leading approaches, one based on a fitting a template cosmology whose amplitude and length scales are allowed to float with one based on a more traditional forward modeling approach, when fitting to the BOSS DR12 data. Holding the input data, scale cuts, window functions and modeling framework fixed we are able to isolate the cause of the differences and discuss the implications for future surveys.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： With the advent of a new generation of cosmological experiments that will provide high-precision measurements of the cosmic microwave background (CMB) and galaxies in the large-scale structure, it is pertinent to examine the potential of performing a joint analysis of multiple cosmological probes. In this paper, we study the cosmological information content contained in the one-loop power spectra and tree bispectra of galaxies cross-correlated with CMB lensing. We use the FFTLog method to compute angular correlations in spherical harmonic space, applicable for wide angles that can be accessed by forthcoming galaxy surveys. We find that adding the bispectra and cross-correlations with CMB lensing offers a significant improvement in parameter constraints, including those on the total neutrino mass, $M_\nu$, and local non-Gaussianity amplitude, $f_{\rm NL}$. In particular, our results suggest that the combination of the Vera C. Rubin Observatory's Legacy Survey of Space and Time (LSST) and CMB-S4 will be able to achieve $\sigma(M_\nu)=42$ meV from galaxy and CMB lensing correlations, and $\sigma(M_\nu)=12$ meV when further combined with the CMB temperature and polarization data, without any prior on the optical depth.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We present a new method for consistent, joint analysis of the pre- and post-reconstruction two-point functions of the BOSS survey. The post-reconstruction correlation function is used to accurately measure the distance-redshift relation and expansion history, while the pre-reconstruction power spectrum multipoles constrain the broad-band shape and the rate-of-growth of large-scale structure. Our technique uses Lagrangian perturbation theory to self-consistently work at the level of two-point functions, i.e.\ directly with the measured data, without approximating the constraints with summary statistics normalized by the drag scale. Combining galaxies across the full redshift range and both hemispheres we constrain $\Omega_m=0.303 \pm 0.0082$, $H_0=69.23 \pm 0.77$ and $\sigma_8=0.733 \pm 0.047$ within the context of $\Lambda$CDM. These constraints are in good agreement both with the Planck primary CMB anisotropy data and recent cosmic shear surveys.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： The Ly$\alpha$ forest provides one of the best means of mapping large-scale structure at high redshift, including our tightest constraint on the distance-redshift relation before cosmic noon. We describe how the large-scale correlations in the Ly$\alpha$ forest can be understood as an expansion in cumulants of the optical depth field, which itself can be related to the density field by a bias expansion. This provides a direct connection between the observable and the statistics of the matter fluctuations which can be computed in a systematic manner. We discuss the way in which complex, small-scale physics enters the predictions, the origin of the much-discussed velocity bias and the `renormalization' of the large-scale bias coefficients. Our calculations are within the context of perturbation theory, but we also make contact with earlier work using the peak-background split. Using the structure of the equations of motion we demonstrate, to all orders in perturbation theory, that the large-scale flux power spectrum becomes the linear spectrum times the square of a quadratic in the cosine of the angle to the line of sight. Unlike the case of galaxies, both the isotropic and anisotropic pieces receive contributions from small-scale physics.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： The optical depth $\tau$ is the least well determined parameter in the standard model of cosmology, and one whose precise value is important for both understanding reionization and for inferring fundamental physics from cosmological measurements. We forecast how well future epoch of reionization experiments could constraint $\tau$ using a symmetries-based bias expansion that highlights the special role played by anisotropies in the power spectrum on large scales. Given a parametric model for the ionization evolution inspired by the physical behavior of more detailed reionization simulations, we find that future 21cm experiments could place tight constraints on the timing and duration of reionization and hence constraints on $\tau$ that are competitive with proposed, space-based CMB missions provided they can measure $k\approx 0.1\,h\,\text{Mpc}^{-1}$ with a clean foreground wedge across redshifts spanning the most active periods of reionization, corresponding to ionization fractions $0.2 \lesssim x \lesssim 0.8$. Significantly improving upon existing CMB-based measurements with next-generation 21cm surveys would require substantially longer observations ($\sim5$ years) than standard $\mathcal{O}(1000 \,\,\text{hour})$ integration times. Precise measurements of smaller scales will not improve constraints on $\tau$ until a better understanding of the astrophysics of reionization is achieved. In the presence of noise and foregrounds even future 21cm experiments will struggle to constrain $\tau$ if the ionization evolution deviates significantly from simple parametric forms.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： We present a formalism for jointly fitting pre- and post-reconstruction redshift-space clustering (RSD) and baryon acoustic oscillations (BAO) plus gravitational lensing (of the CMB) that works directly with the observed 2-point statistics. The formalism is based upon (effective) Lagrangian perturbation theory and a Lagrangian bias expansion, which models RSD, BAO and galaxy-lensing cross correlations within a consistent dynamical framework. As an example we present an analysis of clustering measured by the Baryon Oscillation Spectroscopic Survey in combination with CMB lensing measured by Planck. The post-reconstruction BAO strongly constrains the distance-redshift relation, the full-shape redshift-space clustering constrains the matter density and growth rate, and CMB lensing constrains the clustering amplitude. Using only the redshift space data we obtain $\Omega_\mathrm{m} = 0.303\pm 0.008$, $H_0 = 69.21\pm 0.78$ and $\sigma_8 = 0.743\pm 0.043$. The addition of lensing information, even when restricted to the Northern Galactic Cap, improves constraints to $\Omega_m = 0.300 \pm 0.008$, $H_0 = 69.21 \pm 0.77$ and $\sigma_8 = 0.707 \pm 0.035$, in tension with CMB and cosmic shear constraints. The combination of $\Omega_m$ and $H_0$ are consistent with Planck, though their constraints derive mostly from redshift-space clustering. The low $\sigma_8$ value are driven by cross correlations with CMB lensing in the low redshift bin ($z\simeq 0.38$) and at large angular scales, which show a $20\%$ deficit compared to expectations from galaxy clustering alone. We conduct several systematics tests on the data and find none that could fully explain these tensions.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
摘要： Numerical simulations in cosmology require trade-offs between volume, resolution and run-time that limit the volume of the Universe that can be simulated, leading to sample variance in predictions of ensemble-average quantities such as the power spectrum or correlation function(s). Sample variance is particularly acute at large scales, which is also where analytic techniques can be highly reliable. This provides an opportunity to combine analytic and numerical techniques in a principled way to improve the dynamic range and reliability of predictions for clustering statistics. In this paper we extend the technique of Zel'dovich control variates, previously demonstrated for 2-point functions in real space, to reduce the sample variance in measurements of 2-point statistics of biased tracers in redshift space. We demonstrate that with this technique, we can reduce the sample variance of these statistics down to their shot-noise limit out to $k \sim 0.2\, h\rm Mpc^{-1}$. This allows a better matching with perturbative models and improved predictions for the clustering of e.g.~quasars, galaxies and neutral Hydrogen measured in spectroscopic redshift surveys at very modest computational expense. We discuss the implementation of ZCV, give some examples and provide forecasts for the efficacy of the method under various conditions.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Kuan-Wei Huang
Geoff Chih-Fan Chen
Po-Wen Chang
Sheng-Chieh Lin
Chia-Jung Hsu
Vishal Thengane
Joshua Yao-Yu Lin
摘要： Quantifying the parameters and corresponding uncertainties of hundreds of strongly lensed quasar systems holds the key to resolving one of the most important scientific questions: the Hubble constant ($H_{0}$) tension. The commonly used Markov chain Monte Carlo (MCMC) method has been too time-consuming to achieve this goal, yet recent work has shown that convolution neural networks (CNNs) can be an alternative with seven orders of magnitude improvement in speed. With 31,200 simulated strongly lensed quasar images, we explore the usage of Vision Transformer (ViT) for simulated strong gravitational lensing for the first time. We show that ViT could reach competitive results compared with CNNs, and is specifically good at some lensing parameters, including the most important mass-related parameters such as the center of lens $\theta_{1}$ and $\theta_{2}$, the ellipticities $e_1$ and $e_2$, and the radial power-law slope $\gamma'$. With this promising preliminary result, we believe the ViT (or attention-based) network architecture can be an important tool for strong lensing science for the next generation of surveys. The open source of our code and data is in \url{https://github.com/kuanweih/strong_lensing_vit_resnet}.
分类： 天文学 >> 天文学 提交时间： 2023-02-19
Kuan-Wei Huang
Geoff Chih-Fan Chen
Po-Wen Chang
Sheng-Chieh Lin
Chia-Jung Hsu
Vishal Thengane
Joshua Yao-Yu Lin
摘要： Quantifying the parameters and corresponding uncertainties of hundreds of strongly lensed quasar systems holds the key to resolving one of the most important scientific questions: the Hubble constant ($H_{0}$) tension. The commonly used Markov chain Monte Carlo (MCMC) method has been too time-consuming to achieve this goal, yet recent work has shown that convolution neural networks (CNNs) can be an alternative with seven orders of magnitude improvement in speed. With 31,200 simulated strongly lensed quasar images, we explore the usage of Vision Transformer (ViT) for simulated strong gravitational lensing for the first time. We show that ViT could reach competitive results compared with CNNs, and is specifically good at some lensing parameters, including the most important mass-related parameters such as the center of lens $\theta_{1}$ and $\theta_{2}$, the ellipticities $e_1$ and $e_2$, and the radial power-law slope $\gamma'$. With this promising preliminary result, we believe the ViT (or attention-based) network architecture can be an important tool for strong lensing science for the next generation of surveys. The open source of our code and data is in \url{https://github.com/kuanweih/strong_lensing_vit_resnet}.
分类： 光学 >> 量子光学 提交时间： 2023-02-19
Jia-Mou Chen
Chia-Yu Hsu
Wei-Kai Huang
Shih-Si Hsiao
Fu-Chen Huang
Yi-Hsin Chen
Chih-Sung Chuu
Ying-Cheng Chen
Yong-Fan Chen
Ite A. Yu
摘要： The biphotons, generated from a hot atomic vapor via the process of spontaneous four-wave mixing (SFWM), have the following merits: stable and tunable frequencies as well as linewidth. Such merits are very useful in the applications of long-distance quantum communication. However, the hot-atom SFWM biphoton sources previously had far lower values of generation rate per linewidth, i.e., spectral brightness, as compared with the sources of biphotons generated by the spontaneous parametric down conversion (SPDC) process. Here, we report a hot-atom SFWM source of biphotons with a linewidth of 960 kHz and a generation rate of 3.7$\times$ $10^5$ pairs/s. The high generation rate, together with the narrow linewidth, results in a spectral brightness of 3.8$\times$ $10^5$ pairs/s/MHz, which is 17 times of the previous best result with atomic vapors and also better than all known results with all kinds of media. The all-copropagating scheme together with a large optical depth (OD) of the atomic vapor is the key improvement, enabling the achieved spectral brightness to be about one quarter of the ultimate limit. Furthermore, this biphoton source had a signal-to-background ratio (SBR) of 2.7, which violated the Cauchy-Schwartz inequality for classical light by about 3.6 folds. Although an increasing spectral brightness usually leads to a decreasing SBR, our systematic study indicates that both of the present spectral brightness and SBR can be enhanced by further increasing the OD. This work demonstrates a significant advancement and provides useful knowledge in the quantum technology using photons.
分类： 光学 >> 量子光学 提交时间： 2023-02-19
Yu-Sheng Wang
Kai-Bo Li
Chao-Feng Chang
Tan-Wen Lin
Jian-Qing Li
Shih-Si Hsiao
Jia-Mou Chen
Yi-Hua Lai
Ying-Cheng Chen
Yong-Fan Chen
Chih-Sung Chuu
Ite A. Yu
摘要： We report the generation of biphotons, with a temporal full width at the half maximum (FWHM) of 13.4$\pm$0.3 $\mu$s and a spectral FWHM of 50$\pm$1 kHz, via the process of spontaneous four-wave mixing. The temporal width is the longest, and the spectral linewidth is the narrowest up to date. This is also the first biphoton result that obtains a linewidth below 100 kHz, reaching a new milestone. The very long biphoton wave packet has a signal-to-background ratio of 3.4, which violates the Cauchy-Schwarz inequality for classical light by 4.8 folds. Furthermore, we demonstrated a highly-tunable-linewidth biphoton source and showed that while the biphoton source's temporal and spectral width were controllably varied by about 24 folds, its generation rate only changed by less than 15\%. A spectral brightness or generation rate per pump power per linewidth of 1.2$\times$10$^6$ pairs/(s$\cdot$mW$\cdot$MHz) was achieved at the temporal width of 13.4 $\mu$s. The above results were made possible by the low decoherence rate and high optical depth of the experimental system, as well as the nearly phase-mismatch-free scheme employed in the experiment. This work has demonstrated a high-efficiency ultranarrow-linewidth biphoton source, and has made a substantial advancement in the quantum technology utilizing heralded single photons.
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