scholarly journals Coupled Perturbation Theory Approach to Dual Basis Sets for Molecules and Solids. 1. General Theory and Application to Molecules

2019 ◽  
Vol 16 (1) ◽  
pp. 340-353 ◽  
Author(s):  
Lorenzo Maschio ◽  
Bernard Kirtman
Keyword(s):  
Perturbation Theory ◽  
General Theory ◽  
Basis Sets ◽  
Theory Approach ◽  
Dual Basis

scholarly journals Symmetry‐adapted perturbation theory of nonadditive three‐body interactions in van der Waals molecules. I. General theory

1995 ◽  
Vol 103 (18) ◽  
pp. 8058-8074 ◽  
Author(s):  
Robert Moszynski ◽  
Paul E. S. Wormer ◽  
Bogumil Jeziorski ◽  
Ad van der Avoird
Keyword(s):  
Perturbation Theory ◽  
General Theory ◽  
Van Der Waals ◽  
Van Der Waals Molecules ◽  
Three Body

scholarly journals Perturbation theory approach to predict the covariance matrices of the galaxy power spectrum and bispectrum in redshift space

2020 ◽  
Vol 497 (2) ◽  
pp. 1684-1711 ◽  
Author(s):  
Naonori S Sugiyama ◽  
Shun Saito ◽  
Florian Beutler ◽  
Hee-Jong Seo
Keyword(s):  
Perturbation Theory ◽  
Power Spectrum ◽  
Shot Noise ◽  
Signal To Noise Ratio ◽  
Covariance Matrices ◽  
Theory Approach ◽  
Cross Covariance ◽  
The Galaxy ◽  
The Cross ◽  
Non Gaussian

ABSTRACT In this paper, we predict the covariance matrices of both the power spectrum and the bispectrum, including full non-Gaussian contributions, redshift space distortions, linear bias effects, and shot-noise corrections, using perturbation theory (PT). To quantify the redshift-space distortion effect, we focus mainly on the monopole and quadrupole components of both the power and bispectra. We, for the first time, compute the 5- and 6-point spectra to predict the cross-covariance between the power and bispectra, and the autocovariance of the bispectrum in redshift space. We test the validity of our calculations by comparing them with the covariance matrices measured from the MultiDark-Patchy mock catalogues that are designed to reproduce the galaxy clustering measured from the Baryon Oscillation Spectroscopic Survey Data Release 12. We argue that the simple, leading-order PT works because the shot-noise corrections for the Patchy mocks are more dominant than other higher order terms we ignore. In the meantime, we confirm some discrepancies in the comparison, especially of the cross-covariance. We discuss potential sources of such discrepancies. We also show that our PT model reproduces well the cumulative signal-to-noise ratio of the power spectrum and the bispectrum as a function of maximum wavenumber, implying that our PT model captures successfully essential contributions to the covariance matrices.

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