The XFaster Power Spectrum and Likelihood Estimator for the Analysis of Cosmic Microwave Background Maps

We present the XFaster analysis package, a fast, iterative angular power spectrum estimator based on a diagonal approximation to the quadratic Fisher matrix estimator. It uses Monte Carlo simulations to compute noise biases and filter transfer functions and is thus a hybrid of both Monte Carlo and quadratic estimator methods. In contrast to conventional pseudo-C ℓ –based methods, the algorithm described here requires a minimal number of simulations and does not require them to be precisely representative of the data to estimate accurate covariance matrices for the bandpowers. The formalism works with polarization-sensitive observations and also data sets with identical, partially overlapping, or independent survey regions. The method was first implemented for the analysis of BOOMERanG data and also used as part of the Planck analysis. Here we describe the full, publicly available analysis package, written in Python, as developed for the analysis of data from the 2015 flight of the Spider instrument. The package includes extensions for self-consistently estimating null spectra and estimating fits for Galactic foreground contributions. We show results from the extensive validation of XFaster using simulations and its application to the Spider data set.

Photoemission Spectra from the Extended Koopman’s Theorem, Revisited

The Extended Koopman’s Theorem (EKT) provides a straightforward way to compute charged excitations from any level of theory. In this work we make the link with the many-body effective energy theory (MEET) that we derived to calculate the spectral function, which is directly related to photoemission spectra. In particular, we show that at its lowest level of approximation the MEET removal and addition energies correspond to the so-called diagonal approximation of the EKT. Thanks to this link, the EKT and the MEET can benefit from mutual insight. In particular, one can readily extend the EKT to calculate the full spectral function, and choose a more optimal basis set for the MEET by solving the EKT secular equation. We illustrate these findings with the examples of the Hubbard dimer and bulk silicon.

Analytic Gradients for Complete and Restricted Active Space Second-order Perturbation Theory within the Diagonal Approximation

The computational cost of analytic derivatives in multireference perturbation theory is strongly affected by the size of the active space employed in the reference self-consistent field calculation. To overcome previous limits on active space size, the analytic gradients of single-state complete and restricted active space second-order perturbation theory within the diagonal approximation (CASPT2-D and RASPT2-D) have been developed and implemented in a local version of OpenMolcas. Similar to previous implementations of CASPT2, the RASPT2 implementation employs the Lagrangian or Z-vector method.<br>The numerical results show that restricted active spaces with up to 20 electrons in 20 orbitals can now be employed for geometry optimizations.<br>

Probing phase transitions of holographic entanglement entropy with fixed area states

Recent results suggest that new corrections to holographic entanglement entropy should arise near phase transitions of the associated Ryu-Takayanagi (RT) surface. We study such corrections by decomposing the bulk state into fixed-area states and conjecturing that a certain ‘diagonal approximation’ will hold. In terms of the bulk Newton constant G, this yields a correction of order O(G−1/2) near such transitions, which is in particular larger than generic corrections from the entanglement of bulk quantum fields. However, the correction becomes exponentially suppressed away from the transition. The net effect is to make the entanglement a smooth function of all parameters, turning the RT ‘phase transition’ into a crossover already at this level of analysis.We illustrate this effect with explicit calculations (again assuming our diagonal approximation) for boundary regions given by a pair of disconnected intervals on the boundary of the AdS3 vacuum and for a single interval on the boundary of the BTZ black hole. In a natural large-volume limit where our diagonal approximation clearly holds, this second example verifies that our results agree with general predictions made by Murthy and Srednicki in the context of chaotic many-body systems. As a further check on our conjectured diagonal approximation, we show that it also reproduces the O(G−1/2) correction found Penington et al. for an analogous quantum RT transition. Our explicit computations also illustrate the cutoff-dependence of fluctuations in RT-areas.

Saturation of Energy Levels of the Hydrogen Atom in Strong Magnetic Field

We demonstrate that the finiteness of the limiting values of the lower energy levels of a hydrogen atom under an unrestricted growth of the magnetic field, into which this atom is embedded, is achieved already when the vacuum polarization (VP) is calculated in the magnetic field within the approximation of the local action of Euler–Heisenberg. We find that the mechanism for this saturation is different from the one acting, when VP is calculated via the Feynman diagram in the Furry picture. We study the effective potential that appears when the adiabatic (diagonal) approximation is exploited for solving the Schrödinger equation for the longitudinal degree of freedom of the electron on the lowest Landau level in the atom. We find that the (effective) potential of a point-like charge remains nonsingular thanks to the growing screening provided by VP. The regularizing length turns out to be α/3π¯λC, where ¯λC is the electron Compton length. The family of effective potentials, labeled by growing values of the magnetic field condenses towards a certain limiting, magnetic-field-independent potential-distance curve. The limiting values of even ground-state energies are determined for four magnetic quantum numbers using the Karnakov–Popov method.

Quantum Natural Gradient

A quantum generalization of Natural Gradient Descent is presented as part of a general-purpose optimization framework for variational quantum circuits. The optimization dynamics is interpreted as moving in the steepest descent direction with respect to the Quantum Information Geometry, corresponding to the real part of the Quantum Geometric Tensor (QGT), also known as the Fubini-Study metric tensor. An efficient algorithm is presented for computing a block-diagonal approximation to the Fubini-Study metric tensor for parametrized quantum circuits, which may be of independent interest.

Evaluating prior predictions of production and seismic data

It is common in ensemble-based methods of history matching to evaluate the adequacy of the initial ensemble of models through visual comparison between actual observations and data predictions prior to data assimilation. If the model is appropriate, then the observed data should look plausible when compared to the distribution of realizations of simulated data. The principle of data coverage alone is, however, not an effective method for model criticism, as coverage can often be obtained by increasing the variability in a single model parameter. In this paper, we propose a methodology for determining the suitability of a model before data assimilation, particularly aimed for real cases with large numbers of model parameters, large amounts of data, and correlated observation errors. This model diagnostic is based on an approximation of the Mahalanobis distance between the observations and the ensemble of predictions in high-dimensional spaces. We applied our methodology to two different examples: a Gaussian example which shows that our shrinkage estimate of the covariance matrix is a better discriminator of outliers than the pseudo-inverse and a diagonal approximation of this matrix; and an example using data from the Norne field. In this second test, we used actual production, repeat formation tester, and inverted seismic data to evaluate the suitability of the initial reservoir simulation model and seismic model. Despite the good data coverage, our model diagnostic suggested that model improvement was necessary. After modifying the model, it was validated against the observations and is now ready for history matching to production and seismic data. This shows that the proposed methodology for the evaluation of the adequacy of the model is suitable for large realistic problems.