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The short period luni-solar theory of Kozai is generalized for arbitrary obliquity of the ecliptic and inclination of the moon's orbit to the ecliptic. Analytic first order lunar perturbations to the elements are derived. The theory is illustrated by an application to the communication satellite Intelsat 3F3.
Excited Costrained Density Functional Theory (XCDFT) is a variational excited state method that extends ground state DFT to the computation of low-lying excited states. It borrows much of the machinery of Constrained DFT (CDFT) with a crucial difference: the constraint imposes a population of one electron in the Hilbert space spanned by the virtuals of a reference ground state. Here, we present theory and implementation for evaluating nonadiabatic coupling vectors (NACVs) between the first excited state computed with XCDFT and the ground state. Our NACVs are computed analytically using density functional perturbation theory with a formalism that is general enough that could be applied to CDFT diabatic states. We showcase the new method with pilot NACV calculations for the conical intersection in H 3 , the avoided crossing in selenoacrolein, and the NACV magnitudes in azobenzene. Despite complications from the nonorthogonality of the wavefunctions, XCDFT’s energy surfaces and NACVs reproduce benchmark values and respect known sum rules within a reasonable degree. This shows that XCDFT is a viable method for nonadiabatic dynamics simulations.
Fully occupied or unoccupied bands in a solid are often considered inert and irrelevant to a material's low-energy properties. But the discovery of enhanced superconductivity in heavily electron-doped FeSe-derived superconductors poses questions about the possible role of incipient bands (those laying close to but not crossing the Fermi level) in pairing. To answer this question, researchers have studied pairing correlations in the bilayer Hubbard model, which has an incipient band for large interlayer hopping t⊥, using many-body perturbation theory and variational methods. They have generally found that superconductivity is enhanced as one of the bands approaches the Lifshitz transition and even when it becomes incipient. Here we address this question using the nonperturbative quantum Monte Carlo (QMC) dynamical cluster approximation (DCA) to study the bilayer Hubbard model's pairing correlations. We find that the model has robust s± pairing correlations in the large t⊥ limit, which can become stronger as one band is made incipient. While this behavior is linked to changes in the effective interaction, we further find that it is counteracted by a suppression of the intrinsic pair-field susceptibility and does not translate to an increased Tc. Our results demonstrate that the highest achievable transition temperatures in the bilayer Hubbard model occur when the system has two bands crossing the Fermi level.
In this report I review some open questions relating to the large transverse momentum divergences in transverse moments of transverse momentum dependent (TMD) parton correlation functions. I also explain, in an abbreviated and summarized form, recent work that shows that the resulting violations of a commonly used integral relation are not perturbatively suppressed. I argue that this implies a need for more precise definitions for the correlation functions used to describe transverse moments.
We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of approximation by truncation, i.e., smoothing the initial conditions by various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was crosscorrelation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(exp 2, sub G)) where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. All other schemes, including those proposed as generalizations of the Zel'dovich approximation created by adding forces, were in fact generally worse by this measure. By explicitly checking, we verified that the success of our best-choice was a result of the best treatment of the phases of nonlinear Fourier components. Of all schemes tested, the adhesion approximation produced the most accurate nonlinear power spectrum and density distribution, but its phase errors suggest mass condensations were moved to slightly the wrong location. Due to its better reproduction of the mass density distribution function and power spectrum, it might be preferred for some uses. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present.
We have recently conducted a controlled comparison of a number of approximations for gravitational clustering against the same n-body simulations. These include ordinary linear perturbation theory (Eulerian), the lognormal approximation, the adhesion approximation, the frozen-flow approximation, the Zel'dovich approximation (describable as first-order Lagrangian perturbation theory), and its second-order generalization. In the last two cases we also created new versions of the approximation by truncation, i.e., by smoothing the initial conditions with various smoothing window shapes and varying their sizes. The primary tool for comparing simulations to approximation schemes was cross-correlation of the evolved mass density fields, testing the extent to which mass was moved to the right place. The Zel'dovich approximation, with initial convolution with a Gaussian e(exp -k(exp 2)/k(sub G(exp 2)), where k(sub G) is adjusted to be just into the nonlinear regime of the evolved model (details in text) worked extremely well. Its second-order generalization worked slightly better. We recommend either n-body simulations or our modified versions of the Zel'dovich approximation, depending upon the purpose. The theoretical implication is that pancaking is implicit in all cosmological gravitational clustering, at least from Gaussian initial conditions, even when subcondensations are present. This in turn provides a natural explanation for the presence of sheets and filaments in the observed galaxy distribution. Use of the approximation scheme can permit extremely rapid generation of large numbers of realizations of model universes with good accuracy down to galaxy group mass scales.
An IR–vacuum ultraviolet (VUV) ion-dip spectroscopy method is utilized to examine the IR spectrum of acetaldehyde oxide (CH3CHOO) in the overtone CH stretch (2νCH) spectral region. IR activation creates a depletion of the ground state population that reduces the VUV photoionization signal on the parent mass channel. IR activation of the more stable and populated syn-CH3CHOO conformer results in rapid unimolecular decay to OH + vinoxy products and makes the most significant contribution to the observed spectrum. The resultant IR–VUV ion-dip spectrum of CH3CHOO is similar to that obtained previously for syn-CH3CHOO using IR action spectroscopy with UV laser-induced fluorescence detection of OH products. The prominent IR features at 5984 and 6081 cm−1 are also observed using UV + VUV photoionization of OH products. Complementary theoretical calculations utilizing a general implementation of second-order vibrational perturbation theory provide new insights on the vibrational transitions that give rise to the experimental spectrum in the overtone CH stretch region. The introduction of physically motivated small shifts of the harmonic frequencies yields remarkably improved agreement between experiment and theory in the overtone CH stretch region. The prominent features are assigned as highly mixed states with contributions from two quanta of CH stretch and/or a combination of CH stretch with an overtone in mode 4. The generality of this approach is demonstrated by applying it to three different levels of electronic structure theory/basis sets, all of which provide spectra that are virtually indistinguishable despite showing large deviations prior to introducing the shifts to the harmonic frequencies.
A simple revised secular perturbation theory which incorporates the averaged secular effect of first-order near-resonances is derived. By including the effects of these near-resonances, the largest error in the secular frequencies is reduced from 16 percent to less than 3 percent. It is concluded that the revised secular perturbation theory is adequate for the quantitative modeling of the long-term perturbations in the Uranian satellite system. If incorporated within the general theory of Laskar (1986), this theory would lead to completely analytic theory.
Highlights: • We prove the equivalence of the first and second-order formalism. • We use Lagrange multiplier fields to limit radiative effects to one-loop order. • We prove that the quantized theory is both renormalizable and unitary. The first order form of the Yang–Mills and Einstein–Hilbert actions are quantized, and it is shown how Green’s functions computed using the first and the second order form of these theories are related. Next we show how by use of Lagrange multiplier fields (LM), radiative effects beyond one-loop order can be eliminated. This allows one to compute Green’s functions exactly without loss of unitarity. The consequences of this restriction on radiative effects are examined for the Yang–Mills and Einstein–Hilbert actions. In these two gauge theories, we find that the quantized theory is both renormalizable and unitary once the LM field is used to eliminate effects beyond one-loop order.
Measurements of the differential cross sections of Z + jets and γ + jets production, and their ratio, are presented as a function of the boson transverse momentum. Measurements are also presented of the angular distribution between the Z boson and the closest jet. The analysis is based on pp collisions at a center-of-mass energy of 13 TeV corresponding to an integrated luminosity of 35.9 fb$^{−1}$ recorded by the CMS experiment at the LHC. The results, corrected for detector effects, are compared with various theoretical predictions. In general, the predictions at higher orders in perturbation theory show better agreement with the measurements. This work provides the first measurement of the ratio of the differential cross sections of Z + jets and γ + jets production at 13 TeV, as well as the first direct measurement of Z bosons emitted collinearly with a jet.[graphic not available: see fulltext]
Despite the power and flexibility of configuration interaction (CI) based methods in computational chemistry, their broader application is limited by an exponential increase in both computational and storage requirements, particularly due to the substantial memory needed for excitation lists that are crucial for scalable parallel computing. Here, the objective of this work is to develop a new CI framework, namely, the small tensor product distributed active space (STP-DAS) framework, aimed at drastically reducing memory demands for extensive CI calculations on individual workstations or laptops, while simultaneously enhancing scalability for extensive parallel computing. Moreover, the STP-DAS framework can support various CI-based techniques, such as complete active space (CAS), restricted active space, generalized active space, multireference CI, and multireference perturbation theory, applicable to both relativistic (two- and four-component) and non-relativistic theories, thus extending the utility of CI methods in computational research. We conducted benchmark studies on a supercomputer to evaluate the storage needs, parallel scalability, and communication downtime using a realistic exact-two-component CASCI (X2C-CASCI) approach, covering a range of determinants from 10 9 to 10 12 . Additionally, we performed large X2C-CASCI calculations on a single laptop and examined how the STP-DAS partitioning affects performance.
A structural expansion for the static ground state energy of a simple metal is derived. An approach based on single particle band structure which treats the electron gas as a non-linear dielectric is presented, along with a more general many particle analysis using finite temperature perturbation theory. The two methods are compared, and it is shown in detail how band-structure effects, Fermi surface distortions, and chemical potential shifts affect the total energy. These are of special interest in corrections to the total energy beyond third order in the electron ion interaction, and hence to systems where differences in energies for various crystal structures are exceptionally small. Preliminary calculations using these methods for the zero temperature thermodynamic functions of atomic hydrogen are reported.
In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence both Duffing's equation and the van der Pol equation are solved using each method.
In this investigation, a comparison is made of two methods for developing perturbation theories for non-canonical dynamical systems. The methods compared are the generalized Lie-Hori method and the method of averaging. In the comparison presented here, the equivalence of the methods up to the second order in the small parameter is shown. However, the approach used can be extended to demonstrate the equivalence for higher orders. To illustrate the equivalence Duffing's equation, the van der Pol equation and the oscillator with quadratic damping problem are solved using each method.
Remainder theorem of Rayleigh-Schroedinger perturbation theory for calculating wave functions to higher order
The analysis makes use of a singular perturbation method, the multiple time scaling. Concepts of stable and unstable limit cycles are introduced. The solution is obtained in the form of an asymptotic expansion. Numerical results are presented for the nonlinear flutter of panels and airfoils in supersonic flow. The approach used is an extension of a method for analyzing nonlinear panel flutter reported by Morino (1969).
We describe perturbation theory (PT) models of galaxy bias for applications to photometric galaxy surveys. We model the galaxy-galaxy and galaxy-matter correlation functions in configuration space and validate against measurements from mock catalogs designed for the Dark Energy Survey (DES). We find that an effective PT model with five galaxy bias parameters provides a good description of the 3D correlation functions above scales of 4 Mpc/$h$ and $z < 1$. Our tests show that at the projected precision of the DES-Year 3 analysis, two of the non-linear bias parameters can be fixed to their co-evolution values, and a third (the $k^2$ term for higher derivative bias) set to zero. The agreement is typically at the 2 percent level over scales of interest, which is the statistical uncertainty of our simulation measurements. To achieve this level of agreement, our {\it fiducial} model requires using the full non-linear matter power spectrum (rather than the 1-loop PT one). We also measure the relationship between the non-linear and linear bias parameters and compare them to their expected co-evolution values. We use these tests to motivate the galaxy bias model and scale cuts for the cosmological analysis of the Dark Energy Survey; our conclusions are generally applicable to all photometric surveys.