An official website of the United States government
A<sc>bstract</sc> We review the effective field theory (EFT) bootstrap by formulating it as an infinite-dimensional semidefinite program (SDP), built from the crossing symmetric sum rules and the S-matrix primal ansatz. We apply the program to study the large-Nchiral perturbation theory (χPT) and observe excellent convergence of EFT bounds between the dual (rule-out) and primal (rule-in) methods. This convergence aligns with the predictions of duality theory in SDP, enabling us to analyze the bound states and resonances in the ultra-violet (UV) spectrum. Furthermore, we incorporate the upper bound of unitarity to uniformly constrain the EFT space from the UV scaleMusing the primal method, thereby confirming the consistency of the large-Nexpansion. In the end, we translate the large-N χPT bounds to constrain the higher derivative corrections of holographic QCD models.
more »
« less
Basis Set Superposition Errors in the Many-Body Expansion of Molecular Properties
The underlying reasons for the poor convergence of the venerated many-body expansion (MBE) for higher-order response properties are investigated, with a particular focus on the impact of basis set superposition errors. Interaction energies, dipole moments, dynamic polarizabilities, and specific rotations are computed for three chiral solutes in explicit water cages of varying sizes using the MBE including corrections based on the site–site function counterpoise (or “full-cluster” basis) approach. In addition, we consider other possible causes for the observed oscillatory behavior of the MBE, including numerical precision, basis set size, choice of density functional, and snapshot geometry. Our results indicate that counterpoise corrections are necessary for damping oscillations and achieving reasonable convergence of the MBE for higher order properties. However, oscillations in the expansion cannot be completely eliminated for chiroptical properties such as specific rotations due to their inherently nonadditive nature, thus limiting the efficacy of the MBE for studying solvated chiral compounds.
more »
« less
- PAR ID:
- 10137036
- Date Published:
- Journal Name:
- Journal of physical chemistry
- Volume:
- 123
- Issue:
- 20
- ISSN:
- 1932-7455
- Page Range / eLocation ID:
- 4500-4511
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
This paper describes a modular framework for the description of electroweak scattering and decay processes, including but not limited to Z-resonance physics. The framework consistently combines a complex-pole expansion near an s-channel resonance with a regular fixed-order perturbative description away from the resonance in a manifestly gauge-invariant scheme. Leading vertex correction contributions are encapsulated in form factors that can be predicted or treated as numerical fit parameters. This framework has been implemented in the publicly available object-oriented C++ library GRIFFIN. Version 1.0 of this library provides Standard Model predictions for the IR-subtracted matrix elements for the process f\bar{f} \to f'\bar{f}' with full NNLO and leading higher-order contributions on the Z-resonance, and with NLO corrections off-resonance. The library can straightforwardly be extended to include higher-order corrections, should they become available, or predictions for new physics models. It can be interfaced with Monte-Carlo programs to account for QED and QCD initial-state and final-state radiation.more » « less
-
The correlation consistent basis sets (cc-pVnZ with n = D, T, Q, 5) for the Ga–Br elements have been redesigned, tuning the sets for use for density functional approximations. Steps to redesign these basis sets for an improved correlation energy recovery and efficiency include truncation of higher angular momentum functions, recontraction of basis set coefficients, and reoptimization of basis set exponents. These redesigned basis sets are compared with conventional cc-pVnZ basis sets and other basis sets, which are, in principle, designed to achieve systematic improvement with respect to increasing basis set size. The convergence of atomic energies, bond lengths, bond dissociation energies, and enthalpies of formation to the Kohn–Sham limit is improved relative to other basis sets where convergence to the Kohn–Sham limit is typically not observed.more » « less
-
Abstract Chiral materials with strong linear anisotropies are difficult to accurately characterize with circular dichroism (CD) because of artifactual contributions to their spectra from linear dichroism (LD) and birefringence (LB). Historically, researchers have used a second‐order Taylor series expansion on the Mueller matrix to model the LDLB interaction effects on the spectra in conventional materials, but this approach may no longer be sufficient to account for the artifactual CD signals in emergent materials. In this work, we present an expression to model the measured CD using a third‐order expansion, which introduces “pairwise interference” terms that, unlike the LDLB terms, cannot be averaged out of the signal. We find that the third‐order pairwise interference terms can make noticeable contributions to the simulated CD spectra. Using numerical simulations of the measured CD across a broad range of linear and chiral anisotropy parameters, the LDLB interactions are most prominent in samples that have strong linear anisotropies (LD, LB) but negligible chiral anisotropies, where the measured CD strays from the chirality‐induced CD by factors greater than 103. Additionally, the pairwise interactions are most significant in systems with moderate‐to‐strong chiral and linear anisotropies, where the measured CD is inflated twofold, a figure that grows as linear anisotropies approach their maximum. In summary, media with moderate‐to‐strong linear anisotropy are in great danger of having their CD altered by these effects in subtle manners. This work highlights the significance of considering distortions in CD measurements through higher‐order pairwise interference effects in highly anisotropic nanomaterials.more » « less
-
This paper proposes a novel approach that enables a robot to learn an objective function incrementally from human directional corrections. Existing methods learn from human magnitude corrections; since a human needs to carefully choose the magnitude of each correction, those methods can easily lead to over-corrections and learning inefficiency. The proposed method only requires human directional corrections — corrections that only indicate the direction of an input change without indicating its magnitude. We only assume that each correction, regardless of its magnitude, points in a direction that improves the robot’s current motion relative to an unknown objective function. The allowable corrections satisfying this assumption account for half of the input space, as opposed to the magnitude corrections which have to lie in a shrinking level set. For each directional correction, the proposed method updates the estimate of the objective function based on a cutting plane method, which has a geometric interpretation. We have established theoretical results to show the convergence of the learning process. The proposed method has been tested in numerical examples, a user study on two human-robot games, and a real-world quadrotor experiment. The results confirm the convergence of the proposed method and further show that the method is significantly more effective (higher success rate), efficient/effortless (less human corrections needed), and potentially more accessible (fewer early wasted trials) than the state-of-the-art robot learning frameworks.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/https://doi.org/10.1021/acs.jpca.9b03864
