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I calculate $\frac{1}{Q^2}$ power corrections to unpolarized Drell-Yan hadronic tensor for electromagnetic (EM) current at large N c and demonstrate the EM gauge invariance at this level.
Orientationally-dependent interactions such as dipolar coupling, quadrupolar coupling, and chemical shift anisotropy (CSA) contain a wealth of spatial information that can be used to elucidate molecular conformations and dynamics. To determine the sign of the chemical shift tensor anisotropy parameter (δ aniso ), both the |m| = 1 and |m| = 2 components of the CSA need to be symmetry allowed, while the recoupling of the |m| = 1 term is accompanied with the reintroduction of homonuclear dipolar coupling components. Therefore, previously suggested sequences which solely recouple the |m| = 2 term cannot determine the sign a 1 H's δ aniso in a densely-coupled network. Here, we demonstrate the CSA recoupling of strongly dipolar coupled 1 H spins using the $Cn^1_n (90_{0}360_{180}540_{0}360_{180}90_{0})$ sequence. This pulse scheme recouples both the |m| = 1 and |m| = 2 CSA terms but the scaling factors for the homonuclear dipolar coupling terms are zeroed. Consequently, the sequence is sensitive to the sign of δ aniso but is not influenced by homonuclear dipolar interactions.
Hybrid density functional theory (DFT) remains intractable for large periodic systems due to the demanding computational cost of exact exchange. We apply the tensor hypercontraction (THC) (or interpolative separable density fitting) approximation to periodic hybrid DFT calculations with Gaussian-type orbitals using the Gaussian plane wave approach. This is done to lower the computational scaling with respect to the number of basis functions (N) and k-points (N k ) at a fixed system size. Additionally, we propose an algorithm to fit only occupied orbital products via THC (i.e., a set of points, N ISDF ) to further reduce computation time and memory usage. This algorithm has linear scaling cost with k-points, no explicit dependence of N ISDF on basis set size, and overall cubic scaling with unit cell size. Significant speedups and reduced memory usage may be obtained for moderately sized k-point meshes, with additional gains for large k-point meshes. Adequate accuracy can be obtained using THC-oo-K for self-consistent calculations. In conclusion, we perform illustrative hybrid density function theory calculations on the benzene crystal in the basis set and thermodynamic limits to highlight the utility of this algorithm.
Least Squares Tensor Hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wavefunc- tion based methods in quantum chemistry. However, previous work has demonstrated that the LS-THC factorization performs disproportionately worse in the description of wavefunction components (e.g. cluster amplitudes T 2 ) than Hamiltonian compo- nents (e.g. electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T 2 kernel, and reports, for the first time, the existence of a “correlation feature” in the errors of the LS-THC representation of the “exchange-like” correlation energy EX and T 2 that is remarkably consistent across ten molecular species, three correlated wavefunctions, and four basis sets. This correlation feature portends the existence of a “pair-point kernel” missing in the usual LS-THC representation of the wavefunction, which critically depends upon pairs of grid points situated close to atoms and with inter-pair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.
The single-molecule magnet {Mn 84 } is a challenge to theory because of its high nuclearity. Here, we directly compute two experimentally accessible observables, the field-dependent magnetization up to 75 T and the temperature-dependent heat capacity, using parameter-free theory. In particular, we use first-principles calculations to derive short- and long-range exchange interactions and compute the exact partition function of the resulting classical Potts and Ising spin models for all 84 Mn S = 2 spins to obtain observables. The latter computation is made possible by using hyperoptimized tensor network contractions, a technique developed to simulate quantum supremacy circuits. We also synthesize the magnet and measure its heat capacity and magnetization, observing qualitative agreement between theory and experiment and identifying an unusual bump in the heat capacity and a plateau in the magnetization. Our work also identifies some limitations of current theoretical modeling in large magnets, such as sensitivity to small, long-range exchange couplings.
Abstract The stress tensor is an important property for upper crustal studies such as those that involve pore fluids and earthquake hazards. At tectonic plate scale, plate boundary forces and mantle convection are the primary drivers of the stress field. In many local settings (10–100 s of km and <10 km depth) in tectonic plate interiors, we can simplify by assuming a constant background stress field that is perturbed by local heterogeneity in density and elasticity. Local stress orientation and sometimes magnitude can be estimated from earthquake and borehole‐based observations when available. Modeling of the local stress field often involves interpolating sparse observations. We present a new method to estimate the 3D stress field in the upper crust and demonstrate it for Oklahoma. We created a 3D material model by inverting multiple types of geophysical observations simultaneously. Integrating surface‐wave dispersion, local travel times and gravity observations produces a model of P‐wave velocity, S‐wave velocity, and density. The stress field can then be modeled using finite element simulations. The simulations are performed using our simplified view of the local stress field as the sum of a constant background stress field that is perturbed by local density and elasticity heterogeneity and gravitational body forces. An orientation of N82°E, for the maximum compressive tectonic force, best agrees with previously observed stress orientations and faulting types in Oklahoma. The gravitational contribution of the horizontal stress field has a magnitude comparable to the tectonic contribution for the upper 5 km of the subsurface.
The emergence of a local effective theory from a more fundamental theory of quantum gravity with seemingly fewer degrees of freedom is a major puzzle of theoretical physics. A recent approach to this problem is to consider general features of the Hilbert space maps relating these theories. In this work, we construct approximately local observables, or overlapping qubits, from such non-isometric maps. We show that local processes in effective theories can be spoofed with a quantum system with fewer degrees of freedom, with deviations from actual locality identifiable as features of quantum gravity. For a concrete example, we construct two tensor network models of de Sitter space-time, demonstrating how exponential expansion and local physics can be spoofed for a long period before breaking down. Our results highlight the connection between overlapping qubits, Hilbert space dimension verification, degree-of-freedom counting in black holes, holography, and approximate locality in quantum gravity.
Spatially resolved time and voltage-dependent polarization dynamics in PbTiO 3 thin films is explored using dynamic piezoresponse force microscopy (D-PFM) in conjunction with interferometric displacement sensing. This approach gives rise to 4D data sets containing information on bias-dependent relaxation dynamics at each spatial location without long-range electrostatic artifacts. To interpret these data sets in the absence of defined physical models, we employ a non-negative tensor factorization method which clearly presents the data as a product of simple behaviors allowing for direct physics interpretation. Correspondingly, we perform phase-field modeling finding the existence of ‘hard’ and ‘soft’ domain wall edges. This approach can be extended to other multidimensional spectroscopies for which even exploratory data analysis leads to unsatisfactory results due to many components in the decomposition.
Defect diffusion is a key process in materials science and catalysis, but as migration mechanisms are often too complex to enumerate a priori, calculation of transport tensors typically have no measure of convergence and require significant end-user intervention. These two bottlenecks prevent high-throughput implementations essential to propagate model-form uncertainty from interatomic interactions to predictive simulations. In order to address these issues, we extend a massively parallel accelerated sampling scheme, autonomously controlled by Bayesian estimators of statewide sampling completeness, to build atomistic kinetic Monte Carlo models on a state-space irreducible under exchange and space group symmetries. Focusing on isolated defects, we derive analytic expressions for drift and diffusion coefficients, providing a convergence metric by calculating the Kullback–Leibler divergence across the ensemble of diffusion processes consistent with the sampling uncertainty. The autonomy and efficacy of the method is demonstrated on surface trimers in tungsten and Hexa-interstitials in magnesium oxide, both of which exhibit complex, correlated migration mechanisms.
Understanding the geometric properties of quantum states and their implications in fundamental physical phenomena is a core aspect of contemporary physics. The quantum geometric tensor (QGT) is a central physical object in this regard, encoding complete information about the geometry of the quantum state. The imaginary part of the QGT is the well-known Berry curvature, which plays an integral role in the topological magnetoelectric and optoelectronic phenomena. The real part of the QGT is the quantum metric, whose importance has come to prominence recently, giving rise to a new set of quantum geometric phenomena such as anomalous Landau levels, flat band superfluidity, excitonic Lamb shifts and nonlinear Hall effect. Despite the central importance of the QGT, its experimental measurements have been restricted only to artificial two-level systems. Here, in this work, we develop a framework to measure the QGT in crystalline solids using polarization-, spin- and angle-resolved photoemission spectroscopy. Using this framework, we demonstrate the effective reconstruction of the QGT in the kagome metal CoSn, which hosts topological flat bands. Establishing this momentum- and energy-resolved spectroscopic probe of the QGT is poised to significantly advance our understanding of quantum geometric responses in a wide range of crystalline systems.
Optical materials play a key role in enabling modern optoelectronic technologies in a wide variety of domains such as the medical or the energy sector. Among them, nonlinear optical crystals are of primary importance to achieve a broader range of electromagnetic waves in the devices. However, numerous and contradicting requirements significantly limit the discovery of new potential candidates, which, in turn, hinders the technological development. In the present work, the static nonlinear susceptibility and dielectric tensor are computed via density-functional perturbation theory for a set of 579 inorganic semiconductors. The computational methodology is discussed and the provided database is described with respect to both its data distribution and its format. Several comparisons with both experimental and ab initio results from literature allow to confirm the reliability of our data. The aim of this work is to provide a relevant dataset to foster the identification of promising nonlinear optical crystals in order to motivate their subsequent experimental investigation.
Fast detection and characterization of seismic sources is crucial for decision-making and warning systems that monitor natural and induced seismicity. However, besides the laying out of ever denser monitoring networks of seismic instruments, the incorporation of new sensor technologies such as Distributed Acoustic Sensing (DAS) further challenges our processing capabilities to deliver short turnaround answers from seismic monitoring. In response, this work describes a methodology for the learning of the seismological parameters: location and moment tensor from compressed seismic records. In this method, data dimensionality is reduced by applying a general encoding protocol derived from the principles of compressive sensing. The data in compressed form is then fed directly to a convolutional neural network that outputs fast predictions of the seismic source parameters. Thus, the proposed methodology can not only expedite data transmission from the field to the processing center, but also remove the decompression overhead that would be required for the application of traditional processing methods. An autoencoder is also explored as an equivalent alternative to perform the same job. We observe that the CS-based compression requires only a fraction of the computing power, time, data and expertise required to design and train an autoencoder to perform the same task. Implementation of the CS-method with a continuous flow of data together with generalization of the principles to other applications such as classification are also discussed.
An equivariant graph neural network model enables the rapid and accurate prediction of complete fourth-rank elasticity tensors of inorganic materials, facilitating the discovery of materials with exceptional mechanical properties.
In this work, we present constraints on the tensor-to-scalar ratio r using Planck data. We use the latest release of Planck maps (PR4), processed with the NPIPE code, which produces calibrated frequency maps in temperature and polarization for all Planck channels from 30 GHz to 857 GHz using the same pipeline. We computed constraints on r using the BB angular power spectrum, and we also discuss constraints coming from the TT spectrum. Given Planck's noise level, the TT spectrum gives constraints on r that are cosmic-variance limited (with $\sigma$ r = 0.093), but we show that the marginalized posterior peaks towards negative values of r at about the 1.2$\sigma$ level. We derived Planck constraints using the BB power spectrum at both large angular scales (the 'reionization bump') and intermediate angular scales (the 'recombination bump') from $\ell$=2 to 150, and find a stronger constraint than that from TT, with $\sigma$ r = 0.069. The Planck BB spectrum shows no systematic bias, and is compatible with zero, given both the statistical noise and the systematic uncertainties. The likelihood analysis using B modes yields the constraint r < 0.158 at 95% confidence using more than 50% of the sky. This upper limit tightens to r < 0.069 when Planck EE, BB, and EB power spectra are combined consistently, and it tightens further to r < 0.056 when the Planck TT power spectrum is included in the combination. Finally, combining Planck with BICEP2/Keck 2015 data yields an upper limit of r < 0.044.
We present a reduced scaling formulation of the extended multi-state CASPT2 (XMS-CASPT2) method, which is based on our recently developed state-specific CASPT2 (SS-CASPT2) formulation using supporting subspaces and tensor hyper-contraction. By using these two techniques, the off-diagonal elements of the effective Hamiltonian can be computed with only O(N 3 ) operations and O(N 2 ) memory, where N is the number of basis functions. Furthermore, this limits the overall computational scaling to O(N 4 ) operations and O(N 2 ) memory. Thus, excited states can now be obtained at the same reduced (relative to previous algorithms) scaling we achieved for SS-CASPT2.
Here, we have used reverse non-equilibrium molecular dynamics (RNEMD) simulations to determine the full thermal conductivity tensor for the monoclinic high explosive crystal β-1,3,5,7-tetranitro-1,3,5,7-tetrazoctane (β-HMX). In order to do so for the monoclinic crystal, four directions for heat propagation are used. Effects of the temperature and pressure are investigated between 200 and 500 K and 0 and 5 GPa, respectively, which approximately covers the range where the β polymorph is stable. Simulations are carried out with the Smith–Bharadwaj non-reactive empirical potential [Smith and Bharadwaj, J. Phys. Chem. B 103, 3570 (1999)], which is known to reproduce well the thermo-elastic properties of HMX. Our results indicate that the thermal conductivity, κ, is highly anisotropic, with 36% difference between the two extreme values at 300 K and 0 GPa. A simple function is used to interpolate κ in the pressure-temperature regime considered in this study, which can be used in continuum models. The results from RNEMD simulations compare well with available experimental results from the literature and allow the determination of κ for any direction and temperature and pressure within or around the fitting interval.
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 rank 2 dimension 3 tensor formulation for polarized neutron transport in a magnetic field is derived. Using this formulation, the rotating magnetic field problem is revisited to produce a single 3 × 3 vector-transformation matrix that describes the polarization transport. That result is then used to fashion a new strategy for a numerical approximation of polarization transport in an arbitrary magnetic field using time-dependent perturbation theory.