Perturbative Calculations Research Articles

Shale fault reactivation during hydraulic fracturing in the Sichuan Basin: Evidence from shear experiments and stress perturbation calculations

Induced seismicity triggered during hydraulic fracturing for shale gas exploitation in the Sichuan Basin has aroused wide public concern with these earthquakes closely correlated with the reactivation of faults within the reservoir. The target shale reservoirs in the Sichuan Bain are currently located in the Longmaxi formation. To explore instability on these faults, we conducted shear experiments on simulated fault gouges under hydrothermal conditions to assess frictional stability and also evaluated the stress perturbations resulting from multistage hydraulic fracturing. Experimental results show that the frictional instability on these faults is primarily controlled by both mineral composition and the applied temperatures. With a decrease in the contents of phyllosilicate minerals or an increase in applied temperatures, the shale faults exhibit a transition from velocity-strengthening to velocity-weakening behaviour, indicating the potential for unstable fault slip. The stress perturbations resulting from multistage hydraulic fracturing were calculated from a dislocation model of the fluid-driven fracture. These results show that the stress changes resulting from multistage hydraulic fracturing are sufficient to reactivate adjacent unstable faults in the shale reservoir and trigger the seismicity. Our experimental and modelling results highlight the importance of shale composition, temperature, and stress perturbations on shale fault stability. These results have significant implications for understanding the shale fault instability and the potential triggering of induced seismicity during hydraulic fracturing in the Sichuan Basin.

Investigations on the defect structures for Mn2+ in CdSe nanocrystals and bulk materials and the criterion of occupation for Mn2+ in CdX (X = S, Se, Te) nanocrystals.

The spin Hamiltonian parameters and defect structures are theoretically studied for the substitutional Mn2+ at the core of CdSe nanocrystals and in the bulk materials from the perturbation calculations of spin Hamiltonian parameters for trigonal tetrahedral 3d5 clusters. Both the crystal-field and charge transfer contributions are taken into account in the calculations from the cluster approach. The impurity-ligand bond angles are found to be about 1.84° larger and 0.10° smaller in the CdSe:Mn2+ nanocrystals and bulk materials, respectively, than those (≈109.37°) of the host Cd2+ sites. The quantitative criterion of occupation (at the core or surface) for Mn2+ in CdX (X = S, Se, Te) nanocrystals is presented for the first time based on the inequations of hyperfine structure constants (HSCs). This criterion is well supported by the experimental HSCs data of Mn2+ in CdX nanocrystals. The previous assignments of signals SI as Mn2+ at the core of CdS nanocrystals are renewed as Mn2+ at the surface based on the above criterion. The present studies would be helpful to achieve convenient determination of occupation for Mn2+ impurities in CdX semiconductor nanocrystals by means of spectral (e.g., HSCs) analysis.

Improving gas adsorption modeling for MOFs by local calibration of Hubbard U parameters.

While computational screening with density functional theory (DFT) is frequently employed for the screening of metal-organic frameworks (MOFs) for gas separation and storage, commonly applied generalized gradient approximations (GGAs) exhibit self-interaction errors, which hinder the predictions of adsorption energies. We investigate the Hubbard U parameter to augment DFT calculations for full periodic MOFs, targeting a more precise modeling of gas molecule-MOF interactions, specifically for N2, CO2, and O2. We introduce a calibration scheme for the U parameter, which is tailored for each MOF, by leveraging higher-level calculations on the secondary building unit (SBU) of the MOF. When applied to the full periodic MOF, the U parameter calibrated against hybrid HSE06 calculations of SBUs successfully reproduces hybrid-quality calculations of the adsorption energy of the periodic MOF. The mean absolute deviation of adsorption energies reduces from 0.13eV for a standard GGA treatment to 0.06eV with the calibrated U, demonstrating the utility of the calibration procedure when applied to the full MOF structure. Furthermore, attempting to use coupled cluster singles and doubles with perturbative triples calculations of isolated SBUs for this calibration procedure shows varying degrees of success in predicting the experimental heat of adsorption. It improves accuracy for N2 adsorption for cases of overbinding, whereas its impact on CO2 is minimal, and ambiguities in spin state assignment hinder consistent improvements of O2 adsorption. Our findings emphasize the limitations of cluster models and advocate the use of full periodic MOF systems with a calibrated U parameter, providing a more comprehensive understanding of gas adsorption in MOFs.

QCD corrections to the Golden decay channel of the Higgs boson

Future colliders aim to provide highly precise experimental measurements of the properties of the Higgs boson. In order to benefit from these precision machines, theoretical errors in the Higgs sector observables have to match at least the experimental uncertainties. The theoretical uncertainties in the Higgs sector observables can be reduced by including missing higher-order terms in their perturbative calculations. In this direction, we compute the mixed QCD-electroweak corrections at \\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$\\mathcal{O}\\left({\\alpha \\alpha }_{s}\\right)$$\\end{document} to the Higgs decay into four charged leptons by considering the golden decay channel, H → e+e−μ+μ−. Due to color conservation, these corrections receive contributions only from the two-loop virtual diagrams. In the complex mass scheme, we find that the mixed QCD-electroweak corrections to the partial decay width, relative to the leading order predictions, are positive and about 0.27% for αs(MZ). Relative to the next-to-leading order electroweak corrections, the mixed QCD-electroweak corrections are found to be approximately 18% for αs(MZ). With respect to the leading order, we observe a flat effect of the mixed QCD-electroweak corrections on the invariant mass distribution of the lepton pairs with fixed QCD coupling. The ϕ distribution, due to the mixed QCD-electroweak corrections, follows a (1 − cos ϕ) dependence.

Origin of Enantioselectivity in Engineered Cytochrome c-Catalyzed Carbon-Radical FePP Hydrolysis Revealed Using QM/MM (ABEEM Polarizable Force Field) and MD Simulations.

The origin of highly efficient asymmetric aminohydroxylation of styrene catalyzed by engineered cytochrome c is investigated by the developed Atom-Bond Electronegativity Equalization Method polarizable force field (ABEEM PFF), which is a combined outcome of electronic and steric effects. Model molecules were used to establish the charge parameters of the ABEEM PFF, for which the bond-stretching and angle-bending parameters were obtained by using a combination of modified Seminario and scan methods. The interactions between carbon-radical Fe-porphyrin (FePP) and waters are simulated by molecular dynamics, which shows a clear preference for the pre-R over the pre-S. This preference is attributed to the hydrogen-bond between the mutated 100S and 101P residues as well as van der Waals interactions, enforcing a specific conformation of the carbon-radical FePP complex within the binding pocket. Meanwhile, the hydrogen-bond between water and the nitrogen atom in the active intermediate dictates the stereochemical outcome. Quantum mechanics/molecular mechanics (QM/MM (ABEEM PFF)) and free-energy perturbation calculations elucidate that the 3RTS is characterized by sandwich-like structure among adjacent amino acid residues, which exhibits greater stability than crowed arrangement in 3STS and enables the R enantiomer to form more favorably. Thus, this study provides mechanistic insight into the catalytic reaction of hemoproteins.

Large-N Principal Chiral Model in Arbitrary External Fields.

We report the explicit solution for the vacuum state of the two-dimensional SU(N) principal chiral model at large N for an arbitrary set of chemical potentials and any interaction strength, a unique result of such kind for an asymptotically free quantum field theory. The solution matches one-loop perturbative calculation at weak coupling, and in the opposite strong-coupling regime exhibits an emergent spacial dimension from the continuum limit of the SU(N) Dynkin diagram.

Stochastic thermodynamics of a probe in a fluctuating correlated field

We develop a framework for the stochastic thermodynamics of a probe coupled to a fluctuating medium with spatio-temporal correlations, described by a scalar field. For a Brownian particle dragged by a harmonic trap through a fluctuating Gaussian field, we show that near criticality (where the field displays long-range spatial correlations) the spatially-resolved average heat flux develops a dipolar structure, where heat is absorbed in front and dissipated behind the dragged particle. Moreover, a perturbative calculation reveals that the dissipated power displays three distinct dynamical regimes depending on the drag velocity.

Complex energy-based description of alpha-cluster lifetime in intense laser fields

The phenomenon of laser-assisted alpha decay is studied within the framework of non-Hermitian quantum theory integrated with the (t, t′)-formalism. The width and the lifetime of the alpha cluster of a specific isotope is extracted from the spectrum of the complex-scaled Hamiltonian operator of the nuclear system and estimated numerically. The laser-field-induced correction to the lifetime is computed by first-order (t, t′)-perturbation calculation with regard to different polarization states and control parameters of the external laser field, adjusting appropriate intensity and photon energy pairs by examining the limit of the non-relativistic approximation of the problem.

Fastlomap: faster lead optimization mapper algorithm for large-scale relative free energy perturbation

In recent years, free energy perturbation calculations have garnered increasing attention as tools to support drug discovery. The lead optimization mapper (Lomap) was proposed as an algorithm to calculate the relative free energy between ligands efficiently. However, Lomap requires checking whether each edge in the FEP graph is removable, which necessitates checking the constraints for all edges. Consequently, conventional Lomap requires significant computation time, at least several hours for cases involving hundreds of compounds, and is impractical for cases with more than tens of thousands of edges. In this study, we aimed to reduce the computational cost of Lomap to enable the construction of FEP graphs for hundreds of compounds. We can reduce the overall number of constraint checks required from an amount dependent on the number of edges to one dependent on the number of nodes by using the chunk check process to check the constraints for as many edges as possible simultaneously. Based on the analysis of the execution profiles, we also improved the speed of cycle constraint and diameter constraint checks. Moreover, the output graph is the same as that obtained using the conventional Lomap, enabling direct replacement of the original one with our method. With our improvement, the execution was hundreds of times faster than that of the original Lomap.

Critical Opalescence and Its Impact on the Jet Quenching Parameter q^

Jet quenching parameter q^ is essential for characterizing the interaction strength between jet partons and nuclear matter. Based on the quark-meson model, we develop a new framework for calculating q^ at finite chemical potentials, in which q^ is related to the spectral function of the chiral order parameter. A mean field perturbative calculation up to the one-loop order indicates that the momentum broadening of jets is enhanced at both high temperature and high chemical potential, and approximately proportional to the parton number density in the partonic phase. We further investigate the behavior of q^ in the vicinity of the critical endpoint (CEP) by coupling our calculation with a recently developed equation of state that includes a CEP in the universality class of the Ising model, from which we discover the partonic critical opalescence, i.e., the divergence of scattering rate of jets and their momentum broadening at the CEP, contributed by scatterings via the σ exchange process. Hence, for the first time, jet quenching is connected with the search of CEP.

Landau Singularities Revisited: Computational Algebraic Geometry for Feynman Integrals.

We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the standard model in dimensional regularization. After highlighting issues in the textbook treatment of Landau singularities, we develop an algorithm for classifying and computing them using techniques from computational algebraic geometry. We introduce an algebraic variety called the principal Landau determinant, which captures the singularities even in the presence of massless particles or UV/IR divergences. We illustrate this for 114 example diagrams, including a cutting-edge 2-loop 5-point nonplanar QCD process with multiple mass scales.

The development of computational methods for Feynman diagrams

Over the last 70 years, Feynman diagrams have played an essential role in the development of many theoretical predictions derived from the standard model Lagrangian. In fact, today they have become an essential and seemingly irreplaceable tool in quantum field theory calculations. In this article, we propose to explore the development of computational methods for Feynman diagrams with a special focus on their automation, drawing insights from both theoretical physics and the history of science. From the latter perspective, the article particularly investigates the emergence of computer algebraic programs, such as the pioneering SCHOONSCHIP, REDUCE, and ASHMEDAI, designed to handle the intricate calculations associated with Feynman diagrams. This sheds light on the many challenges faced by physicists when working at higher orders in perturbation theory and reveal, as exemplified by the test of the validity of quantum electrodynamics at the turn of the 1960s and 1970s, the indispensable necessity of computer-assisted procedures. In the second part of the article, a comprehensive overview of the current state of the algorithmic evaluation of Feynman diagrams is presented from a theoretical point of view. It emphasizes the key algorithmic concepts employed in modern perturbative quantum field theory computations and discusses the achievements, ongoing challenges, and potential limitations encountered in the application of the Feynman diagrammatic method. Accordingly, we attribute the enduring significance of Feynman diagrams in contemporary physics to two main factors: the highly algorithmic framework developed by physicists to tackle these diagrams and the successful advancement of algebraic programs used to process the involved calculations associated with them.

Closer look at the matching condition for radiative QCD θ parameter

In this paper, we scrutinize a radiatively generated QCD θ parameter at the two-loop level based on both full analytical loop functions with the Fock-Schwinger gauge method and the effective field theory approach, using simplified models. We observe that the radiatively generated θ parameters at the low energy scale precisely match between them. It provides validity to perturbative loop calculations of the QCD θ parameter with the Fock-Schwinger gauge method. Furthermore, it is also shown that the ordinary Fujikawa method for the radiative θ parameter by using θ¯\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ \\overline{\ heta} $$\\end{document} = −arg det Mqloop\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$ {\\mathcal{M}}_q^{\ extrm{loop}} $$\\end{document} does not cover all contributions in the simplified models. But, we also find that when there is a scale hierarchy in CP-violating sector, evaluation of the Fujikawa method is numerically sufficient. As an application, we calculate the radiative θ parameter at the two-loop level in a slightly extended Nelson-Barr model, where the spontaneous CP violation occurs to solve the strong CP problem. It is found a part of the radiative θ parameters cannot be described by the Fujikawa method.

Resummation schemes for high-electric-charge objects leading to improved experimental mass limits

High-electric-charge compact objects (HECOs) appear in several theoretical particle physics models beyond the Standard Model, and are actively searched for in current colliders, such as the Large Hadron Collider at CERN. In such searches, mass bounds of these objects have been placed, using Drell-Yan and photon-fusion processes at tree level so far. However, such mass-bound estimates are not reliable, given that, as a result of the large values of the electric charge of the HECO, perturbative quantum electrodynamics calculations break down. In this work, we perform a Dyson-Schwinger resummation scheme (as opposed to lattice strong-coupling approach), which makes the computation of the pertinent HECO-production cross sections reliable, thus allowing us to extract improved mass bounds for such objects from ATLAS and MoEDAL searches. Published by the American Physical Society 2024

Chaos perturbation in terms of cycles

The conventional perturbation theory encounters formidable challenges when applied to the quantitative analysis or computation of chaotic systems, due to possibly numerous bifurcations as system parameters vary. In this manuscript, however, based on the cycle expansions formulation we found that the preservation of symbolic dynamics is the key to maintain the analyticity and thus to implement a perturbation computation. Even in the presence of bifurcations, a subset of unstable periodic orbits (UPOs) can be selected to resume the computation, giving rise to new perspectives of treating chaos.

Coalescence of limit cycles in the presence of noise.

Complex dynamical systems may exhibit multiple steady states, including time-periodic limit cycles, where the final trajectory depends on initial conditions. With tuning of parameters, limit cycles can proliferate or merge at an exceptional point. Here we ask how dynamics in the vicinity of such a bifurcation are influenced by noise. A pitchfork bifurcation can be used to induce bifurcation behavior. We model a limit cycle with the normal form of the Hopf oscillator, couple it to the pitchfork, and investigate the resulting dynamical system in the presence of noise. We show that the generating functional for the averages of the dynamical variables factorizes between the pitchfork and the oscillator. The statistical properties of the pitchfork in the presence of noise in its various regimes are investigated and a scaling theory is developed for the correlation and response functions, including a possible symmetry-breaking field. The analysis is done by perturbative calculations as well as numerical means. Finally, observables illustrating the coupling of a system with a limit cycle to a pitchfork are discussed and the phase-phase correlations are shown to exhibit nondiffusive behavior with universal scaling.

Anomalous Transport of Small Polarons Arises from Transient Lattice Relaxation or Immovable Boundaries.

Elucidating transport mechanisms is crucial for advancing material design, yet state-of-the-art theory is restricted to exact simulations of small lattices with severe finite-size effects or approximate ones that assume the nature of transport. We leverage algorithmic advances to tame finite-size effects and exactly simulate small polaron formation and transport in the Holstein model. We further analyze the applicability of the ubiquitously used equilibrium-based Green-Kubo relations and nonequilibrium methods to predict charge mobility. We find that these methods can converge to different values and track this disparity to finite-size dependence and the sensitivity of Green-Kubo relations to the system's topology. Contrary to standard perturbative calculations, our results demonstrate that small polarons exhibit anomalous transport that manifests transiently due to nonequilibrium lattice relaxation or permanently as a signature of immovable boundaries. These findings can offer new interpretations of transport experiments on polymers and transition metal oxides.

Bond dissociation energy of FeCr+ determined through threshold photodissociation in a cryogenic ion trap.

The bond dissociation energy of FeCr+ is measured using resonance enhanced photodissociation spectroscopy in a cryogenic ion trap. The onset for FeCr+ → Fe + Cr+ photodissociation occurs well above the lowest Cr+(6S, 3d5) + Fe(5D, 3d64s2) dissociation limit. In contrast, the higher energy FeCr+ → Fe+ + Cr photodissociation process exhibits an abrupt onset at the energy of the Cr(7S, 3d54s1) + Fe+(6D, 3d64s1) limit, enabling accurate dissociation energies to be extracted: D(Fe-Cr+) = 1.655 ± 0.006eV and D(Fe+-Cr) = 2.791 ± 0.006eV. The measured D(Fe-Cr+) bond energy is 10%-20% larger than predictions from accompanying CAM (Coulomb Attenuated Method)-B3LYP and NEVPT2 and coupled cluster singles, doubles, and perturbative triples electronic structure calculations, which give D(Fe-Cr+) = 1.48, 1.40, and 1.35eV, respectively. The study emphasizes that an abrupt increase in the photodissociation yield at threshold requires that the molecule possesses a dense manifold of optically accessible, coupled electronic states adjacent to the dissociation asymptote. This condition is not met for the lowest Cr+(6S, 3d5) + Fe(5D, 3d64s2) dissociation limit of FeCr+ but is satisfied for the higher energy Cr(7S, 3d54s1) + Fe+(6D, 3d64s1) dissociation limit.

Bootstrapping bulk locality. Part I: Sum rules for AdS form factors

The problem of constructing local bulk observables from boundary CFT data is of paramount importance in holography. In this work, we begin addressing this question from a modern bootstrap perspective. Our main tool is the boundary operator expansion (BOE), which holds for any QFT in AdS. Following Kabat and Lifschytz, we argue that the BOE is strongly constrained by demanding locality of correlators involving bulk fields. Focusing on ‘AdS form factors’ of one bulk and two boundary insertions, we reformulate these locality constraints as a complete set of sum rules on the BOE data. We show that these sum rules lead to a manifestly local representation of form factors in terms of ‘local blocks’. The sum rules are valid non-perturbatively, but are especially well-adapted for perturbative computations in AdS where they allow us to bootstrap the BOE data in a systematic fashion. Finally, in the flat space limit, we show that the AdS form factor reduces to an ordinary QFT form factor. We provide a phase shift formula for it in terms of the BOE and CFT data. In two dimensions, this formula makes manifest Watson’s equations for integrable form factors under certain extremality assumptions on the CFT. We discuss the eventual modifications of our formalism to account for dressed operators in AdS.

Perturbative computation of nonlinear harvesting through a path integral approach.

Statistical field theories provide powerful tools to study complex dynamical systems. In this work those tools are used to analyze the dynamics of a kinetic energy harvester, which is modeled by a system of coupled stochastic nonlinear differential equationsand driven by colored noise. Using the Martin-Siggia-Rose response fields we analytically approach the problem through path integrals in the phase space and represent the moments that correspond to physical observables through Feynman diagrams. This analysis method is tested by comparing the solution to the linear case with previous analytical results. Through a perturbative expansion it is calculated how the nonlinearity affects, to the first order, the energy harvest supporting the results through numerical simulations.