Nonperturbative Method Research Articles

Nonassociative gauge gravity theories with R-flux star products and Batalin-Vilkovisky quantization in algebraic quantum field theory

Abstract Nonassociative modifications of general relativity, GR, and quantum gravity, QG, models naturally arise as star product and R-flux deformations considered in string/ M-theory. Such nonassociative and noncommutative geometric and quantum information theories were formulated on phase spaces defined as cotangent Lorentz bundles enabled with nonassociative symmetric and nonsymmetric metrics and nonlinear and linear connection structures. We outline the analytic methods and proofs that corresponding geometric flow evolution and dynamical field equations can be decoupled and integrated in certain general off-diagonal forms. New classes of solutions describing nonassociative black holes, wormholes, and locally anisotropic cosmological configurations are constructed using such methods. We develop the Batalin-Vilkovisky, BV, formalism for quantizing modified gravity theories, MGTs, involving twisted star products and semi-classical models of nonassociative gauge gravity with de Sitter/affine/ Poincar'{e} double structure groups. Such theories can be projected on Lorentz spacetime manifolds in certain forms equivalent to GR or MGTs with torsion generalizations etc. We study the properties of the classical and quantum BV operators for nonassociative phase spaces and nonassociative gauge gravity. Recent results and methods from algebraic QFT are generalized to involve nonassociative star product deformations of the anomalous master Ward identity. Such constructions are elaborated in a nonassociative BV perspective and for developing non-perturbative methods in QG.

Perturbative QCD meets phase quenching: The pressure of cold quark matter

Nonperturbative inequalities constrain the thermodynamic pressure of quantum chromodynamics (QCD) with its phase-quenched version, a sign-problem-free theory amenable to lattice treatment. In the perturbative regime with a small QCD coupling constant αs, one of these inequalities manifests as an O(αs3) difference between the phase-quenched and QCD pressures at large baryon chemical potential. In this work, we generalize state-of-the-art algorithmic techniques used in collider physics to address large-scale multiloop computations at finite chemical potential, by direct numerical integration of Feynman diagrams in momentum space. Using this novel approach, we evaluate this O(αs3) difference and show that it is a gauge-independent and small positive number compared to the known perturbative coefficients at this order. This implies that at high baryon densities, phase-quenched lattice simulations can provide a complementary nonperturbative method for accurately determining the pressure of cold quark matter at O(αs3). Published by the American Physical Society 2024

Ligand-induced conformational changes in protein molecules detected by sum-frequency generation

We present the first demonstration of ligand-induced conformational changes in a biological molecule, a protein, by sum-frequency generation (SFG). Constructs of KRasG12D protein were prepared by selectively deuterating residues of a single amino acid type using isotope-labeled amino acids and cell-free protein synthesis. By attaching labeled protein to a supported bilayer membrane via a His-tag to Ni-NTA-bearing lipids, we ensured that single layers of ordered molecules were formed while preserving the protein’s native structure. Exceptionally large SFG amide I signals were produced in both labeled and unlabeled proteins, demonstrating a high degree of orientational order upon attachment to the bilayer. Deuterated protein also produced SFG signals in the CDx spectral region, which were not present in the unlabeled protein. The CDx signals were measured before and after binding a peptide inhibitor, KRpep-2d, revealing shifts in SFG intensity due to conformational changes at the labeled sites. In particular, peaks associated with CDx stretching vibrations for alanine, valine, and glycine changed substantially in amplitude upon inhibitor binding. By inspection of the crystal structure, these three residues are uniquely colocated on the protein surface in and near the nucleotide binding site, which is in allosteric communication with the site of peptide inhibitor binding, suggesting an approach to identify a ligand’s binding site. The technique offers a highly sensitive, nonperturbative method of mapping ligand-induced conformational changes and allosteric networks in biological molecules for studies of the relationship between structure and function and mechanisms of action in drug discovery.

Deeper-band electron contributions to stopping power of silicon for low-energy ions.

This study provides accurate results for the electronic stopping cross sections of H, He, N, and Ne in silicon in low to intermediate energy ranges using various non-perturbative theoretical methods, including real-time time-dependent density functional theory, transport cross section, and induced-density approach. Recent experimental findings [Ntemou et al., Phys. Rev. B 107, 155145 (2023)] revealed discrepancies between the estimates of density functional theory and the observed values. We show that these discrepancies vanish by considering the nonuniform electron density of the deeper silicon bands for ion velocities approaching zero (v → 0). This indicates that mechanisms such as "elevator" and "promotion," which can dynamically excite deeper-band electrons, are active, enabling a localized free-electron gas to emulate ion energy loss, as pointed out by Lim et al. [Phys. Rev. Lett. 116, 043201 (2016)]. The observation and the description of a velocity-proportionality breakdown in electronic stopping cross sections at very low velocities are considered to be a signature of the contributions of deeper-band electrons.

A comprehensive study of stability analysis for nonlinear Mathieu equation without a perturbative technique

AbstractThe present research focuses on the challenges engineers face in predicting the behavior of nonlinear vibration systems accurately. The nonperturbative method is highlighted as a solution that provides insights into chaos, bifurcation, resonance response, and stability attributes. Specifically, the study delves into the dynamic analysis of the nonlinear Mathieu equation. The research involves a complex and extensive analytical exploration, transitioning from a nonlinear state to a linear one through various stages. The introduced computational method aims to examine the resonance response of the nonlinear Mathieu equation and offer innovative solutions for the Mathieu–Duffing–type oscillator. The nonperturbative approach remains essential in gaining a deeper understanding of nonlinear vibration systems.

Perturbation-based nonperturbative method

This paper presents a nonperturbative method for solving eigenproblems. This method applies to almost all potentials and provides nonperturbative approximations for any energy level. The method converts an eigenproblem into a perturbation problem, obtains perturbation solutions through standard perturbation theory, and then analytically continues the perturbative solution into a nonperturbative solution. Concretely, we follow three main steps: (1) Introduce an auxiliary potential that can be solved exactly and treat the potential to be solved as a perturbation on this auxiliary system. (2) Use perturbation theory to obtain an approximate polynomial of the eigenproblem. (3) Use a rational approximation to analytically continue this approximate polynomial into the nonperturbative region.

Estimation of the lateral mis-registrations of the GRAVITY+ adaptive optics system

Context. The GRAVITY+ upgrade implies a complete renewal of its adaptive optics (AO) systems. Its complex design, featuring moving components between the deformable mirrors and the wavefront sensors, requires the monitoring and auto-calibrating of the lateral mis-registrations of the system while in operation. Aims. For preset and target acquisition, large lateral registration errors must be assessed in open loop to bring the system to a state where the AO loop closes. In closed loop, these errors must be monitored and corrected, without impacting the science. Methods. With respect to the first requirement, our method is perturbative, with two-dimensional modes intentionally applied to the system and correlated to a reference interaction matrix. For the second requirement, we applied a non-perturbative approach that searches for specific patterns in temporal correlations in the closed loop telemetry. This signal is produced by the noise propagation through the AO loop. Results. Our methods were validated through simulations and on the GRAVITY+ development bench. The first method robustly estimates the lateral mis-registrations, in a single fit and with a sub-subaperture resolution while in an open loop. The second method is not absolute, but it does successfully bring the system towards a negligible mis-registration error, with a limited turbulence bias. Both methods proved to robustly work on a system still under development and not fully characterised. Conclusions. Tested with Shack-Hartmann wavefront sensors, the proposed methods are versatile and easily adaptable to other AO instruments, such as the pyramid, which stands as a baseline for all future AO systems. The non-perturbative method, not relying on an interaction matrix model and being sparse in the Fourier domain, is particularly suitable to the next generation of AO systems for extremely large telescopes that will present an unprecedented level of complexity and numbers of actuators.

Ghost-gluon vertex in the presence of the Gribov horizon: General kinematics

Correlation functions are important probes for the behavior of quantum field theories. Already at tree-level, the refined Gribov-Zwanziger (RGZ) effective action for Yang-Mills theories provides a good approximation for the gluon propagator, as compared to that calculated by nonperturbative methods such as lattice field theory and Dyson-Schwinger equations. However, the study of higher correlation functions of the RGZ theory is still at its beginning. In this work we evaluate the ghost-gluon vertex function in Landau gauge at one-loop level, in d=4 space-time dimensions for the gauge groups SU(2) and SU(3). More precisely, we extend the analysis conducted in [1] for the soft-gluon limit to an arbitrary kinematic configuration. We introduce renormalization group effects by means of a toy model for the running coupling and investigate the impact of such a model in the ultraviolet tails of our results. We find that RGZ results match fairly closely those from lattice simulations, Schwinger-Dyson equations and the Curci-Ferrari model for three different kinematic configurations. This is compatible with RGZ being a feasible theory for the strong interaction in the infrared regime. Published by the American Physical Society 2024

The masking technique for forced nonlinear oscillator stability behavior analysis using the non-perturbative approach

The study utilized the masking technique to explore the stability behavior of a forced nonlinear oscillator through the non-perturbative approach, with a particular focus on a Van der Pol oscillator subjected to external force, characterized by both cubic and quadratic nonlinearities. The application of the non-perturbative method (NPM) in conjunction with the masking technique was a pivotal aspect of this research, transforming the inherently non-homogeneous, nonlinear system into a homogeneous linear system. This transformation was crucial as it simplified the complex dynamics of the system, rendering it more amenable to analysis. Through this method, the research successfully established the system’s overall frequency, meticulously accounting for the impact of the periodic external force. The study also identified a distinct type of resonance response, where the system’s frequency incorporates the excited frequency in a nonlinear relationship. The masking technique proved to be an invaluable tool for examining the stability behavior of forced vibrations in oscillators via the NPM, providing profound insights into stability under external forces and enhancing the understanding and control of oscillatory behaviors in nonlinear dynamical systems. A critical confirmation of the current methodology is provided by the remarkable agreement found between the numerical solution and the provided analytical solution. This agreement shows that the analytical method produces trustworthy predictions and appropriately describes the system’s behavior. The plotted stability diagrams, which demonstrate that the model’s simulation of stability behavior is consistent with observed events, particularly resonance phenomena, offer further validity for the findings. In the resonance case, the effects of the damping coefficient and the external force’s magnitude are significant. The results of the analysis show that an increase in the damping coefficient has a destabilizing effect that causes unstable zones to expand. In contrast, in the resonance state, the quadratic and cubic nonlinearity factors both contribute to stabilization. Understanding how various system factors impact stability dynamics particularly in relation to resonance phenomena is made easier with the help of this insight.

Underestimation of the tidal force and apsidal motion in close binary systems by the perturbative approach: Comparisons with non-perturbative models

Context. Stellar deformations play a significant role in the dynamical evolution of stars in binary systems, impacting the tidal dissipation and the outcomes of mass transfer processes. The prevalent method for modelling the deformations and tidal interactions of celestial bodies solely relies on the perturbative approach, which assumes that stellar deformations are minor perturbations to the spherical symmetry. An observable consequence of stellar deformations is the apsidal motion in eccentric systems, which has be observationally determined across numerous binary systems. Aims. Our objective is to assert the reliability of the perturbative approach when applied to close and strongly deformed binary systems. Methods. We have developed a non-perturbative 3D modelling method designed to account for high stellar deformations. We focus on comparing the properties of perturbatively deformed stellar models with our 3D models, particularly in terms of apsidal motion. Results. Our research highlights that the perturbative model becomes imprecise and underestimates the tidal force and rate of apsidal motion at a short orbital separation. This discrepancy primarily results from the first-order treatment in the perturbative approach, and cannot be rectified using straightforward mathematical corrections due to the strong non-linearity and numerous parameters of the problem. We have determined that our methodology affects the modelling of approximately 42% of observed binary systems with measured apsidal motion, introducing a discrepancy greater than 2% when the normalised orbital separation verifies q−1/5a(1 − e2)/R1 ≲ 6.5 (q is the mass ratio of the system, a is its semi-major axis, e is its orbital eccentricity and R1 is the radius of the primary star). Conclusions. The perturbative approach underestimates tidal interactions between bodies up to ∼40% for close low-mass binaries. All the subsequent modelling is impacted by our findings, in particular, the tidal dissipation is significantly underestimated. As a result, all binary stellar models are imprecise when applied to systems with a low orbital separation, and the outcomes of these models are also affected by these inaccuracies.

Tidal Migration of Exoplanets around M Dwarfs: Frequency-dependent Tidal Dissipation

The orbital architectures of short-period exoplanet systems are shaped by tidal dissipation in their host stars. For low-mass M dwarfs whose dynamical tidal response comprises a dense spectrum of inertial modes at low frequencies, resolving the frequency dependence of tidal dissipation is crucial to capturing the effect of tides on planetary orbits throughout the evolutionary stages of the host star. We use nonperturbative spectral methods to calculate the normal mode oscillations of a fully convective M dwarf modeled using realistic stellar profiles from MESA. We compute the dissipative tidal response composed of contributions from each mode, as well as nonadiabatic coupling between the modes, which we find to be an essential component of the dissipative calculations. Using our results for dissipation, we then compute the evolution of circular, coplanar planetary orbits under the influence of tides in the host star. We find that orbital migration driven by resonance locking affects the orbits of Earth-mass planets at orbital periods P orb ≲ 1.5 days and of Jupiter-mass planets at P orb ≲ 2.5 days. Due to resonantly driven orbital decay and outward migration, we predict a dearth of small planets closer than P orb ∼ 1 day and similarly sparse numbers of more massive planets out to P orb ∼ 3 days.

Chain-mapping methods for relativistic light-matter interactions

The interaction between localized emitters and quantum fields, both in relativistic settings and in the case of ultra-strong couplings, requires non-perturbative methods beyond the rotating-wave approximation. In this work we employ chain-mapping methods to achieve a numerically exact treatment of the interaction between a localized emitter and a scalar quantum field. We extend the application range of these methods beyond emitter observables and apply them to study field observables. We first provide an overview of chain-mapping methods and their physical interpretation, and discuss the thermal double construction for systems coupled to thermal field states. Modelling the emitter as an Unruh-DeWitt particle detector, we then calculate the energy density emitted by a detector coupling strongly to the field. As a stimulating demonstration of the approach's potential, we calculate the radiation emitted from an accelerated detector in the Unruh effect, which is closely related to the thermal double construction as we discuss. We comment on prospects and challenges of the method.

Diffusion Monte Carlo calculations of the polarizability of a confined hydrogen atom: benchmarking and application to high symmetry wells

We present a non-perturbative direct method to calculate the polarizability of a hydrogen atom confined in a three-dimensional potential well of any geometry. The calculation is based on the diffusion Monte Carlo method. The advantage of the method is simplicity of implementation and immediate adaptability to any well shape. The method is validated for the well-studied spherically confined hydrogen atom, and demonstrated in the case of two other geometries (cube and octahedron), for which this paper provides the first set of results. Although demonstrated here for the confined hydrogen atom, the method can be immediately applied to any single-electron system placed in a three-dimensional potential well of any type and geometry. Results for a hydrogen atom confined in potential wells of cubic or spherical symmetry suggests that the polarizability in these cases is a universal function of the volume of the well. This result can simplify calculations for real situations such as in quantum dots.

Coordinate-space calculation of QED corrections to the hadronic vacuum polarization contribution to (g − 2)μ with SU(3) flavor symmetry

Lattice QCD (LQCD) has proven to be an important tool in understanding the tension between the experimental value for the anomalous magnetic moment of the muon (g − 2)μ and its prediction from the standard model. The lattice provides a non-perturbative method for evaluating the hadronic contributions to (g − 2)μ, which contributes the largest amount to the uncertainty of the theoretical prediction. Among these the hadronic vacuum polarization aμHVP is the dominant contribution. In order to match the uncertainty of the experiment, lattice QCD needs to reach sub-percent precision. This requires the calculation of QED corrections to aμHVP, which are represented by additional Feynman diagrams. We present a lattice calculation of the UV-finite (2+2) diagram at the SU(3) flavor symmetric point and compare this to the pseudoscalar meson exchange model with a vector-meson dominance parametrization of the transition form factor.

Method of spectral response to stochastic processes for measuring the nonreciprocal effective interactions.

The theoretical background of the nonperturbative method of spectral response to stochastic processes (SRSP) for measuring the nonreciprocal interparticle effective interactions in strongly coupled underdamped systems is described. Analytical expressions for vibrational spectral density of confined Brownian particles with a nonreciprocal effective interaction are presented. The changes in the vibrational spectral density with varying different parameters of the system (nonreciprocity, viscosity, ratios of particle sizes, and intensities of random processes acting on each particle) are discussed using the example of a pair of nonidentical particles in a harmonic trap. The SRSP method is compared to three other nonperturbative methods. The SRSP method demonstrates an undeniable advantage when processing particle trajectories with errors in particle tracking.

2-index chiral gauge theories

We undertake a systematic study of the 4-dimensional SU(N) 2-index chiral gauge theories and investigate their faithful global symmetries and dynamics. These are a finite set of theories with fermions in the 2-index symmetric and anti-symmetric representations, with no fundamentals, and they do not admit a large-N limit. We employ a combination of perturbative and nonperturbative methods, enabling us to constrain their infrared (IR) phases. Specifically, we leverage the ’t Hooft anomalies associated with continuous and discrete groups to eliminate a few scenarios. In some cases, the anomalies rule out the possibility of fermion composites. In other cases, the interplay between the continuous and discrete anomalies leads to multiple higher-order condensates, which inevitably form to match the anomalies. Further, we pinpoint the most probable symmetry-breaking patterns by searching for condensates that match the full set of anomalies resulting in the smallest number of IR degrees of freedom. Higher-loop β-function analysis suggests that a few theories may flow to a conformal fixed point.

On stability issues of the HEOM method

AbstractThe Hierarchical Equations of Motion (HEOM) method has become one of the cornerstones in the simulation of open quantum systems and their dynamics. It is commonly referred to as a non-perturbative method. Yet, there are certain instances, where the necessary truncation of the hierarchy of auxiliary density operators seems to introduce errors which are not fully controllable. We investigate the nature and causes of this type of critical error both in the case of pure decoherence, where exact results are available for comparison, and in the spin-boson system, a full system-reservoir model. We find that truncating the hierarchy to any finite size can be problematic for strong coupling to a dissipative reservoir, in particular when combined with an appreciable reservoir memory time.

A novel methodology for a time-delayed controller to prevent nonlinear system oscillations

The paper investigates the nonlinear transversal vibrations of a cantilever beam structure in the primary resonance case. A time-delayed position-velocity control is suggested to reduce the nonlinear vibrations of the structure under consideration. A non-perturbative method (NPM) is used to get an equivalent analogous linear differential equation (DE) to the original nonlinear one. For the benefit of the readers, a comprehensive description of the NPM method is provided. The theoretical findings are validated through a numerical comparison carried out by employed the Mathematica Software. Both the numerical solutions and the theoretical outcomes showed excellent agreement. As well-known, all classic perturbation techniques use Taylor expansion, when the restoring forces are present, to expand these forces and therefore lessen the difficulty of the given problem. Under the NPM, this weakness is no longer present. Furthermore, one may examine the stability examination of the issue with the NPM something that was not possible with prior traditional techniques. The controlled linear equivalent model is examined using the multiple-scales homotopy method. The amplitude-phase modulation equations which control the dynamics of the structure at the various resonance circumstances are established. The loop-delay stability diagrams are analyzed. It is looked at how the different controller parameters impact the oscillation behaviors of the system. The obtained theoretical outcomes showed that the loop delay has an important impact on the effectiveness of the control. Therefore, the ideal loop-delay values are given and used to develop the enactment of the organized control. The completed analytical results are also numerically validated, to reveal their good correlation with the achieved theoretical new results.

MoBiDICT: New 3D static models of close synchronised binaries in hydrostatic equilibrium

Context. In close binary systems, tidal interactions and rotational effects can strongly influence stellar evolution as a result of mass transfer and common envelope phases. These aspects can only be treated following improvements of theoretical models to take into account the breaking of spherical symmetry occurring in close binaries. Current models of binary stars rely on either the so-called Roche model or the perturbative approach, both of which result in several assumptions concerning the gravitational, tidal, and centrifugal potentials. Aims. Our aim is to develop a precise 3D model of stellar deformations and to study the robustness of the Roche and perturbative models in different deformation regimes. Methods. We developed a new non-perturbative method to compute the precise structural deformation of a binary system in three dimensions that is valid even in the most distorted cases. We then compared our new method to the Roche and perturbative models for different orbital separations and binary components. Results. We found that in the most distorted cases, both the Roche and perturbative models significantly underestimate the deformation of binaries. The effective gravity and the overall structural deformations are also noticeably different in the most distorted cases, leading to modifications of the usual gravity darkening generally obtained through the Roche model when interpreting the observations. Moreover, we found that the dipolar term of the gravitational potential, usually neglected by the perturbative theory, has the same order of magnitude as the leading tidal term in the most distorted cases. Conclusions. We developed a new method that is capable of precisely computing the deformations of a binary system composed of any type of stars, even compact objects. For all the stars we studied, the differences in deformation with respect to the Roche or perturbative models are significant in the most distorted cases, which impacts both the interpretation of observations and the theoretical structural depiction of these distorted bodies. In the weaker deformation regimes, the Roche model is a viable option for studying the surface properties of binaries, while the perturbative model is strongly favoured when evaluating structural deformations.

Real-Time Nonperturbative Dynamics of Jet Production in Schwinger Model: Quantum Entanglement and Vacuum Modification.

The production of jets should allow testing the real-time response of the QCD vacuum disturbed by the propagation of high-momentum color charges. Addressing this problem theoretically requires a real-time, nonperturbative method. It is well known that the Schwinger model [QED in (1+1) dimensions] shares many common properties with QCD, including confinement, chiral symmetry breaking, and the existence of vacuum fermion condensate. As a step in developing such an approach, we report here on fully quantum simulations of a massive Schwinger model coupled to external sources representing quark and antiquark jets as produced in e^{+}e^{-} annihilation. We study, for the first time, the modification of the vacuum chiral condensate by the propagating jets and the quantum entanglement between the fragmenting jets. Our results indicate strong entanglement between the fragmentation products of the two jets at rapidity separations Δη≤2, which can potentially exist also in QCD and can be studied in experiments.