Perturbation Theory Research Articles

Amplitudes and polarizations of quadratic quasi-normal modes for a Schwarzschild black hole

General Relativity predicts the existence of quadratic quasi-normal modes at second order in perturbation theory. Building on our recent work, we compute the amplitudes and polarizations of these modes for non-rotating black holes, showing that they are completely determined by the amplitudes and polarizations of linear modes. We obtain the ratio of quadratic to linear amplitudes, which still depends on the initial conditions of the merger through the polarization of linear modes. However, we demonstrate that this dependence is captured by four fundamental numbers, independent of initial conditions, representing four different combinations of linear modes parities. Additionally, we prove two selection rules regarding the vanishing of classes of quadratic modes. Our results are available online as a package which provides the ratio of amplitudes across a broad spectrum of angular momenta.

Integrated perturbation theory for cosmological tensor fields. III. Projection effects

Integrated perturbation theory for cosmological tensor fields. III. Projection effects

Extreme-Mass-Ratio Inspirals in Ultralight Dark Matter.

Previous works have argued that future gravitational-wave detectors will be able to probe the properties of astrophysical environments where binaries coalesce, including accretion disks, but also dark matter structures. Most analyses have resorted to a Newtonian modeling of the environmental effects, which are not suited to study extreme-mass-ratio inspirals immersed in structures of ultralight bosons. In this Letter, we use relativistic perturbation theory to consistently study these systems in spherical symmetry. We compute the flux of scalar particles and the rate at which orbital energy is dissipated via gravitational radiation and depletion of scalars, i.e., dynamical friction. Our results confirm that the Laser Interferometer Space Antenna will be able to probe ultralight dark matter structures by tracking the phase of extreme-mass-ratio inspirals.

First principles study on the dielectric and infrared properties of single crystal Al3BC3

The dielectric and infrared vibrational properties of single crystal Al3BC3 were computed using density functional perturbation theory. Utilizing a group theory approach, the frequencies and vibrational modes of all the infrared active modes at the Brillouin zone center were determined. The study explored the dielectric function, infrared reflectivity, and Born effective charge of Al3BC3 in directions both parallel and perpendicular to the c-axis. The analysis of the Born effective charge confirmed the existence of strong covalent bonds between B and C, as well as ionic bonds between Al and C in Al3BC3 ceramics.

Achieving Sub‐ppm Sensitivity in SO2 Detection with a Chemically Stable Covalent Organic Framework

We report the inaugural experimental investigation of covalent organic frameworks (COFs) to address the formidable challenge of SO2 detection. Specifically, an imine‐functionalized COF (SonoCOF‐9) demonstrated a modest and reversible SO2 sorption of 3.5 mmol g‐1 at 1 bar and 298 K. At 0.1 bar (and 298 K), the total SO2 uptake reached 0.91 mmol g‐1 with excellent reversibility for at least 50 adsorption‐desorption cycles. An isosteric enthalpy of adsorption (ΔHads) for SO2 equaled −42.3 kJ mol−1, indicating a relatively strong interaction of SO2 molecules with the COF material. Also, molecular dynamics simulations and Møller–Plesset perturbation theory calculations showed the interaction of SO2 with π density of the rings and lone pairs of the N atoms of SonoCOF‐9. The combination of experimental data and theoretical calculations corroborated the potential use of this COF for the selective detection and sensing of SO2 at the sub‐ppm level (0.0064 ppm of SO2).

Integrated perturbation theory for cosmological tensor fields. II. Loop corrections

Integrated perturbation theory for cosmological tensor fields. II. Loop corrections

Integrated perturbation theory for cosmological tensor fields. I. Basic formulation

Integrated perturbation theory for cosmological tensor fields. I. Basic formulation

Integrated perturbation theory for cosmological tensor fields. IV. Full-sky formulation

Integrated perturbation theory for cosmological tensor fields. IV. Full-sky formulation

Achieving Sub‐ppm Sensitivity in SO2 Detection with a Chemically Stable Covalent Organic Framework

We report the inaugural experimental investigation of covalent organic frameworks (COFs) to address the formidable challenge of SO2 detection. Specifically, an imine‐functionalized COF (SonoCOF‐9) demonstrated a modest and reversible SO2 sorption of 3.5 mmol g‐1 at 1 bar and 298 K. At 0.1 bar (and 298 K), the total SO2 uptake reached 0.91 mmol g‐1 with excellent reversibility for at least 50 adsorption‐desorption cycles. An isosteric enthalpy of adsorption (ΔHads) for SO2 equaled −42.3 kJ mol−1, indicating a relatively strong interaction of SO2 molecules with the COF material. Also, molecular dynamics simulations and Møller–Plesset perturbation theory calculations showed the interaction of SO2 with π density of the rings and lone pairs of the N atoms of SonoCOF‐9. The combination of experimental data and theoretical calculations corroborated the potential use of this COF for the selective detection and sensing of SO2 at the sub‐ppm level (0.0064 ppm of SO2).

Quantum Field Theory of Black Hole Perturbations with Backreaction: I General Framework

In a seminal work, Hawking showed that natural states for free quantum matter fields on classical spacetimes that solve the spherically symmetric vacuum Einstein equations are KMS states of non-vanishing temperature. Although Hawking’s calculation does not include the backreaction of matter on geometry, it is more than plausible that the corresponding Hawking radiation leads to black hole evaporation which is, in principle, observable. Obviously, an improvement of Hawking’s calculation including backreaction is a problem of quantum gravity. Since no commonly accepted quantum field theory of general relativity is available yet, it has been difficult to reliably derive the backreaction effect. An obvious approach is to use the black hole perturbation theory of a Schwarzschild black hole of fixed mass and to quantize those perturbations. However, it is not clear how to reconcile perturbation theory with gauge invariance beyond linear perturbations. In recent work, we proposed a new approach to this problem that applies when the physical situation has an approximate symmetry, such as homogeneity (cosmology), spherical symmetry (Schwarzschild), or axial symmetry (Kerr). The idea, which is surprisingly feasible, is to first construct the non-perturbative physical (reduced) Hamiltonian of the reduced phase space of fully gauge invariant observables and only then apply perturbation theory directly in terms of observables. The task to construct observables is then disentangled from perturbation theory, thus allowing to unambiguously develop perturbation theory to arbitrary orders. In this first paper of the series we outline and showcase this approach for spherical symmetry and second order in the perturbations for Einstein–Klein–Gordon–Maxwell theory. Details and generalizations to other matter and symmetry and higher orders will appear in subsequent companion papers.

Fully relativistic energies, transition properties, and lifetimes of lithium-like germanium

Abstract Employing two fully relativistic methods, the multi-reference configuration Dirac–Hartree–Fock (MCDHF) method and the relativistic many-body perturbation theory (RMBPT) method, we report energies and lifetime values for the lowest 35 energy levels of the (1s2)nl configurations (where the principal quantum number n = 2–6 and the angular quantum number l = 0, …, n–1) of lithium-like germanium (Ge XXX), as well as complete data on the transition wavelengths, radiative rates, absorption oscillator strengths, and line strengths between the levels. Both the allowed (E1) and forbidden (magnetic dipole M1, magnetic quadrupole M2, and electric quadrupole E2) ones are reported. The results from the two methods are consistent with each other and align well with previous accurate experimental and theoretical findings. We assess the overall accuracies of present RMBPT results to be likely the most precise ones to date. The present fully relativistic results should be helpful for soft x-ray laser research, spectral line identification, plasma modeling and diagnosing. The datasets presented in this paper are openly available at https://doi.org/10.57760/sciencedb.j00113.00135.

Peculiar velocities in Friedmann universes with nonzero spatial curvature

We extend the earlier linear studies of cosmological peculiar velocities to Friedmann universes with nonzero spatial curvature. In the process, we also compare our results with those obtained in cosmologies with Euclidean spatial sections. Employing relativistic cosmological perturbation theory, we first provide the differential formulas governing the evolution of peculiar velocities on all Friedmann backgrounds. The technical complexities of the curved models, however, mean that analytic solutions are possible only in special, though characteristic, moments in the lifetime of these universes. Nevertheless, our solutions exhibit persistent patterns that make us confident enough to generalize them. Thus, we confirm earlier claims that, compared to the Newtonian and the quasi-Newtonian studies, the relativistic analysis supports considerably stronger linear growth rates for peculiar-velocity perturbations. This result holds irrespective of the background curvature. Moreover, for positive curvature, the peculiar growth rate is found to be faster than that obtained in a spatially flat Friedman universe. In contrast, linear peculiar velocities appear to grow at a slower pace when their Friedmann host is spatially open. Extrapolating them to the present, our results seem to suggest faster bulk peculiar motions in overdense, rather than in underdense, regions of the Universe. Published by the American Physical Society 2024

Optimization of damping function parameters for -D3 and -D4 dispersion models for Hartree-Fock based symmetry-adapted perturbation theory.

Symmetry-adapted perturbation theory (SAPT) directly computes intermolecular interaction energy in terms of electrostatics, exchange-repulsion, induction/polarization, and London dispersion components. In SAPT based on Hartree-Fock ("SAPT0") or based on density functional theory, the most time-consuming step is the computation of the dispersion terms. Previous work has explored the replacement of these expensive dispersion terms with simple damped asymptotic models. We recently examined [Schriber et al. J. Chem. Phys. 154, 234107 (2021)] the accuracy of SAPT0 when replacing its dispersion term with Grimme's popular -D3 correction, reducing the computational cost scaling from O(N5) to O(N3). That work optimized damping function parameters for SAPT0-D3/jun-cc-pVDZ using estimates of the coupled-cluster complete basis set limit [CCSD(T)/CBS] on a 8299 dimer dataset. Here, we explore the accuracy of SAPT0-D3 with additional basis sets, along with an analogous model using -D4. Damping parameters are rather insensitive to basis sets, and the resulting SAPT0-D models are more accurate on average for total interaction energies than SAPT0. Our results are surprising in several respects: (1) improvement of -D4 over -D3 is negligible for these systems, even charged systems where -D4 should, in principle, be more accurate; (2) addition of Axilrod-Teller-Muto terms for three-body dispersion does not improve error statistics for this test set; and (3) SAPT0-D is even more accurate on average for total interaction energies than the much more computationally costly density functional theory based SAPT [SAPT(DFT)] in an aug-cc-pVDZ basis. However, SAPT0 and SAPT0-D3/D4 interaction energies benefit from significant error cancellation between exchange and dispersion terms.

First-principle study on the structural, electronic and mechanical properties of High Entropy Alloy TiZrFeRu for hydrogen storage applications

High-entropy alloys are promising for hydrogen storage, especially in terms of their tunable hydrogen storage properties. Although several experimental studies, a fundamental and detailed atomistic comprehension of physical and electronic of the hydrogenation process is still lacking. This work investigated the structural, electronic and mechanical properties of TiZrFeRu high-entropy alloys (HEAs) using first-principle calculation. Indeed, we employed both density functional theory and density functional perturbation theory in the calculations with generalized gradient approximation and plane-waves pseudo-potential formalism. In addition, we used Virtual crystal approximation (VCA) to describe HEA as is well suited for predicting elastic properties. We have calculated relevant physical parameters, including lattice constants, elastic constants, elastic modulus, Poisson's ratio, Pugh's ratio, anisotropy factors and Vickers hardness..etc. Our calculated finding show that that TiZrFeRuH2 is mechanically stable and has a good ductility with a Pugh’s ratio (B/G) greater than 1.75. Lastly, we investigated and discussed electronic bandstructure, the total and partial electronic density of state. The results indicate that this compound exhibit a metallic character concentrated in a zone between -5 and 5 eV. The value of the Poisson ration (0.35) confirm again that this compound is metallic (for metal materials the Poisson ratio is above 0.25).

Transient Dynamics in Fast–Slow Predator–Prey Model with Monod–Haldane Functional Response and Asymptotic Behaviors

This paper studies the transient dynamics in a fast–slow ecological model with a Monod–Haldane functional response. Geometric singular perturbation theory is utilized to examine the transient dynamics generated by intrinsic multiple time scales. An asymptotic series solution is derived for the normally hyperbolic sub-manifold in the slow flow. The paper proves the existence of relaxation oscillations near fold points and the existence of a smooth family of canard cycles arising from folded singularities. Furthermore, it investigates the resulting canard explosion and transient dynamics numerically. By incorporating the Monod–Haldane functional response, which represents the inhibitory effect on predation at high prey population levels, this study illustrates the occurrence of transient dynamics under this mechanism.

Time-dependent microstrata in AdS3

We use perturbation theory to construct a family of time-dependent microstrata: a set of non-extremal solutions of IIB supergravity asymptotic to AdS3 × S3 × T4. Our construction shows that the “special locus” constraints of [1] can be broken by allowing the solutions to depend on time. We study the secular terms appearing in the perturbation theory. Some of them can be resummed into frequency shifts, with the same interpretation as for the previously-studied microstrata solutions. Other secular terms appear harder to resum, questioning the long-term stability of the solutions.

Optimal Control of Underdamped Systems: An Analytic Approach

Optimal control theory deals with finding protocols to steer a system between assigned initial and final states, such that a trajectory-dependent cost function is minimized. The application of optimal control to stochastic systems is an open and challenging research frontier, with a spectrum of applications ranging from stochastic thermodynamics to biophysics and data science. Among these, the design of nanoscale electronic components motivates the study of underdamped dynamics, leading to practical and conceptual difficulties. In this work, we develop analytic techniques to determine protocols steering finite time transitions at a minimum thermodynamic cost for stochastic underdamped dynamics. As cost functions, we consider two paradigmatic thermodynamic indicators. The first is the Kullback–Leibler divergence between the probability measure of the controlled process and that of a reference process. The corresponding optimization problem is the underdamped version of the Schrödinger diffusion problem that has been widely studied in the overdamped regime. The second is the mean entropy production during the transition, corresponding to the second law of modern stochastic thermodynamics. For transitions between Gaussian states, we show that optimal protocols satisfy a Lyapunov equation, a central tool in stability analysis of dynamical systems. For transitions between states described by general Maxwell-Boltzmann distributions, we introduce an infinite-dimensional version of the Poincaré-Lindstedt multiscale perturbation theory around the overdamped limit. This technique fundamentally improves the standard multiscale expansion. Indeed, it enables the explicit computation of momentum cumulants, whose variation in time is a distinctive trait of underdamped dynamics and is directly accessible to experimental observation. Our results allow us to numerically study cost asymmetries in expansion and compression processes and make predictions for inertial corrections to optimal protocols in the Landauer erasure problem at the nanoscale.

A novel combined control of flexible single-link manipulator based on singularly perturbed theory

Purpose This study aims to improve the control accuracy and antidisturbance performance of the manipulator with the flexible link, a combined controller, which combines the novel backstepping sliding mode controller based on the extended state observer (ESO) and super-twisting sliding mode controller. Design/methodology/approach First, the dynamic of the system is constructed by Lagrange method and assumed mode method, and then the dynamic is decoupled by the singular perturbation theory to obtain the slow-varying subsystem and fast-varying subsystem. For the slow-varying subsystem, the novel backstepping sliding mode controller based on ESO is used to achieve joint tracking. For the fast-varying subsystem, the super-twisting sliding mode controller is used for vibration suppression. At the same time, to suppress chattering, the tanh function is used to replace the sign function in the reaching law. Findings The simulation results show that the combined control has better trajectory tracking performance, antiinterference performance and vibration suppression performance than traditional sliding mode control (SMC). Originality/value A novel backstepping sliding mode controller based on ESO is designed to guarantee the performance of the tracking trajectory. The new controller improves the converge rate. A super-twisting sliding mode controller, which can stabilize the fast-varying subsystem, is used to suppress the vibration of flexible link.

Two-Gap Superconductivity and the Decisive Role of Rare-Earth d Electrons in Infinite-Layer Nickelates.

We present a theoretical prediction of a phonon-mediated two-gap superconductivity in infinite-layer nickelates Nd_{1-x}Sr_{x}NiO_{2} by performing abinitio GW and GW perturbation theory calculations. Electron GW self-energy effects significantly alter the characters of the two-band Fermi surface and enhance the electron-phonon coupling, compared with results based on density functional theory. Solutions of the fully k-dependent anisotropic Eliashberg equations yield two dominant s-wave superconducting gaps-a large gap on a band of rare-earth Nd d and interstitial orbital characters and a small gap on a band of transition-metal Ni d character. Increasing hole doping induces a non-rigid-band response in the electronic structure, leading to a rapid drop of the superconducting T_{c} in the overdoped regime in agreement with experiments.

Entanglement harvesting in buckled honeycomb lattices by vacuum fluctuations in a microcavity

We study the entanglement harvesting between two identical buckled honeycomb lattices placed inside a planar microcavity. By applying time dependent perturbation theory, we obtain quantum correlations between both layers induced by the cavity field. Considering the vacuum state as the initial state of the cavity field and tracing out the time-evolved degrees of freedom, we analyze the entanglement formation using the concurrence measure. We show that the concurrence depends on the virtual photon exchanged and the positions of the layer through the interlayer photon propagator. Furthermore, we find that the formation of entanglement between equal energy electrons tends to be enhanced when they move in perpendicular directions. Our results indicate that a buckled honeycomb structure and a large spin-orbit interaction favor the entanglement harvesting.