Small Coupling Constant Research Articles

Synthesis and Conformational Analysis of α,β‐Dichlorocarbonyl Compounds

α,β‐Dichlorocarbonyl compounds were synthesized by facile dichlorination of α,β‐unsaturated amides with TCIA‐PPh3 and the resultant amides were converted to ketones. Conformational analyses of the products were performed to confirm our previous hypothesis regarding vicinal dichlorinated carbonyl compounds. The compounds exhibited 1H NMR signals with large coupling constants (7‐11 Hz) for the 1,2‐anti‐configuration and small coupling constants (3‐4 Hz) for the 1,2‐syn‐configuration. The syn‐pentane interaction enabled rational conformational analysis of the α,β‐dichlorinated carbonyl compounds, although some interesting exceptions were observed. Consideration of these conformations is helpful in assigning relative configurations of α,β‐dihalogenated carbonyl compounds in general.

Investigations on the Carrier Mobility of Cs2NaFeCl6 Double Perovskites

Double perovskite materials have gradually become widely studied due to their potential applications in solar cells and other optoelectronic devices. We take Cs2NaFeCl6 as an example to investigate the carrier mobility with respect to the acoustic phonon and the optical phonon scattering mechanisms. By considering the deformation potential, carrier effective mass, and bulk modulus, the longitudinal acoustic (LA) phonon-determined mobilities for electrons and holes in Cs2NaFeCl6 are found to be μe = 2886.08 cm2 v−1 s−1 and μh = 39.09 cm2 v−1 s−1, respectively. The optical scattering mechanism involves calculating the Fröhlich coupling constant, dielectric constant, and polaron mass to determine the multiple polar optical (PO) phonon-scattering-determined mobilities, resulting in μe = 279.25 cm2 v−1 s−1 and μh = 21.29 cm2 v−1 s−1, respectively. By combining both interactions, the total electron mobility and hole mobility are determined to be 254.61 cm2 v−1 s−1 and 13.78 cm2 v−1 s−1, respectively. The findings suggest that the polarization of both electrons and ions, small coupling constant, and bulk modulus in Cs2NaFeCl6’s lattice make PO scattering a significant contribution to carrier mobility in this specific double perovskite, highlighting the importance of considering this in enhancing the optoelectronic properties of Cs2NaFeCl6 and other double perovskites.

Thermal curvature perturbations in thermal inflation

We compute the power spectrum of super-horizon curvature perturbations generated during a late period of thermal inflation, taking into account fluctuation-dissipation effects resulting from the scalar flaton field's interactions with the ambient radiation bath. We find that, at the onset of thermal inflation, the flaton field may reach an equilibrium with the radiation bath even for relatively small coupling constants, maintaining a spectrum of thermal fluctuations until the critical temperature T c, below which thermal effects stop holding the field at the false potential minimum. This enhances the field variance compared to purely quantum fluctuations, therefore increasing the average energy density during thermal inflation and damping the induced curvature perturbations. In particular, we find that this inhibits the later formation of primordial black holes, at least on scales that leave the horizon for T > T c. The larger thermal field variance also reduces the duration of a period of fast-roll inflation below T c, as the field rolls to the true potential minimum, which should also affect the generation of (large) curvature perturbations on even smaller scales.

A model of pseudo-Nambu-Goldstone dark matter with two complex scalars

Pseudo-Nambu-Goldstone (pNG) dark matter (DM) is a promising DM candidate and able to explain the measured DM abundance by the thermal freeze-out mechanism evading the stringent bound from DM direct detection experiments. We propose a new model providing a pNG DM by introducing two Standard-Model-singlet complex scalars with the same charges of a dark U(1) gauge symmetry. They are also charged under a U(1) global symmetry corresponding to their relative phase rotations, which is explicitly broken by a soft-breaking term in the scalar potential. The both U(1) symmetries are spontaneously broken by their vacuum expectation values, giving rise to one real pNG boson. We also introduce a discrete ℤ2 symmetry exchanging the two scalars to stabilize the pNG boson as DM. It is shown that this model reproduces the DM abundance consistently with the current bound from the direct detection experiments. The model has a gauge kinetic mixing between the dark and U(1)Y gauge fields, which allows the dark gauge boson to decay even with a relatively light mass and prevents it from being an additional DM component. The Landau pole is avoided thanks to the small gauge coupling constant. In addition, a DM pair dominantly annihilates into a pair of the dark gauge bosons if the gauge boson mass is lighter than the DM mass, and thus its cross section has significantly different parameter dependence from other pNG DM models. We also calculate the DM-nucleon scattering cross section at the loop level. It turns out that it is necessary to probe region covered by the neutrino fog in order to test this model.

Improved uniform error bounds of an exponential wave integrator method for the Klein–Gordon–Schrödinger equation with the small coupling constant

Improved uniform error bounds of an exponential wave integrator method for the Klein–Gordon–Schrödinger equation with the small coupling constant

Improved error estimates of the time‐splitting methods for the long‐time dynamics of the Klein–Gordon–Dirac system with the small coupling constant

AbstractWe provide improved uniform error estimates for the time‐splitting Fourier pseudo‐spectral (TSFP) methods applied to the Klein–Gordon–Dirac system (KGDS) with the small parameter . We first reformulate the KGDS into a coupled Schrödinger–Dirac system (CSDS) and then apply the second‐order Strang splitting method to CSDS with the spatial discretization provided by Fourier pseudo‐spectral method. Based on rigorous analysis, we establish improved uniform error bounds for the second‐order Strang splitting method at up to the long time at . In addition to the conventional analysis methods, we mainly apply the regularity compensation oscillation technique for the analysis of long time dynamic simulation. The numerical results show that our method and conclusion are not only suitable for one‐dimensional problem, but also can be directly extended to higher dimensional problem and highly oscillatory problem. As far as we know there has not been any relevant long time analysis and any improved uniform error bounds for the TSFP method solving the KGDS. Our methods are novel and provides a reference for analyzing the improved error bounds of other coupled systems similar to the KGDS.

On Schrödinger operators modified by [formula omitted] interactions

We study the spectral properties of a Schrödinger operator H0 modified by δ interactions and show explicitly how the poles of the new Green’s function are rearranged relative to the poles of original Green’s function of H0. We prove that the new bound state energies are interlaced between the old ones, and the ground state energy is always lowered if the δ interaction is attractive. We also derive an alternative perturbative method of finding the bound state energies and wave functions under the assumption of a small coupling constant in a somewhat heuristic manner. We further show that these results can be extended to cases in which a renormalization process is required. We consider the possible extensions of our results to the multi center case, to δ interaction supported on curves, and to the case, where the particle is moving in a compact two-dimensional manifold under the influence of δ interaction. Finally, the semi-relativistic extension of the last problem has been studied explicitly.

Blandford–Znajek process in Einsteinian cubic gravity

In this paper, we investigate the Blandford–Znajek (BZ) process within the framework of Einsteinian cubic gravity (ECG). To analytically study the BZ process using the split monopole configuration, we construct a slowly rotating black hole in ECG up to cubic order in small spin, considering the leading order in small coupling constant of higher curvature terms. By deriving the magnetosphere solution around the black hole, we determine the BZ power up to the second relative order in spin. The BZ power is modified by the coupling constant compared to Kerr black hole case. Although the general nature of the BZ process in ECG remains unchanged at the leading order in spin, the coupling constant introduces modification at the second relative order in spin. Therefore, we anticipate that it is feasible to discern general relativity from higher derivative gravities by examining the BZ power in rapidly rotating black holes.

Looking at QED with Dyson–Schwinger Equations: Basic Equations, Ward–Takahashi Identities and the Two-Photon-Two-Fermion Irreducible Vertex

A minimal truncated set of the integral Dyson–Schwinger equations, in Minkowski spacetime, that allows to explore QED beyond its perturbative solution is derived for general linear covariant gauges. The minimal set includes the equations for the fermion and photon propagators, the photon-fermion vertex, and the two-photon-two-fermion one-particle-irreducible diagram. If the first three equations are exact, to build a closed set of equations, the two-photon-two-fermion equation is truncated ignoring the contribution of Green functions with large number of external legs. It is shown that the truncated equation for the two-photon-two-fermion vertex reproduces the lowest-order perturbative result in the limit of the small coupling constant. Furthermore, this equation allows to define an iterative procedure to compute higher order corrections in the coupling constant. The Ward–Takahashi identity for the two-photon-two-fermion irreducible vertex is derived and solved in the soft photon limit, where one of the photon momenta vanish, in the low photon momenta limit and for general kinematics. The solution of the Ward–Takahashi identity determines the longitudinal component of the two-photon-two-fermion irreducible vertex, while it is proposed to use the Dyson–Schwinger equation to determine the transverse part of this irreducible diagram. The two-photon-two-fermion DSE is solved in heavy fermion limit, considering a simplified version of the QED vertices. The contribution of this irreducible vertex to a low-energy effective photon-fermion vertex is discussed and the fermionic operators that are generated are computed in terms of the fermion propagator functions.

Active Site Descriptors from 95Mo NMR Signatures of Silica-Supported Mo-Based Olefin Metathesis Catalysts.

The olefin metathesis activity of silica-supported molybdenum oxides depends strongly on metal loading and preparation conditions, indicating that the nature and/or amounts of the active sites vary across compositionally similar catalysts. This is illustrated by comparing Mo-based (pre)catalysts prepared by impregnation (2.5-15.6 wt % Mo) and a model material (2.3 wt % Mo) synthesized via surface organometallic chemistry (SOMC). Analyses of FTIR, UV-vis, and Mo K-edge X-ray absorption spectra show that these (pre)catalysts are composed predominantly of similar isolated Mo dioxo sites. However, they exhibit different reaction properties in both liquid and gas-phase olefin metathesis with the SOMC-derived catalyst outperforming a classical catalyst of a similar Mo loading by ×1.5-2.0. Notably, solid-state 95Mo NMR analyses leveraging state-of-the-art high-field (28.2 T) measurement conditions resolve four distinct surface Mo dioxo sites with distributions that depend on the (pre)catalyst preparation methods. The intensity of a specific deshielded 95Mo NMR signal, which is most prominent in the SOMC-derived catalyst, is linked to reducibility and catalytic activity. First-principles calculations show that 95Mo NMR parameters directly manifest the local strain and coordination environment: acute (SiO-Mo(O)2-OSi) angles and low coordination numbers at Mo lead to highly deshielded 95Mo chemical shifts and small quadrupolar coupling constants, respectively. Natural chemical shift analyses relate the 95Mo NMR signature of strained species to low LUMO energies, which is consistent with their high reducibility and corresponding reactivity. The 95Mo chemical shifts of supported Mo dioxo sites are thus linked to their specific electronic structures, providing a powerful descriptor for their propensity toward reduction and formation of active sites.

Improved uniform error bounds of a time-splitting Fourier pseudo-spectral scheme for the Klein–Gordon–Schrödinger equation with the small coupling constant

Recently, the long time numerical simulation of PDEs with weak nonlinearity (or small potentials) becomes an interesting topic. In this paper, for the Klein–Gordon–Schrödinger equation (KGSE) with a small coupling constant ɛ∈(0,1], we proposed a time-splitting Fourier pseudo-spectral (TSFP) scheme by reformulating the KGSE into a coupled nonlinear Schrödinger system (CNLSS). Through rigorous error analysis, we establish improved error bounds for the scheme at O(hm+ɛτ2) up to the long time at O(1/ɛ) where h is the mesh size and τ is the time step, respectively, and m depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGSE with the small coupling constant. The tools for error analysis mainly include the mathematical induction and the standard energy method as well as the regularity compensation oscillation (RCO) technique which has been developed recently. The numerical experiments support our theoretical analysis. Our scheme is novel because that to the best of our knowledge there has not been any TSFP scheme and any relevant long time analysis for the KGSE.

Comparison of methods for 14N-1H recoupling in 14N-1H HMQC MAS NMR

1H-detected 14N heteronuclear multiple-quantum coherence (HMQC) magic-angle-spinning (MAS) NMR experiments performed at fast magic-angle spinning (≥50 kHz) are finding increasing application, e.g., to pharmaceuticals. Of importance to the efficacy of these techniques is the recoupling technique applied to reintroduce the 1H-14N dipolar coupling. In this paper, we compare, by experiment and 2-spin density matrix simulations, two classes of recoupling scheme: first, those based on n = 2 rotary resonance, namely R3 and spin-polarisation inversion SPI-R3, and the symmetry based SR412 method and, second, the TRAPDOR method. Both classes require optimisation depending on the magnitude of the quadrupolar interaction, and thus there is a compromise choice for samples with more than one nitrogen site, as is the case for the studied dipeptide β-AspAla that contains two nitrogen sites with a small and large quadrupolar coupling constant. Considering this, we observe better sensitivity for the TRAPDOR method, though noting the marked sensitivity of TRAPDOR to the 14N transmitter offset, with both SPI-R3 and SR412 giving similar recoupling performance.

Structure‐preserving exponential wave integrator methods and the long‐time convergence analysis for the Klein‐Gordon‐Dirac equation with the small coupling constant

AbstractRecently, the numerical methods for long‐time dynamics of PDEs with weak nonlinearity (or small potentials) have received more and more attention. For the Klein‐Gordon‐Dirac (KGD) equation with the small coupling constant , we propose two time symmetric and structure‐preserving exponential wave integrator Fourier pseudo‐spectral (TSSPEWIFP) methods under periodic boundary conditions. The new methods are proved to preserve the energy in discrete level and in addition the first one preserves the modified discrete mass. Through rigorous error analysis, we establish uniform error bounds of the numerical solutions at up to the time at for where and are the mesh size and time step, respectively, and depends on the regularity conditions. Compared with the results of existing numerical analysis, our analysis has the advantage of showing the long time numerical errors for the KGD equation with the small coupling constant. The tools for error analysis mainly include cut‐off technique and the standard energy method. We also extend the results on error bounds, structure‐preservation and time symmetry to the oscillatory KGD equation with wavelength at in time which is equivalent to the KGD equation with small coupling constant. Numerical experiments confirm that the theoretical results are correct. Our methods are novel because that to the best of our knowledge there has not been any energy‐preserving exponential wave integrator method and any relevant long time analysis for the KGD equation.

On the Problem of Bound States of Electron and Hole in Transition Metal Dichalcogenides

The interacting electron and hole in transition metal dichalcogenides are considered. To investigate the interaction the Bethe-Salpeter equation was obtained in the leading order in the interaction potential. It is shown that the behavior of the potential at short distances significantly affects the binding energy of the electron and the hole. We demonstrate that the expansion of the Bethe-Salpeter equation in the small coupling constant does not contain singular operators. Therefore, the binding energy of the electron and the hole does not contain the regularization parameter. Using the perturbation theory in the coupling constant we analytically calculated the energies of the ground and first excited states of the exiton. For arbitrary values of the coupling constant, the energies of the bound states of the electron and the hole are obtained numerically. The critical values of the coupling constant for the Coulomb potential and for the exponentially decreasing potential are also found numerically.

Proposal for the search for exotic spin-spin interactions at the micrometer scale using functionalized cantilever force sensors

Spin-dependent exotic interactions can be generated by exchanging hypothetical bosons, which were introduced to solve some puzzles in physics. Many precision experiments have been performed to search for such interactions, but no confirmed observations have been made. We propose new experiments to search for the exotic spin-spin interactions that can be mediated by axions or ${\mathrm{Z}}^{\ensuremath{'}}$ bosons. A sensitive functionalized cantilever is utilized as a force sensor to measure the interactions between the spin-polarized electrons in a periodic magnetic source structure and a closed-loop magnetic structure integrated on the cantilever. The source is set to oscillate during data acquisition to modulate the exotic force signal to high harmonics of the oscillating frequency. This helps to suppress the spurious signals at the signal frequency. Different magnetic source structures are designed for different interaction detections. A magnetic stripe structure is designed for ${\mathrm{Z}}^{\ensuremath{'}}$-mediated interactions, which are insensitive to the detection of axion-mediated interactions. This allows us to measure the coupling constant of both if we assume that both exist. With the force sensitivity achievable at low temperatures, the proposed experiments are expected to search for parameter spaces with much smaller coupling constants than the current stringent constraints from micrometer to millimeter range. Specifically, the lower bound of the parameter space will be 7 orders of magnitude lower than the stringent constraints for ${\mathrm{Z}}^{\ensuremath{'}}$-mediated interactions, and an order of magnitude lower for axion-mediated interactions, at the interaction range of $10\text{ }\text{ }\mathrm{\ensuremath{\mu}}\mathrm{m}$.

Forecast analysis on interacting dark energy models from future generation PICO and DESI missions

ABSTRACT The next-generation cosmic microwave background (CMB) satellite missions are expected to provide robust constraints on a wide range of cosmological parameters with unprecedented precision. But these constraints on the parameters could weaken if we do not attribute dark energy to a cosmological constant. The cosmological models involving interaction between dark energy and dark matter can give rise to comparable energy densities at the present epoch, thereby alleviating the so-called cosmic coincidence problem. In the present paper, we perform a forecast analysis to test the ability of the future generation high-sensitive CMB, and baryon acoustic oscillation (BAO) experiments to constrain phenomenological interacting dark energy models. We consider cosmic variance limited future CMB experiment Probe of Inflation and Cosmic Origins (PICO) along with BAO information from the Dark Energy Spectroscopic Instrument (DESI), to constrain the parameters of the interacting dark sector. Based on the stability of the cosmological perturbations, we consider two possibilities for the interaction scenario. We investigate the impact of both coupling constant and equation of state parameter of dark energy on CMB temperature power spectrum, matter power spectrum, and fσ8. We have used simulated temperature and polarization data from PICO within the multipole ranges (ℓ = 2–4000), and as expected, we do see PICO alone produces better constraints than Planck on the ΛCDM parameters. With the integration of PICO and DESI missions, we observe a significant improvement in the constraints on several cosmological parameters, especially the equation of state parameter of dark energy. However, we note that additional data are required to constrain a small positive coupling constant.

D-term inflation in braneworld models: Consistency with cosmic-string bounds and early-time Hubble tension resolving models

We revisit D-term inflation with the bounds of the cosmic string tension from gravitational wave observations and consider the possible deviation of the spectral index compared with the $\Lambda$CDM model in light of prerecombination resolutions of the Hubble tension. D-term inflation requires very small coupling constants under these constraints. We show that natural coupling constants ($g=\lambda=0.1$) can be achieved in the case of D-term inflation on the brane.

Gravitational production of dark photon dark matter with mass generated by the Higgs mechanism

We study the gravitational production of dark photon dark matter during inflation, when dark photons acquire mass by the Higgs mechanism. In the previous study, it was assumed that the dark photon has a Stückelberg mass, or a mass generated by the Higgs mechanism with a sufficiently heavy Higgs boson. In this paper we consider a case in which the Higgs boson is not fully decoupled; the Higgs field changes its vacuum expectation value after inflation. Then, the dark photon mass also changes with time after inflation, and the time evolution of the longitudinal mode is different from the case with a Stückelberg mass. Consequently, the spectrum of the dark photon energy density can have two peaks at an intermediate scale and a small scale. We show that the dark photon can explain the dark matter if its current mass is larger than 6 μeV × (HI /1014 GeV)-4 and smaller than 0.8 GeV × (HI /1014 GeV)-3/2, with HI being the Hubble parameter during inflation. A higher mass is required if one considers a larger gauge coupling constant. The result for the Stückelberg mass can be reproduced in the limit of a small gauge coupling constant. We also comment on the constraints set by various conjectures in quantum gravity theory.

Magnetic and electric black holes in the vector-tensor Horndeski theory

We construct exact solutions of magnetically charged black holes in the vector-tensor Horndeski gravity and discuss their main features. Unlike the analogous electric case, the field equations are linear in a simple (quite standard) parametrization of the metric tensor, and they can be solved analytically even when a cosmological constant is added. The solutions are presented in terms of hypergeometric functions, which makes the analysis of the black hole properties relatively straightforward. Some of the aspects of these black holes are quite ordinary, like the existence of extremal configurations with maximal magnetic charge for a given mass or the existence of a mass with maximal temperature for a given charge, but others are somewhat unexpected, like the existence of black holes with a repulsive gravitational field. We perform our analysis for both signs of the nonminimal coupling constant and find black hole solutions in both cases but with significant differences between them. The most prominent difference is the fact that the black holes for the negative coupling constant have a spherical surface of curvature singularity rather than a single point. On the other hand, the gravitational field produced around this kind of black holes is always attractive. Also, for small enough magnetic charge and negative coupling constant, extremal black holes do not exist, and all magnetic black holes have a single horizon. In addition, we study the trajectories around these magnetic black holes for light as well as massive particles either neutral or electrically charged. Finally, we compare the main features of these black holes with their electric counterparts, adding some aspects that have not been discussed before, like temperature, particle trajectories, and light deflection by electrically charged Horndesky black holes.

Large N Limit of the O(N) Linear Sigma Model in 3D

In this paper we study the large N limit of the O(N)-invariant linear sigma model, which is a vector-valued generalization of the $$\Phi ^4$$ quantum field theory, on the three dimensional torus. We study the problem via its stochastic quantization, which yields a coupled system of N interacting SPDEs. We prove tightness of the invariant measures in the large N limit. For large enough mass or small enough coupling constant, they converge to the (massive) Gaussian free field at a rate of order $$1/\sqrt{N}$$ with respect to the Wasserstein distance. We also obtain tightness results for certain O(N) invariant observables. These generalize some of the results in Shen et al. (Ann Probab 50(1):131–202, 2022) from two dimensions to three dimensions. The proof leverages the method recently developed by Gubinelli and Hofmanová (Commun Math Phys 384(1):1–75, 2021) and combines many new techniques such as uniform in N estimates on perturbative objects as well as the solutions.