A variant of the Brillouin-Wigner perturbation theory with Epstein-Nesbet partitioning

We present an elementary pedagogical derivation of the Brillouin-Wigner and the Rayleigh-Schr\"odinger perturbation theories with Epstein-Nesbet partitioning. A variant of the Brillouin-Wigner perturbation theory is also introduced, which can be easily extended to the quasi-degenerate case. A main advantage of the new theory is that the computing time required for obtaining the successive higher-order results is negligible after the third-order calculation. We illustrate the accuracy of the new perturbation theory for some simple model systems like the perturbed harmonic oscillator and the particle in a box.Comment: 15 page

The doubly virtual (π0,η,η′)→γ∗γ∗(\pi^0,\eta,\eta')\to\gamma^*\gamma^* transition form factors in the light-front quark model

We report our investigation on the doubly virtual TFFs $F_{{\rm P}\gamma^*}(Q^2_1,Q^2_2)$ for the ${\rm P}\to\gamma^*(q_1)\gamma^*(q_2) \;({\rm P}=\pi^0,\eta,\eta')$ transitions using the light-front quark model (LFQM). Performing a LF calculation in the exactly solvable manifestly covariant Bethe-Salpeter (BS) model as the first illustration, we used $q^+_1=0$ frame and found that both LF and manifestly covariant calculations produce exactly the same results for $F_{{\rm P}\gamma^*}(Q^2_1,Q^2_2)$. This confirms the absence of the LF zero mode in the doubly virtual TFFs. We then mapped this covariant BS model to the standard LFQM using the more phenomenologically accessible Gaussian wave function provided by the LFQM analysis of meson mass spectra. For the numerical analyses of $F_{{\rm P}\gamma^*}(Q^2_1,Q^2_2)$, we compared our LFQM results with the available experimental data and the perturbative QCD (pQCD) and the vector meson dominance (VMD) model predictions. As $(Q^2_1, Q^2_2)\to\infty$, our LFQM result for doubly virtual TFF is consistent with the pQCD prediction, i.e. $F_{{\rm P}\gamma^*}(Q^2_1, Q^2_2)\sim 1/(Q^2_1 + Q^2_2)$, while it differs far from the result of VMD model which behaves $F^{\rm VMD}_{{\rm P}\gamma^*}(Q^2_1, Q^2_2)\sim 1/(Q^2_1 Q^2_2)$. Our LFQM prediction for $F_{\eta'\gamma^*}(Q^2_1,Q^2_2)$ shows an agreement with the very recent experimental data obtained from the BaBar collaboration for the ranges of $2< Q^2_1, Q^2_1 <60$ GeV$^2$.Comment: 7 pages, 6 figures. Slight change of title, Correct some typos; version to appear in Phys. Rev.D. arXiv admin note: substantial text overlap with arXiv:1708.0073

Systematic twist expansion of (ηc,ηb)→γ∗γ(\eta_c,\eta_b)\to\gamma^*\gamma transition form factors in light-front quark model

The light-front quark model analysis of the meson-photon transition form factor $F_{P\gamma} (Q^2)$ amenable both for the spacelike region ($Q^2 >0$) and the timelike region ($Q^2 <0$) provides a systematic twist expansion of $Q^2 F_{P\gamma} (Q^2)$ for the high $|Q^2|$ region. Investigating $F_{P\gamma} (Q^2) (P = \eta_c,\eta_b)$ for the entire kinematic regions of $Q^2$, we examine the twist-2 and twist-3 distribution amplitudes of $(\eta_c,\eta_b)$ mesons in the light-front quark model and quantify their contributions to $Q^2 F_{(\eta_c,\eta_b)\gamma}(Q^2)$. Our numerical results for the normalized transition form factor $F_{(\eta_c,\eta_b)\gamma}(Q^2)/F_{(\eta_c,\eta_b)\gamma}(0)$ and the decay width $\Gamma_{(\eta_c,\eta_b)\to\gamma\gamma}$ are compared with the available data checking the sensitivity of our model to the variation of the constituent quark masses.Comment: 9 pages, 6 figures, Version to appear in Phys.Rev. D. arXiv admin note: text overlap with arXiv:1708.0073

Spacelike and timelike form factors for the (π0,η,η′)→γ∗γ(\pi^0,\eta,\eta')\to\gamma^*\gamma transitions in the light-front quark model

We investigate the $(\pi^0,\eta,\eta')\to\gamma^*\gamma$ transitions both for the spacelike region and the timelike region using the light-front quark model (LFQM). In particular, we present the new direct method to explore the timelike region without resorting to mere analytic continuation from the spacelike region to the timelike region. Our direct calculation in timelike region shows the complete agreement not only with the analytic continuation result from the spacelike region but also with the result from the dispersion relation between the real and imaginary parts of the form factor. For the low energy regime, we compare our LFQM results of the transition form factors (TFFs) for the low timelike momentum transfer region and the slope parameters at $q^2=0$ with the recent experimental data from the Dalitz decays of $(\pi^0,\eta,\eta')$. For the high energy regime, we incorporate the QCD factorization in our LFQM to examine the asymptotic behavior of TFFs both for the spacelike region and the timelike region. We compare our results with the available experimental data.Comment: 13 pages, 7 figures, changed the title and corrected typ

Variational Analysis of Mass Spectra and Decay Constants for Ground State Pseudoscalar and Vector Mesons in Light-Front Quark Model

Using the variational principle, we compute mass spectra and decay constants of ground state pseudoscalar and vector mesons in the light-front quark model (LFQM) with the QCD-motivated effective Hamiltonian including the hyperfine interaction. By smearing out the Dirac delta function in the hyperfine interaction, we avoid the issue of negative infinity in applying the variational principle to the computation of meson mass spectra and provide analytic expressions for the meson mass spectra. Our analysis with the smeared hyperfine interaction indicates that the interaction for the heavy meson sector including the bottom and charm quarks gets more point-like. We also consider the flavor mixing effect in our analysis and determine the mixing angles from the mass spectra of $(\omega,\phi)$ and $(\eta,\eta')$. Our variational analysis with the trial wave function including the two lowest order harmonic oscillator basis functions appears to improve the agreement with the data of meson decay constants and the heavy meson mass spectra over the previous computation handling the hyperfine interaction as perturbation.Comment: 5 figures. Added the flavor mixing effect in our analysis and determine the mixing angles from the mass spectra of (\omega,\phi) and (\eta,\eta'). Improved the fitting for the hyperfine splitting in heavy mesons. arXiv admin note: text overlap with arXiv:1206.335

Consistent Community Identification in Complex Networks

We have found that known community identification algorithms produce inconsistent communities when the node ordering changes at input. We propose two metrics to quantify the level of consistency across multiple runs of an algorithm: pairwise membership probability and consistency. Based on these two metrics, we address the consistency problem without compromising the modularity. Our solution uses pairwise membership probabilities as link weights and generates consistent communities within six or fewer cycles. It offers a new tool in the study of community structures and their evolutions.Comment: 4 pages, 4 figure

General Geometric Fluctuation Modeling for Device Variability Analysis

The authors propose a new modeling approach based on the impedance field method (IFM) to analyze the general geometric variations in device simulations. Compared with the direct modeling of multiple variational devices, the proposed geometric variation (GV) model shows a better efficiency thanks to its IFM based nature. Compared with the existing random geometric fluctuation (RGF) model where the noise sources are limited to the interfaces, the present GV model provides better accuracy and wider application areas as it transforms the geometric variation into global mesh deformation and computes the noise sources induced by the geometric variation in the whole simulation domain. GV model also provides great insights into the device by providing the effective noise sources, equation-wise contributions, and sensitivity maps that are useful for device characterization and optimization

Hybridized/Coupled Multiple Resonances in Nacre

We report that nacre (also known as mother-of-pearl), a wondrous nanocomposite found in nature, is a rich photonic nanomaterial allowing the experimental realization of collective excitation and light amplification via coupled states. Localized modes in three-dimensional complex media are typically isolated in frequency and space. However, multiple local resonances can be hybridized in multilayered nanostructures of nacre so that the effective cavity size for efficient disordered resonators is scaled up. Localized modes in hybridized states in nacre are overlapped in frequency with similar shapes in space, thus being collectively excited and synergistically amplified. These hybridized states boost light amplification, leading to stable and regular multimode lasing at low excitation energy. The simplicity of ameliorating disordered resonators by mimicking nacre can further serve as platforms for developing cost-effective photonic systems and provide materials for fundamental research on complex mediaComment: 7 pages and 6 figure

Interference effect on Raman spectrum of graphene on SiO_2/Si

The intensity ratio between two major Raman bands in graphene is one of the most important information for physics of graphene and has been believed to represent various intrinsic properties of graphene without critical assessment of extrinsic effects. We report a micro Raman spectroscopy study on the Raman intensity ratio of the 2D band to the G Raman band of graphene varying the thickness of dielectric layers (SiO_2) underneath it. The ratio is shown to change by almost 370% when the thickness is varied by 60%. The large variation in the ratio is well explained by theoretical calculations considering multiple Raman scattering events at the interfaces. Our analysis shows that the interference effect is critical in extracting the intrinsic 2D to G intensity ratio and therefore must be taken into account in extracting various physical properties of graphene from Raman measurements.Comment: 21 pages, 5 figures. Phys. Rev. B; in pres

Large Language Models can Share Images, Too!

This paper explores the image-sharing capability of Large Language Models (LLMs), such as InstructGPT, ChatGPT, and GPT-4, in a zero-shot setting, without the help of visual foundation models. Inspired by the two-stage process of image-sharing in human dialogues, we propose a two-stage framework that allows LLMs to predict potential image-sharing turns and generate related image descriptions using our effective restriction-based prompt template. With extensive experiments, we unlock the \textit{image-sharing} capability of LLMs in zero-shot prompting, with GPT-4 achieving the best performance. Additionally, we uncover the emergent \textit{image-sharing} ability in zero-shot prompting, demonstrating the effectiveness of restriction-based prompts in both stages of our framework. Based on this framework, we augment the PhotoChat dataset with images generated by Stable Diffusion at predicted turns, namely PhotoChat++. To our knowledge, this is the first study to assess the image-sharing ability of LLMs in a zero-shot setting without visual foundation models. The source code and the dataset will be released after publication