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The formalism developed in Refs.\cite{Guo:2023ecc,Guo:2024zal} that connects integrated correlation function of a trapped two-particle system to infinite volume scattering phase shift is further extended to coupled-channel systems in the present work. Using a trapped non-relativistic two-channel system as an example, a new relation is derived that retains the same structure as in the single channel, and has explicit dependence on the phase shifts in both channels but not on the inelasticity. The relation is illustrated by an exactly solvable coupled-channel quantum mechanical model with contact interactions. It is further validated by path integral Monte Carlo simulation of a quasi-one-dimensional model that can admit general interaction potentials. In all cases, we found rapid convergence to the infinite volume limit as the trap size is increased, even at short times, making it potentially a good candidate to overcome signal-to-noise issues in Monte Carlo applications.

We report a proof-of-principle lattice QCD simulation of the electric and magnetic polarizabilities for a neutral pion in the four-point function method. The results are based on the same quenched Wilson ensembles on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV previously used for a charged pion. For electric polarizability, the results are largely consistent with those from the background field method and ChPT. In contrast, there are significant differences for magnetic polarizability among the four-point function method, the background field method, and ChPT. The situation points to the potentially important role of disconnected diagrams for a neutral pion. We elucidate a transparent quark decomposition in the four-point function method that can be used to shed light on the issue., Comment: 11 pages, 9 figures, 1 table. This version matches the one published in NPB in content. arXiv admin note: text overlap with arXiv:2307.08620

Electromagnetic dipole polarizabilities are fundamental properties of a hadron that represent its resistance to deformation under external fields. For a charged hadron, the presence of acceleration and Landau levels complicates the isolation of its deformation energy in the conventional background field method. In this work, we explore a general method based on four-point functions in lattice QCD that takes into account all photon, quark and gluon interactions. The electric polarizability ($\alpha_E$) has been determined from the method in a previous proof-of-principle simulation. Here we focus on the magnetic polarizability ($\beta_M$) using the same quenched Wilson action on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV. The results from the connected diagrams show a large cancellation between the elastic and inelastic contributions, leading to a relatively small and negative value for $\beta_M$ consistent with chiral perturbation theory. We also discuss the mechanism for $\alpha_E+\beta_M$ from combining the two studies., Comment: 11 pages, 8 figures, 1 table. Version accepted for publication in PRD. arXiv admin note: substantial text overlap with arXiv:2301.05200

We present a novel method for solving the linearized Vlasov--Poisson equation, based on analyticity properties of the equilibrium and initial condition through Cauchy-type integrals, that produces algebraic expressions for the distribution and field, i.e., the solution is expressed without integrals. Standard extant approaches involve deformations of the Bromwich contour that give erroneous results for certain physically reasonable configurations or eigenfunction expansions that are misleading as to the temporal structure of the solution. Our method is more transparent, lacks these defects, and predicts previously unrecognized behavior., Comment: Accepted for publication as a letter at PRE

Polarizabilities reveal valuable information on the internal structure of hadrons in terms of charge and current distributions. For neutral hadrons, the standard approach is the background field method. But for a charged hadron, its acceleration under the applied field complicates the isolation of the polarization energy. In this work, we explore an alternative method based on four-point functions in lattice QCD. The approach offers a transparent picture on how polarizabilities arise from photon, quark, and gluon interactions. We carry out a proof-of-concept simulation on the electric polarizability of a charged pion, using quenched Wilson action on a $24^3\times 48$ lattice at $\beta=6.0$ with pion mass from 1100 to 370 MeV. We show in detail the evaluation and analysis of the four-point correlation functions and report results on charge radius and electric polarizability. Our results from connected diagrams suggest that charged pion $\alpha_E$ is due to a cancellation between elastic and inelastic contributions. It would be interesting to see how the cancellation plays out at smaller pion masses in future simulations., Comment: 24 pages, 13 figures, 2 tables. Version accepted for publication in PRD

Two-dimensional van der Waals (2D-vdW) layered hexagonal boron nitride (h-BN) has gained tremendous research interest over recent years due to its unconventional domain growth morphology, fascinating properties and application potentials as an excellent dielectric layer for 2D-based nano-electronics. However, the unidirectional domain growth of h-BN thin films directly on insulating substrates remains significantly challenging because of high-bonding anisotropicity and complex growth kinetics than the conventional thin films growth, thus resulting in the formation of randomly oriented domains morphology, and hindering its usefulness in integrated nano-devices. Here, ultra-wide bandgap h-BN thin films are grown directly on low-miscut atomically smooth highly insulating c-plane sapphire substrates (without using any metal catalytic layer) by pulsed laser deposition, showing remarkable unidirectional triangular-shape domains morphology. This unidirectional domain growth is attributed to the step-edge guided nucleation caused by reducing the film-substrate interfacial symmetry and energy, thereby breaking the degeneracy of nucleation sites of random domains, as revealed by the density functional theory (DFT) calculations. Through extensive characterizations, we further demonstrate the excellent single crystal-like functional properties of films. Our findings might pave the way for feasible large-area direct growth of electronic-quality h-BN thin films on insulating substrates for high-performance 2D-electronics, and in addition would be beneficial for hetero engineering of 2D-vdW materials with emergent phenomena., Comment: 39 pages, 7 figures, Revised accepted version of the article

Room temperature growth of two-dimensional van der Waals (2D-vdW) materials is indispensable for state-of-the-art nanotechnology. The low temperature growth supersedes the requirement of elevated growth temperature accompanied with high thermal budgets. Moreover, for electronic applications, low or room temperature growth reduces the possibility of intrinsic film-substrate interfacial thermal diffusion related deterioration of functional properties and consequent device performance. Here, we demonstrated the growth of ultrawide-bandgap boron nitride (BN) at room temperature by using the pulsed laser deposition (PLD) process and demonstrated various functionalities for potential applications. Comprehensive chemical, spectroscopic and microscopic characterization confirms the growth of ordered nanosheet-like hexagonal BN. Functionally, nanosheets show hydrophobicity, high lubricity (low coefficient of friction), low refractive index within the visible to near-infrared wavelength range, and room temperature single-photon quantum emission. Our work unveils an important step that brings a plethora of applications potential for room temperature grown h-BN nanosheets as it can be feasible on any given substrate, thus creating a scenario for h-BN on demand at frugal thermal budget., Comment: 27 pages, 4 figures, Authors version of the article

Masses, widths, and branching ratios of hadronic resonances are quantified by their pole positions and residues with respect to transition amplitudes on the Riemann sheets of the complex energy-plane. In this study we discuss the analytic structure in the physical energy region of three-body scattering amplitudes on such manifolds. As an application, we determine the pole position of the $a_1(1260)$ meson from the ALEPH experiment by allowing for $\pi\rho$ coupled channels in S- and D-wave. We find it to be $\sqrt{s_0}=(1232^{+15+9}_{-0-11}-i266^{+0+15}_{-22-27})~\text{MeV}$., Comment: 17 pages, 13 figures

Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed L\"uscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we derive higher-order quantization conditions and introduce a method to transparently cross-check our results. This is an important step given the involved derivations of these formulae. We derive quantization conditions up to $\ell=5$ partial waves in both cubic and elongated geometries, and for states with zero and non-zero total momentum. All 45 quantization conditions we include here (22 in cubic box, 23 in elongated box) pass our cross-check test., Comment: 10 pages, 3 figures, 1 table, presented at The 38th International Symposium on Lattice Field Theory, LATTICE2021 26th-30th July, 2021 Zoom/Gather@Massachusetts Institute of Technology

We show how to compute electromagnetic polarizabilities of charged hadrons without the use of background fields in lattice QCD. The low-energy behavior of the Compton scattering amplitude is matched to matrix elements of current-current correlation functions on the lattice. Working in momentum space, formulas for electric polarizability ($\alpha_E$) and magnetic polarizability ($\beta_M$) are derived for both charged pion and proton. Lattice four-point correlation functions are constructed from quark and gluon fields to be used in Monte-Carlo simulations. We also draw attention to the potential of four-point functions as a multi-purpose tool for hadron structure., Comment: 9 pages, 1 figure, presented at the 38th International Symposium on Lattice Field Theory, LATTICE2021, July 36-30, 2021 Zoom/Gather@Massachusetts Institute of Technology

Lattice QCD calculations of scattering phaseshifts and resonance parameters in the two-body sector are becoming precision studies. Early calculations employed L\"uscher's formula for extracting these quantities at lowest order. As the calculations become more ambitious, higher-order relations are required. In this study we present a way to validate the higher-order quantization conditions. This is an important step given the involved derivations of these formulae. We derive and validate quantization conditions up to $\ell=5$ partial waves in both cubic and elongated geometries, and for states zero and non-zero total momentum. For all 45 quantization conditions we considered (22 in cubic box, 23 in elongated box) we find perfect agreement., Comment: 55 pages, 9 figures, 45 tables, 1 supplement. This update matches the published version in PRD

Resonant hadronic systems often exhibit a complicated decay pattern in which three-body dynamics play a relevant or even dominant role. In this work we focus on the $a_1(1260)$ resonance. For the first time, the pole position and branching ratios of a three-body resonance are calculated from lattice QCD using one-, two-, and three-meson interpolators and a three-body finite-volume formalism extended to spin and coupled channels. This marks a new milestone for ab-initio studies of ordinary resonances along with hybrid and exotic hadrons involving three-body dynamics., Comment: 14 pages, 7 figures

We show how to compute electromagnetic polarizabilities of charged hadrons using four-point functions in lattice QCD. The low-energy behavior of Compton scattering amplitude is matched to matrix elements of current-current correlation functions on the lattice. Working in momentum space, formulas for electric polarizability ($\alpha_E$) and magnetic polarizability ($\beta_M$) are derived for both charged pion and proton. Lattice four-point correlation functions are constructed from quark and gluon fields to be used in Monte-Carlo simulations. The content of the functions is assessed in detail and specific prescriptions are given to isolate the polarizabilities. The connected quark-line diagrams can be done today as a small lattice project. The disconnected diagrams are more challenging but are within reach of dedicated resources for medium to large lattice projects. We also draw attention to the potential of four-point functions as a multi-purpose tool for hadron structure., Comment: 13 pages, 3 figures. This version provides some corrections and clarifications to V2

We present a calculation of the charged pion electric polarizability using the background field method. To extract the mass-shift induced by the electric field for the accelerated charged particle we fit the lattice QCD correlators using correlators derived from an effective model. The methodology outlined in this study (boundary conditions, fitting procedure, etc.) is designed to ensure that the results are invariant under gauge transformations of the background field. We apply the method to four $N_f=2$ dynamical ensembles to extract $\alpha_{\pi^\pm}$ at pion mass of $315$ MeV.

We perform a fit of the finite-volume QCD spectrum of three pions at maximal isospin to constrain the three-body force. We use the unitarity-based relativistic three-particle quantization condition, with the GWUQCD spectrum obtained at 315 MeV and 220 MeV pion mass in two-flavor QCD. For the heavier pion mass we find that the data is consistent with a constant contact term close to zero, whereas for the lighter mass we see a statistically significant energy dependence in tension with the prediction of leading order ChPT. Our results also suggest that with enough three-body energy levels, the two-body amplitude could be constrained., Comment: 17 pages, 6 figures. Updated to match published version

The dynamics of multi-kaon systems are of relevance for several areas of nuclear physics. However, even the simplest systems, two and three kaons, are hard to prepare and study experimentally. Here we show how to extract this information using first-principle lattice QCD results. We (1) extend the relativistic three-body quantization condition to the strangeness sector, predicting for the first time the excited level finite-volume spectrum of three kaon systems at maximal isospin, and (2) present a first lattice QCD calculation of the excited levels of this system in a finite box. We compare our predictions with the lattice results reported here and with previous ground state calculations and find very good agreement., Comment: 9 pages, 3 figures; v2 -- typos corrected

Lattice QCD calculations using gauge smearing for fermion kernels are computationally efficient. Hypercubic blocking (nHYP smearing) has been shown to reduce scaling errors. In this work we use an improved action for $N_f=2$ QCD, based on the L\"uscher-Weisz gauge action and clover-improved Wilson fermions with nHYP smeared gauge links. We perform a parameter scan in the region with lattice spacing between $0.066 \mathop{\hbox{fm}}$ and $0.115 \mathop{\hbox{fm}}$ and pion mass between $207 \mathop{\hbox{MeV}}$ and $834 \mathop{\hbox{MeV}}$. We determine the lattice spacing and pion mass as a function of the bare coupling parameters ($\beta$ and $\kappa$). The results are obtained from twenty-two ensembles on a $24^3\times 48$ lattice to percent level in statistical accuracy. The finite-volume effects for these ensemble are at the sub-percent level. From these measurements we produce easy-to-use parameterizations to help tune simulations with this action. The lattice spacing is fixed using a mass-independent procedure, by matching observables in the chiral limit. We also provide a parameterization for the chiral extrapolation which is universal and should hold for all discretizations of $N_f=2$ QCD.

The Roper state is extracted with valence overlap fermions on a $2+1$-flavor domain-wall fermion lattice (spacing $a = 0.114$ fm and $m_{\pi} = 330$ MeV) using both the Sequential Empirical Bayes (SEB) method and the variational method. The results are consistent, provided that a large smearing-size interpolation operator is included in the variational calculation to have better overlap with the lowest radial excitation. Similar calculations carried out for an anisotropic clover lattice with similar parameters find the Roper $\approx 280$ MeV higher than that of the overlap fermion. The fact that the prediction of the Roper state by overlap fermions is consistently lower than those of clover fermions, chirally improved fermions, and twisted-mass fermions over a wide range of pion masses has been dubbed a "Roper puzzle." To understand the origin of this difference, we study the hairpin $Z$-diagram in the isovector scalar meson ($a_0$) correlator in the quenched approximation. Comparing the $a_0$ correlators for clover and overlap fermions, at a pion mass of 290 MeV, we find that the spectral weight of the ghost state with clover fermions is smaller than that of the overlap at $a = 0.12$ fm and $0.09$ fm, whereas the whole $a_0$ correlators of clover and overlap at $a = 0.06$ fm coincide within errors. This suggests that chiral symmetry is restored for clover at $a \le 0.06$ fm and that the Roper should come down at and below this $a$. We conclude that this work supports a resolution of the "Roper puzzle" due to $Z$-graph type chiral dynamics. This entails coupling to higher components in the Fock space (e.g. $N\pi$, $N\pi\pi$ states) to induce the effective flavor-spin interaction between quarks as prescribed in the chiral quark model, resulting in the parity-reversal pattern as observed in the experimental excited states of $N, \Delta$ and $\Lambda$., Comment: 15 pages, 16 figures, revised manuscript accepted for publication in Phys. Rev. D

We use a chiral model for pion interactions, in the inverse amplitude formalism, to perform a simultaneous analysis of lattice QCD results for pion-pion scattering in all three isospin channels. The input is the finite-volume two-pion spectrum computed using lattice QCD from six ensembles on lattices elongated in one of the spatial dimensions. A two-flavor dynamical lattice QCD action is used with two quark masses corresponding to a pion mass of 315 MeV and 224 MeV. The spectrum in the elastic region is subjected to a global fit which takes into account full correlations across isospin, pion mass and decay constant. The parameters from the fit are used to perform a chiral extrapolation to the physical point. The cross-channel fit results in a more precise determination of the parameters of the model when compared with single channel fits. We obtain $m_\pi a_0^{I=0}=0.2132(9)$, and $m_\pi a_0^{I=2}=0.0433(2)$ as well as $m_\sigma=443(3)-i221(6)$ MeV and $m_\rho=724(4)-i67(1)$ MeV. Several aspects of scale setting and consistency with previous analyses of lattice QCD results are discussed as well., Comment: 11 pages, 3 figures

Internal gravity wave energy contributes significantly to the energy budget of the oceans, affecting mixing and the thermohaline circulation. Hence it is important to determine the internal wave energy flux $\mathbf{J} = p \, \mathbf{v}$, where $p$ is the pressure perturbation field and $\mathbf{v}$ is the velocity perturbation field. However, the pressure perturbation field is not directly accessible in laboratory or field observations. Previously, a Green's function based method was developed to calculate the instantaneous energy flux field from a measured density perturbation field $\rho(x,z,t)$, given a $constant$ buoyancy frequency $N$. Here we present methods for computing the instantaneous energy flux $\mathbf{J}(x,z,t)$ for a spatially varying $N(z)$, as in the oceans where $N(z)$ typically decreases by two orders of magnitude from shallow water to the deep ocean. Analytic methods are presented for computing $\mathbf{J}(x,z,t)$ from a density perturbation field for $N(z)$ varying linearly with $z$ and for $N^2(z)$ varying as $\tanh (z)$. To generalize this approach to $arbitrary$ $N(z)$, we present a computational method for obtaining $\mathbf{J}(x,z,t)$. The results for $\mathbf{J}(x,z,t)$ for the different cases agree well with results from direct numerical simulations of the Navier-Stokes equations. Our computational method can be applied to any density perturbation data using the MATLAB graphical user interface EnergyFlux.

We derive L\"{u}scher phaseshift formulas for two-particle states in boxes elongated in one of the dimensions. Such boxes offer a cost-effective way of varying the relative momentum of the particles. Boosted states in the elongated direction, which allow wider access to energies, are also considered. The formulas for the various scenarios (moving and zero-momentum states in cubic and elongated boxes) are compared and relations between them are clarified. The results are applicable to a wide set of meson-meson and meson-baryon elastic scattering processes, with the two-particle system having equal or unequal masses., Comment: 28 pages, 2 figures, 16 tables. Updated to match published version

Determination of energy transport is crucial for understanding the energy budget and fluid circulation in density varying fluids such as the ocean and the atmosphere. However, it is rarely possible to determine the energy flux field $\mathbf{J} = p \mathbf{u}$, which requires simultaneous measurements of the pressure and velocity perturbation fields, $p$ and $\mathbf{u}$. We present a method for obtaining the instantaneous $\mathbf{J}(x,z,t)$ from density perturbations alone: a Green's function-based calculation yields $p$, and $\mathbf{u}$ is obtained by integrating the continuity equation and the incompressibility condition. We validate our method with results from Navier-Stokes simulations: the Green's function method is applied to the density perturbation field from the simulations, and the result for $\mathbf{J}$ is found to agree typically to within $1\%$ with $\mathbf{J}$ computed directly using $p$ and $ \mathbf{u}$ from the Navier-Stokes simulation. We also apply the Green's function method to density perturbation data from laboratory schlieren measurements of internal waves in a stratified fluid, and the result for $\mathbf{J}$ agrees to within $6\%$ with results from Navier-Stokes simulations. Our method for determining the instantaneous velocity, pressure, and energy flux fields applies to any system described by a linear approximation of the density perturbation field, e.g., to small amplitude lee waves and propagating vertical modes. The method can be applied using our Matlab graphical user interface EnergyFlux.