Multipole Polarizabilities Research Articles

Multipolar polarizabilities and hyperpolarizabilities for alkaline-earth-metal ions

Multipolar polarizabilities and hyperpolarizabilities for alkaline-earth-metal ions

A comparative study of transition oscillator strengths and static polarizabilities of the hydrogen atom confined in Gaussian potential

Abstract The multipole (dipole, quadrupole, and octopole) photon-absorption transition oscillator strengths for the ground state of hydrogen atom confined in Gaussian potential are investigated for a great variety of potential depths and confining radii. It is interestingly found that at fixed potential depth the gradual increase of confining radius shows first destructive and then constructive effect on the multipole oscillator strengths. Such an effect can be understood from the overlap between the initial and final states. Multipole polarizabilities of the system are obtained through the sum-over-states formalism where the contributions from both the bound and continuum spectra of the system are included. Although the separate bound and continuum contributions can not be determined accurately, due to the long-range nature of the Coulomb potential introduced by the nucleus, their summations can be obtained to reasonably good accuracy, leading to fast convergence of numerical calculations of multipole polarizabilities. The present results are compared with previous calculations available in the literature. Although good agreement is observed for the dipole polarizability, significant differences exist in the quadrupole polarizability and orders-of-magnitude differences appear in the octopole polarizability. The possible reason for such large differences is analyzed by comparing the sum rule of corresponding oscillator strengths.

Control of dual-channel optical bistability in a carbon nanotube nanoresonator coupled with a metallic nanoshell.

We theoretically present a flexible method to obtain dual-channel optical bistability (OB) in a coupled system consisting of a metallic nanoshell (MNS) and a carbon nanotube (CNT) nanomechanical resonator (NR) beyond the dipole approximation. The MNS is made of a metallic core and a dielectric shell. The results show that, the four-wave mixing signal is suppressed significantly due to multipole polarizations in comparison to that in the dipole approximation. Also, the four-wave mixing signal can be enhanced greatly with the exciton-phonon coupling strength g increasing. Especially, bistability phase diagrams plotted show that, for a given shell thickness, it is realizable to achieve one (or two) bistable region(s) by adjusting the pumping intensity (or the MNS-NR distance). In a strong exciton-plasmon coupling regime, OB can be switched from single-channel to dual-channel by only changing the dielectric shell thickness or the metallic core radius. This indicates that the system proposed can behave as a channel-tunable bistable switch. Our findings may have potential applications in various domains such as quantum communication and optical functional devices.

Developing a Differentiable Long-Range Force Field for Proteins with E(3) Neural Network-Predicted Asymptotic Parameters.

Accurately describing long-range interactions is a significant challenge in molecular dynamics (MD) simulations of proteins. High-quality long-range potential is also an important component of the range-separated machine learning force field. This study introduces a comprehensive asymptotic parameter database encompassing atomic multipole moments, polarizabilities, and dispersion coefficients. Leveraging active learning, our database comprehensively represents protein fragments with up to 8 heavy atoms, capturing their conformational diversity with merely 78,000 data points. Additionally, the E(3) neural network (E3NN) is employed to predict the asymptotic parameters directly from the local geometry. The E3NN models demonstrate exceptional accuracy and transferability across all asymptotic parameters, achieving an R2 of 0.999 for both protein fragments and 20 amino acid dipeptide test sets. The long-range electrostatic and dispersion energies can be obtained using the E3NN-predicted parameters, with an error of 0.07 and 0.02 kcal/mol, respectively, when compared to symmetry-adapted perturbation theory (SAPT). Therefore, our force fields demonstrate the capability to accurately describe long-range interactions in proteins, paving the way for next-generation protein force fields.

ABLRI: A program for calculating the long-range interaction energy between two monomers in their non-degenerate states.

An accurate description of the long-range (LR) interaction is essential for understanding the collision between cold or ultracold molecules. However, to our best knowledge, there lacks a general approach to construct the intermolecular potential energy surface (IPES) between two arbitrary molecules and/or atoms in the LR region. In this work, we derived analytical expressions of the LR interaction energy, using the multipole expansion of the electrostatic interaction Hamiltonian and the non-degenerate perturbation theory. To make these formulae practical, we also derived the independent Cartesian components of the electrostatic properties, including the multipole moments and polarizabilities, of the monomer for a given symmetry using the properties of these components and the group-theoretical methods. Based on these newly derived formulae, we developed a FORTRAN program, namely ABLRI, which is capable of calculating the interaction energy between two arbitrary monomers both in their non-degenerate electronic ground states at large separations. To test the reliability of this newly developed program, we constructed IPESs for the electronic ground state of H2O-H2 and O2-H systems in the LR region. The interaction energy computed by our program agreed well with the abinitio calculation, which shows the validity of this program.

Contribution of negative-energy states to multipolar polarizabilities of the Sr optical lattice clock

Contribution of negative-energy states to multipolar polarizabilities of the Sr optical lattice clock

Optical bistability in a heterodimer composed of a quantum dot and a metallic nanoshell.

We theoretically explore the conditions for generating optical bistability (OB) in a heterodimer comprised of a semiconductor quantum dot (SQD) and a metallic nanoshell (MNS). The MNS is made of a metallic nanosphere as a core and a dielectric material as a shell. For the specific hybrid system considered, the bistable effect appears only if the frequency of the pump field is equal to (or slightly less than) the exciton frequency for a proper shell thickness. Bistability phase diagrams, when plotted, show that the dipole-induced bistable region can be greatly broadened by changing the shell thickness of the MNS in a strong exciton-plasmon coupling regime. In particular, we demonstrate that the multipole polarization not only narrows the bistable zone but also enlarges the corresponding thresholds for a given intermediate scaled pumping intensity. On the other hand, when the SQD couples strongly with the MNS, the multipole polarization can also significantly broaden the bistable region and induce a great suppression of the FWM (four-wave mixing) signal for a fixed shell thickness. These interesting findings offer a fresh understanding of the bistability conditions in an SQD/MNS heterodimer, and may be useful in the fabrication of high-performance and low-threshold optical bistable nanodevices.

Pre/Post-Merger Consistency Test for Gravitational Signals from Binary Neutron Star Mergers

Gravitational waves from binary neutron star (BNS) mergers can constrain nuclear models, predicting their equation of state (EOS). Matter effects on the inspiral-merger signal are encoded in the multipolar tidal polarizability parameters, whose leading order combination is sufficient to capture, with high accuracy, the key features of the merger waveform. Similar EOS-insensitive relations exist for the post-merger signal and can be used to model the emissions from the remnant. Several works suggested that the appearance of new degrees of freedom in high-density post-merger matter can be inferred by observing a violation of these EOS-insensitive relations. Here, we demonstrate a Bayesian method to test such an EOS-insensitive relation between the tidal polarizability parameters (or any other equivalent parameter) and the dominant post-merger frequency using information from the pre-and-post-merger signal. Technically, the method is similar to the inspiral-merger-ringdown consistency tests of General Relativity with binary black holes. However, differently from the latter, BNS pre/post-merger consistency tests are conceptually less informative and they only address the consistency of the assumed EOS-insensitive relation. Specifically, we discuss how such tests cannot conclusively discriminate between an EOS without respecting such a relation and the appearance of new degrees of freedom (or phase transitions) in high-density matter.

Multipole polarization assisted optical bistability in a semiconductor quantum dot/metal nanoparticle hybrid molecule

We theoretically study the optical bistability assisted by multipole polarizations in a semiconductor quantum dot (SQD)/metal nanoparticle (MNP) hybrid molecule. We map out bistability phase diagrams within the parameter subspace spanned by (the pumping intensity Ipu, interparticle distance, d) under dipole and multipole approximations. It is shown that the Ipu-correlated bistable region will be broadened greatly in the strong exciton–plasmon coupling regime, and the corresponding lower (upper) bistable threshold is enlarged significantly due to multipole polarization (N = 10) in comparison to that in the dipole approximation (N = 1). However, under the same conditions, the d-correlated bistable region is shrunk at high pump intensities. Our contribution not only offers a better understanding of exciton–plasmon coupling systems but also expands the application of SQD/MNP hybrid molecules in the field of optical bistable nanodevices.

Higher-order topological insulator in a spring-mass system

Higher-order topological insulators (HOTIs) have attracted much attention in various fields in the recent years. In this work, we propose a two-dimensional (2D) square lattice spring-mass model, where restoring forces between nearest neighbors can be induced by either longitudinal or transverse vibrations. Edge states exist on the interface between topological nontrivial and trivial lattices, and two different types of corner states are identified. The proposed spring-mass model has plenty of degrees of freedoms (DOFs), including both longitudinal and transverse spring constants as well as the mass of each particle. It turns out that edge and corner states with flexible spatial distributions can be realized by slightly tuning the elastic and inertial parameters. A lot of interesting topological patterns such as edge states along 4, 2, or only 1 edge, and second-order corner states around 4, 2, or 1 corner are unambiguously demonstrated. Our work provides an easy-to-tune platform to realize HOTIs, which is useful when multipole bulk polarizations or negative couplings are absent or difficult to realize. Classical spring-mass models governed by Newton's laws also have the advantage of superior controllability and feasible experimental implementability.

Is the Harrison-Zel’dovich spectrum coming back? ACT preference forns∼ 1 and its discordance with Planck

ABSTRACTThe Data Release 4 of the Atacama Cosmology Telescope (ACT) shows an agreement with an Harrison-Zel’dovich primordial spectrum (ns = 1.009 ± 0.015), introducing a tension with a significance of 99.3 per cent Confidence Level (CL) with the results from the Planck satellite. The discrepancy on the value of the scalar spectral index is neither alleviated with the addition of large scale structure information nor with the low multipole polarization data. We discuss possible avenues to alleviate the tension relying on either neglecting polarization measurements from ACT or in extending different sectors of the theory.

Multipole polarizabilities of spherically confined hydrogen atom and positronium in screened Coulomb potential

AbstractThe static multipole polarizabilities of the hydrogen atom interacting with a screened Coulomb potential confined in an impenetrable spherical box are calculated in the sum‐over‐states formalism. The system eigenenergies and wave functions are produced by employing the generalized pseudospectral method. High‐precision results are obtained to resolve the discrepancies between previous predictions, and used to analyze the critical behavior of the system with varying the confinement radius and screening parameter. A scaling law of the multipole polarizabilities with respect to the nuclear charge and electron reduced mass is proposed. Based on the scaling law we extend the investigation to the spatially confined positronium atom in a screened Coulomb potential by utilizing a reduced one‐electron model. The results are in good agreement with previous estimates. However, it is conjectured that when the confinement radius is small the confined positronium atom should be treated more reasonably by an effective two‐electron model.

Physical mechanisms of intermolecular interactions from symmetry-adapted perturbation theory.

Symmetry-adapted perturbation theory (SAPT) is a method for computational studies of noncovalent interactions between molecules. This method will be discussed here from the perspective of establishing the paradigm for understanding mechanisms of intermolecular interactions. SAPT interaction energies are obtained as sums of several contributions. Each contribution possesses a clear physical interpretation as it results from some specific physical process. It also exhibits a specific dependence on the intermolecularseparationR. The four major contributions are the electrostatic, induction, dispersion, and exchange energies, each due to a different mechanism, valid at anyR. In addition, at large R, SAPT interaction energies are seamlessly connected with the corresponding terms in the asymptotic multipole expansion of interaction energy in inverse powers of R. Since such expansion explicitly depends on monomers' multipole moments and polarizabilities, this connection provides additional insights by rigorously relating interaction energies to monomers' properties.

Multipole oscillator strength and polarizability for confined hydrogen-like atoms under high pressure

Multipole oscillator strength (f (k)) acts as a foundation in estimating multipole polarizability in a quantum system. Moreover, a knowledge of f (k) as well as under extreme pressure may be treated as the benchmark in high pressure spectroscopy. Further, an investigation of rate of change of these quantities and transition moment integral as a function of confinement radius (R) may offer many hitherto unexplained features. Here, we derive several such relations for confined H-like atom as a test case. In this regard, a virial theorem is utilized. The versatility of these derived relations in the context of atom is also discussed. Apart from that, we report numerically calculated results of α (k), f (k) for a confined H-like atom trapped inside a spherical cavity of radius R. A detailed and systematic analysis of these are undertaken in case of k ranging from 1–4, with special emphasis on 1s, 2s, 2p, 3d states. Their behavior is found to be significantly different from their respective free counterparts.

Multipole polarizabilities and dipole oscillator strengths of H-atom in nonideal classical plasmas

Multipole polarizabilities and dipole oscillator strengths of H-atom in nonideal classical plasmas

Generalization of the Optical Theorem to an Arbitrary Multipole Excitation of a Particle near a Transparent Substrate

In the present paper, the generalization of the optical theorem to the case of a penetrable particle deposited near a transparent substrate that is excited by a multipole of an arbitrary order and polarization has been derived. In the derivation we employ classic Maxwell’s theory, Gauss’s theorem, and use a special representation for the multipole excitation. It has been shown that the extinction cross-section can be evaluated by the calculation of some specific derivatives from the scattered field at the position of the multipole location, in addition to some finite integrals which account for the multipole polarization and the presence of the substrate. Finally, the present paper considers some specific examples for the excitation of a particle by an electric quadrupole.

Quantum-mechanical force balance between multipolar dispersion and Pauli repulsion in atomic van der Waals dimers

The structure and stability of atomic and molecular systems with van der Waals (vdW) bonding are often determined by the interplay between attractive dispersion interactions and repulsive interactions caused by electron confinement. Arising due to different mechanisms -- electron correlation for dispersion and the Pauli exclusion principle for exchange-repulsion -- these interactions do not appear to have a straightforward connection. In this paper, we use a coarse-grained approach for evaluating the exchange energy for two coupled quantum Drude oscillators and investigate the mutual compensation of the attractive and repulsive forces at the equilibrium distance within the multipole expansion of the Coulomb potential. This compensation yields a compact formula relating the vdW radius of an atom to its multipole polarizabilities, $R_{\rm vdW} = A_l^{\,}\, \alpha_l^{{2}/{7(l+1)}}$, where $l$ is the multipole rank and $A_l$ is a conversion factor. Such a relation is compelling because it connects an electronic property of an isolated atom (atomic polarizability) with an equilibrium distance in a dimer composed of two closed-shell atoms. We assess the accuracy of the revealed formula for noble-gas, alkaline-earth, and alkali atoms and show that the $A_l$ can be assumed to be universal constants. Besides a seamless definition of vdW radii, the proposed relation can also be used for the efficient determination of atomic multipole polarizabilities solely based on the corresponding dipole polarizability and the vdW radius. Finally, our work provides a basis for the construction of efficient and minimally-empirical interatomic potentials by combining multipolar interatomic exchange and dispersion forces on an equal footing.

Inference of the optical depth to reionization from low multipole temperature and polarization Planck data

ABSTRACT This paper explores methods for constructing low multipole temperature and polarization likelihoods from maps of the cosmic microwave background anisotropies that have complex noise properties and partial sky coverage. We use Planck 2018 High Frequency Instrument (HFI) and updated SRoll2 temperature and polarization maps to test our methods. We present three likelihood approximations based on quadratic cross spectrum estimators: (i) a variant of the simulation-based likelihood (SimBaL) techniques used in the Planck legacy papers to produce a low multipole EE likelihood; (ii) a semi-analytical likelihood approximation (momento) based on the principle of maximum entropy; (iii) a density-estimation ‘likelihood-free’ scheme (delfi). Approaches (ii) and (iii) can be generalized to produce low multipole joint temperature-polarization (TTTEEE) likelihoods. We present extensive tests of these methods on simulations with realistic correlated noise. We then analyse the Planck data and confirm the robustness of our method and likelihoods on multiple inter- and intra-frequency detector set combinations of SRoll2 maps. The three likelihood techniques give consistent results and support a low value of the optical depth to reoinization, τ, from the HFI. Our best estimate of τ comes from combining the low multipole SRoll2momento (TTTEEE) likelihood with the CamSpec high multipole likelihood and is $\tau = 0.0627^{+0.0050}_{-0.0058}$. This is consistent with the SRoll2 team’s determination of τ, though slightly higher by ∼0.5σ, mainly because of our joint treatment of temperature and polarization.

Confined hydrogenlike ions in plasma environments

The behavior of H-like ions embedded in astrophysical plasmas in the form of \emph{dense, strongly and weakly coupled} plasmas are investigated. In these, the increase and decrease in temperature is impacted with a change in confinement radius $(r_{c})$. Two independent and generalized scaling ideas have been applied to modulate the effect of plasma screening constant ($\lambda$) and charge of ion ($Z$) on such systems. Several new relations are derived to interconnect the original Hamiltonian and two scaled Hamiltonians. In exponential cosine screened Coulomb potential (ECSCP) (dense) and weakly coupled plasma (WCP) these scaling relations have provided a linear equation connecting the critical screening constant $(\lambda^{(c)})$ and $Z$. Their ratio offers a state-dependent constant, beyond which, a particular state vanishes. Shannon entropy has been employed to understand the plasma effect on the ion. With increase in $\lambda$, the accumulation of opposite charge surrounding the ion increases leading to a reduction in number of bound states. However, with rise in ionic charge $Z$, this effect can be delayed. The competing effect of plasma charge density ($n_e$) and temperature in WCP and ECSCP is investigated. A recently proposed simple virial-like theorem has been established for these systems. Multipole ($k=1-4$) oscillator strength (OS) and polarizabilities for these are studied considering $1s, 2s$ states. As a bonus, analytical closed-form expressions are derived for $f^{(k)}$ and $\alpha^{(k)} (k=1-4)$ involving $1s$ and $2s$ state, for \emph{free H-like ion}.

Multipole polarizabilities for hydrogen-like atoms in Hulthén potential with and without spherical confinement

The multipole polarizabilities for hydrogen-like atoms with Hulthen potential are calculated with the sum-over-states formalism where the system bound and pseudocontinuum states are produced by employing the generalized pseudospectral method. Energies for nonzero angular momentum states, transition oscillator strengths, and dipole polarizabilities for the ground state of H atom with HP are calculated with high accuracy and compared with previous calculations. Quadrupole, octupole, and hexadecapole polarizabilities for both the ground and excited states are reported for the first time. The combined effect of Hulthen potential and impenetrable sphere on the polarizabilities is investigated, and the relation of such system with the confined H atom and particle in a box is discussed. Further comparison among Hulthen, screened Coulomb, and exponential cosine screened Coulomb potentials reveals that although the ground state energies follow the comparison theorem very well, their first-order energy corrections show complicated variations.