Model Wave Functions Research Articles

Flavor asymmetry of light sea quarks in proton: a light-front spectator model

We formulate a light-front spectator model for the proton that incorporates the presence of light sea quarks. In this particular model, the sea quarks are seen as active partons, whereas the remaining components of the proton are treated as spectators. The proposed model relies on the formulation of the light-front wave function constructed by the soft wall AdS/QCD. The model wave functions are parameterized by fitting the unpolarized parton distribution functions of light sea quarks from the CTEQ18 global analysis. We then employ the light-front wave functions to obtain the sea quarks generalized parton distribution functions, transverse momentum dependent parton distributions, and their asymmetries, which are accessible in the upcoming Electron-Ion-Colliders. We investigate sea quarks’ spin and orbital angular momentum contributions to the proton spin.

Theoretical triple differential cross sections for ionization of N 2 and CH 4 molecules by electron impact

We present the angular distribution of electron emission by calculating the triple differential cross sections for (e, 2e) process on N 2 and CH 4 by using the three-body formalism of molecular first Born approximation (MFBA), two-Coulomb wave (M2CW), and three-Coulomb wave (M3CW) models, respectively. In these models, a Coulomb distorted wave is considered for the motion of the incident electron. We have considered the continuum-continuum correlation effect by choosing the final state as the three-Coulomb and two-Coulomb wave functions in M3CW and M2CW models, whereas the ejected electron is affected by a single centre field of the target in the MFBA model. In the M2CW model, the interaction between scattered electron-residual target ion has been described as a plane wave. The distinguishing feature among the three models has been noted in the TDCS as a strong binary peak with and without a recoil peak for several electron emission energies at fixed scattering angle. In the case of N 2 molecule, the TDCS shows oscillatory behaviour with the variation of the electron emission angle. The positions of the binary peak obtained by our theoretical models are well established by the experimental findings, but a large deviation is found in the region of the recoil peak. The contributions of TDCS for different molecular orbitals of the molecules to the spectrum of angular distributions at different electron emission energies have also been analyzed. Finally, a comparison is made with the measurement in coplanar asymmetry geometry. Overall, good agreement was found between experiments and M3CW theory.

Towards a transferable fermionic neural wavefunction for molecules.

Deep neural networks have become a highly accurate and powerful wavefunction ansatz in combination with variational Monte Carlo methods for solving the electronic Schrödinger equation. However, despite their success and favorable scaling, these methods are still computationally too costly for wide adoption. A significant obstacle is the requirement to optimize the wavefunction from scratch for each new system, thus requiring long optimization. In this work, we propose a neural network ansatz, which effectively maps uncorrelated, computationally cheap Hartree-Fock orbitals, to correlated, high-accuracy neural network orbitals. This ansatz is inherently capable of learning a single wavefunction across multiple compounds and geometries, as we demonstrate by successfully transferring a wavefunction model pre-trained on smaller fragments to larger compounds. Furthermore, we provide ample experimental evidence to support the idea that extensive pre-training of such a generalized wavefunction model across different compounds and geometries could lead to a foundation wavefunction model. Such a model could yield high-accuracy ab-initio energies using only minimal computational effort for fine-tuning and evaluation of observables.

Microscopic study of normal deformed bands in 167,169,171Lu

The normal deformed bands of [Formula: see text]Lu isotopes have been studied by using projected shell model approach. The band head spins, configurations and energies of all the normal deformed bands are reproduced well by the above said approach. The present calculations have predicted [Formula: see text] band head spin for [523]7/2− bands of [Formula: see text]Lu. The observed systematics of aligned angular momenta and the experimental differences in frequencies around the backbends for all the normal deformed bands are reproduced well by the theoretical results. Besides this, the observed backbends or upbends in these isotopes may be ascribed to the alignment of a pair of neutrons in the neutron [Formula: see text] orbital. Although the theoretical [Formula: see text] values obtained from the projected shell model wavefunctions overestimate the experimental [Formula: see text] values in [Formula: see text]Lu, yet they are close to the measured values, considering the precision of measurement. The reduction in the theoretical [Formula: see text] values around the band crossing region may be ascribed to change in nuclear structure of yrast bands due to neutron pair alignment in [Formula: see text] orbital.

How to Compute Atomistic Insight in DFT Clusters: The REG-IQA Approach.

The relative energy gradient (REG) method is paired with the topological energy partitioning method interacting quantum atoms (IQA), as REG-IQA, to provide detailed and unbiased knowledge on the intra- and interatomic interactions. REG operates on a sequence of geometries representing a dynamical change of a system. Its recent application to peptide hydrolysis of the human immunodeficiency virus-1 (HIV-1) protease (PDB code: 4HVP) has demonstrated its full potential in recovering reaction mechanisms and through-space electrostatic and exchange-correlation effects, making it a compelling tool for analyzing enzymatic reactions. In this study, the computational efficiency of the REG-IQA method for the 133-atom HIV-1 protease quantum mechanical system is analyzed in every detail and substantially improved by means of three different approaches. The first approach of smaller integration grids for IQA integrations reduces the computational overhead by about a factor of 3. The second approach uses the line-simplification Ramer-Douglas-Peucker (RDP) algorithm, which outputs the minimal number of geometries necessary for the REG-IQA analysis for a predetermined root mean squared error (RMSE) tolerance. This cuts the computational time of the whole REG analysis by a factor of 2 if an RMSE of 0.5 kJ/mol is considered. The third approach consists of a "biased" or "unbiased" selection of a specific subset of atoms of the whole initial quantum mechanical model wave-function, which results in more than a 10-fold speed-up per geometry for the IQA calculation, without deterioration of the outcome of the REG-IQA analysis. Finally, to show the capability of these approaches, the findings gathered from the HIV-1 protease system are also applied to a different system named haloalcohol dehalogenase (HheC). In summary, this study takes the REG-IQA method to a computationally feasible and highly accurate level, making it viable for the analysis of a multitude of enzymatic systems.

Entanglement complexity of the Rokhsar-Kivelson-sign wavefunctions

Entanglement comes in different forms, some more complex than others. In this paper we study the transitions of entanglement complexity in an exemplary family of states---the Rokhsar-Kivelson-sign wavefunctions---whose degree of entanglement is controlled by a single parameter. This family of states is known to feature a transition between a phase exhibiting volume-law scaling of entanglement entropy and a phase with subextensive scaling of entanglement, reminiscent of the many-body-localization transition of disordered quantum Hamiltonians. We study the singularities of the Rokhsar-Kivelson-sign wavefunctions and their entanglement complexity across the transition using several tools from quantum information theory: fidelity metric, entanglement spectrum statistics, entanglement entropy fluctuations, stabilizer R\'enyi entropy, and the performance of a disentangling algorithm. Across the whole volume-law phase the states feature universal entanglement spectrum statistics. Yet a ``superuniversal'' regime appears for small values of the control parameter in which all metrics become independent of the parameter itself, the entanglement entropy as well as the stabilizer R\'enyi entropy appear to approach their theoretical maximum, the entanglement fluctuations scale to zero as in output states of random universal circuits, and the disentangling algorithm has essentially null efficiency. All these indicators consistently reveal a complex pattern of entanglement. In the sub-volume-law phase, on the other hand, the entanglement spectrum statistics is no longer universal, entanglement fluctuations are larger and exhibiting a nonuniversal scaling, and the efficiency of the disentangling algorithm becomes finite. Our results, based on model wavefunctions, suggest that a similar combination of entanglement scaling properties and of entanglement complexity features may be found in high-energy Hamiltonian eigenstates---a very strong candidate being offered by the many-body localization transition of disordered lattice-spin models.

Nuclear structure properties of Si and P isotopes with the microscopic effective interactions

In the present work, we have reported comprehensive study of the sd-shell nuclei Si and P with neutron number varying from N=9 to N=20 using the microscopic effective valence shell interactions, namely, N3LO, JISP16 and DJ16A. These effective sd-shell interactions are developed using the ab initio no-core shell model wave functions and the Okubo-Lee-Suzuki transformation method. For comparison, we have also performed shell model calculations with the empirical USDB interaction. Energy spectra and electromagnetic properties of these isotopic chains have been studied. Theoretically calculated shell model results are compared with the available experimental data, to check the predictive strength of these microscopic interactions. It is found that the binding energies of the ground states are better reproduced with the DJ16A interaction as compared to other microscopic interactions and a proton subshell closure at Z=14 is obtained in Si. Spin-tensor decomposition of two-body interaction is presented to understand the contributions from central, vector and tensor components into these interactions. Spectroscopic strengths of 23Al(d,n)24Si are examined for the newly performed experiment at NSCL.

Study of structure and radii for 20−31Na isotopes using microscopic interactions

In this work, Na isotopes with mass varying from A=20 to 31 have been studied using DJ16A, JISP16 and N3LO microscopic effective interactions in the sd-shell. These effective interactions are derived for sd-shell using no-core shell model wavefunctions and a unitary transformation method. We have also performed calculation with IMSRG effective interactions targeted for a particular nucleus. The studies include a detailed analysis of ground state binding energy, low-lying spectra, and electromagnetic properties such as reduced electric quadrupole transition strengths, quadrupole and magnetic dipole moments of the Na chain. The results obtained from these microscopic effective interactions were compared with the experimental data as well as with the results of phenomenological interaction USDB. The charge radii of Na isotopes are evaluated using shell model harmonic oscillator wave functions. In addition to charge radii, matter radii and neutron skin thickness in the Na chain are discussed with a focus on neutron-deficient Na isotopes.

Recent advances in theab initiotheory of solid-state defect qubits

AbstractSolid-state defects acting as single photon sources and quantum bits are leading contenders in quantum technologies. Despite great efforts, not all the properties and behaviours of the presently known solid-state defect quantum bits are understood. Furthermore, various quantum technologies require novel solutions, thus new solid-state defect quantum bits should be explored to this end. These issues call to developab initiomethods which accurately yield the key parameters of solid-state defect quantum bits and vastly accelerate the identification of novel ones for a target quantum technology application. In this review, we describe recent developments in the field including the calculation of excited states with quantum mechanical forces, treatment of spatially extended wavefunctions in supercell models, methods for temperature-dependent Herzberg–Teller fluorescence spectrum and photo-ionisation thresholds, accurate calculation of magneto-optical parameters of defects consisting of heavy atoms, as well as spin-phonon interaction responsible for temperature dependence of the longitudonal spin relaxationT1time and magneto-optical parameters, and finally the calculation of spin dephasing and spin-echo times. We highlight breakthroughs including the description of effective-mass like excited states of deep defects and understanding the leading microscopic effect in the spin-relaxation of isolated nitrogen-vacancy centre in diamond.

Stronger C -odd color charge correlations in the proton at higher energy

The non-forward eikonal scattering matrix for dipole-proton scattering at high energy obtains an imaginary part due to a $C$-odd three gluon exchange. We present numerical estimates for the perturbative Odderon amplitude as a function of dipole size, impact parameter, their relative azimuthal angle, and light-cone momentum cutoff $x$. The proton is approximated as $\psi_\mathrm{qqq}|qqq\rangle + \psi_\mathrm{qqqg}|qqqg\rangle$, where $\psi_\mathrm{qqq}$ is a non-perturbative three quark model wave function while the gluon emission is computed in light-cone perturbation theory. We find that the Odderon amplitude increases as $x$ decreases from 0.1 to 0.01. At yet lower $x$, the reversal of this energy dependence would reflect the onset of universal small-$x$ renormalization group evolution.

Sensitivity of Kβ mainline X-ray emission to structural dynamics in iron photosensitizer.

Photochemistry and photophysics processes involve structures far from equilibrium. In these reactions, there is often strong coupling between nuclear and electronic degrees of freedom. For first-row transition metals, Kβ X-ray emission spectroscopy (XES) is a sensitive probe of electronic structure due to the direct overlap between the valence orbitals and the 3p hole in the final state. Here the sensitivity of Kβ mainline (Kβ1,3) XES to structural dynamics is analyzed by simulating spectral changes along the excited state dynamics of an iron photosensitizer [FeII(bmip)2]2+ [bmip = 2,6-bis(3-methyl-imidazole-1-ylidine)-pyridine], using both restricted active space (RAS) multiconfigurational wavefunction theory and a one-electron orbital-energy approach in density-functional theory (1-DFT). Both methods predict a spectral blue-shift with increasing metal-ligand distance, which changes the emission intensity for any given detection energy. These results support the suggestion that the [FeII(bmip)2]2+ femtosecond Kβ XES signal shows oscillations due to coherent wavepacket dynamics. Based on the RAS results, the sensitivity to structural dynamics is twice as high for Kβ compared to Kα, with the drawback of a lower signal-to-noise ratio. Kβ sensitivity is favored by a larger spectral blue-shift with increasing metal-ligand distance and larger changes in spectral shape. Comparing the two simulations methods, 1-DFT predicts smaller energy shifts and lower sensitivity, likely due to missing final-state effects. The simulations can be used to design and interpret XES probes of non-equilibrium structures to gain mechanistic insights in photocatalysis.

Fanpy: A python library for prototyping multideterminant methods in ab initio quantum chemistry.

Fanpy is a free and open-source Python library for developing and testing multideterminant wavefunctions and related ab initio methods in electronic structure theory. The main use of Fanpy is to quickly prototype new methods by making it easier to convert the mathematical formulation of a new wavefunction ansätze to a working implementation. Fanpy is designed based on our recently introduced Flexible Ansatz for N-electron Configuration Interaction (FANCI) framework, where multideterminant wavefunctions are represented by their overlaps with Slater determinants of orthonormal spin-orbitals. In the simplest case, a new wavefunction ansatz can be implemented by simply writing a function for evaluating its overlap with an arbitrary Slater determinant. Fanpy is modular in both implementation and theory: the wavefunction model, the system's Hamiltonian, and the choice of objective function are all independent modules. This modular structure makes it easy for users to mix and match different methods and for developers to quickly explore new ideas. Fanpy is written purely in Python with standard dependencies, making it accessible for various operating systems. In addition, it adheres to principles of modern software development, including comprehensive documentation, extensive testing, quality assurance, and continuous integration and delivery protocols. This article is considered to be the official release notes for the Fanpy library.

Atoms and interatomic bonding synergism inherent in molecular electronic wave functions.

The chemical model of matter consists of atoms held together by bonds. The success of this model implies that the physical interactions of the electrons and nuclei in molecules combine into compound interactions that create the bonding. In the quantum mechanical description, the modified atoms in molecules and the bonding synergism are contained in the molecular electronic wave function. So far, only part of this information has been recovered from the wave function. Notably, the atoms have remained unidentified in the wave function. One reason is that conventional energy decomposition analyses formulate separate model wave functions, independent of the actual wave function, to represent "prepared atoms" and preconceived interactions and, then, intuitively catenate the parts. In the present work, the embedded modified atoms and the inherent physical synergisms between them are determined by a unified derivation entirely from the actual molecular valence space wave function. By means of a series of intrinsic orbital and configurational transformations of the wave function, the energy of formation of a molecule is additively resolved in terms of intra-atomic energy changes, interference energies, and quasi-classical, non-classical, and charge-transfer Coulombic interactions. The analysis furnishes an algorithm for the quantitative resolution of the energy of formation, which enables analyses elucidating reaction energies.

Family of Ideal Chern Flatbands with Arbitrary Chern Number in Chiral Twisted Graphene Multilayers.

We consider a family of twisted graphene multilayers consisting of n-untwisted chirally stacked layers, e.g., AB, ABC, etc, with a single twist on top of m-untwisted chirally stacked layers. Upon neglecting both trigonal warping terms for the untwisted layers and the same sublattice hopping between all layers, the resulting models generalize several remarkable features of the chiral model of twisted bilayer graphene (CTBG). In particular, they exhibit a set of magic angles which are identical to those of CTBG at which a pair of bands (i) are perfectly flat, (ii)have Chern numbers in the sublattice basis given by ±(n,-m) or ±(n+m-1,-1) depending on the stacking chirality, and (iii)satisfy the trace condition, saturating an inequality between the quantum metric and the Berry curvature, and thus realizing ideal quantum geometry. These are the first higher Chern bands that satisfy (iii)beyond fine-tuned models or combinations of Landau levels. We show that ideal quantum geometry is directly related to the construction of fractional quantum Hall model wave functions. We provide explicit analytic expressions for the flatband wave functions at the magic angle in terms of the CTBG wave functions. We also show that the Berry curvature distribution in these models can be continuously tuned while maintaining perfect quantum geometry. Similar to the study of fractional Chern insulators in ideal C=1 bands, these models pave the way for investigating exotic topological phases in higher Chern bands for which no Landau level analog is available.

Mesoscopic quantum thermo-mechanics: A new frontier of experimental physics

In the last decade, experimentalists have demonstrated their impressive ability to control mechanical modes within mesoscopic objects down to the quantum level: it is now possible to create mechanical Fock states, to entangle mechanical modes from distinct objects, and to store quantum information or transfer it from one quantum bit to another, among the many possibilities found in today's literature. Indeed, mechanics is quantum, very much like spins or electromagnetic degrees of freedom; and all of this is, in particular, referred to as a new engineering resource for quantum technologies. However, there is also much more beyond this utilitarian aspect: invoking the original discussions of Braginsky and Caves, where a quantum oscillator is thought of as a quantum detector for a classical field, namely, a gravitational wave, which is also a unique sensing capability for quantum fields. The subject of study is then the baths to which the mechanical mode is coupled to, let them be known or unknown in nature. This Perspective is about this new potentiality that addresses stochastic thermodynamics, potentially down to its quantum version, the search for a fundamental underlying (random) field postulated in recent theories that can be affiliated to the class of the wave-function collapse models, and more generally open questions of condensed matter like the actual nature of the elusive (and ubiquitous) two-level systems present within all mechanical objects. However, such research turns out to be much more demanding than the use of a few quantum mechanical modes: all the known baths have to be identified, experiments have to be conducted in-equilibrium, and the word “mechanics” needs to be justified by a real ability to move substantially the center-of-mass when a proper drive tone is applied to the system.

Anisotropy and quench dynamics of quasiholes in fractional quantum Hall liquids

We present a microscopic study of quasiholes in bosonic fractional quantum Hall (FQH) liquids at filling factor $\nu=1/2$ in the lowest Landau level with anisotropic band mass tensors. We use the spatial density profile to characterize the shape of a quasihole and analyze its anisotropy. We then compare the quasihole's anisotropy with the intrinsic geometric metric of the system that is extracted from the maximal overlap between the numerically obtained quasihole ground state and a set of model wave functions of anisotropic quasiholes. For a static system, we find that the quasihole's anisotropy, similar to the intrinsic metric, grows with the anisotropy of the band mass tensor. When the quasihole develops well, we observe a correspondence between the anisotropy of the quasihole and the intrinsic metric of the underlying anisotropic FQH state. We also drive the system out of equilibrium by suddenly changing the band mass tensor. In this case, the shape of the quasihole evolves with time and shows similar dynamics with the intrinsic metric of the postquench state. The evolving frequency matches the energy of a spin-$2$ quadrupole degree of freedom in the system. Our results suggest that the density profile of a quasihole is a useful tool to estimate the intrinsic metric and capture the dynamics of an FQH system.

A Nuclear Electric Quadrupole Moment Of 6Li Nucleus Using Hyperfine Structure In Atomic Spectra

The nuclear electric quadrupole moment (QM) is one of the most important bulk properties of the nucleus with which nuclear deformations can be investigated. In this paper the electric quadrupole moment for 6Li nucleus in the ground state is calculated from the hyperfine structure of atomic spectra. Initially a cluster model wavefunction is constructed in shell model using Resonating Group Method (RGM), Generate coordinate method (GCM) and Complex Generator Coordinate Technique (CGCT). CGCT transforms the cluster model wavefunction into antisymmetrized product of single particle wavefunction. The wavefunction is written with the total angular momentum, relative motion between alpha and deuteron clusters, definite parity and spin. The calculations have been made by taking Wood- Saxon potential. The results obtained are compared and found reasonably well in agreement with the experimental results.

Accurate Exponential Representations for the Ground State Wave Functions of the Collinear Two-Electron Atomic Systems

In the framework of the study of helium-like atomic systems possessing the collinear configuration, we propose a simple method for computing compact but very accurate wave functions describing the relevant S-state. It is worth noting that the considered states include the well-known states of the electron–nucleus and electron–electron coalescences as a particular case. The simplicity and compactness imply that the considered wave functions represent linear combinations of a few single exponentials. We have calculated such model wave functions for the ground state of helium and the two-electron ions with nucleus charge 1≤Z≤5. The parameters and the accompanying characteristics of these functions are presented in tables for number of exponential from 3 to 6. The accuracy of the resulting wave functions are confirmed graphically. The specific properties of the relevant codes by Wolfram Mathematica are discussed. An example of application of the compact wave functions under consideration is reported.

Higher mass spectra of the fully-charmed and fully-bottom tetraquarks

In this work, we calculate the higher mass spectra for the $2S$- and $1D$-wave fully-charmed and fully-bottom tetraquark states in a nonrelativistic potential quark model. The $2S$-wave fully-charmed/bottom tetraquark states lie in the mass range of $\ensuremath{\sim}(6.9,7.1)/(19.7,19.9)\text{ }\mathrm{GeV}$, apart from the highest ${0}^{++}$ state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)/{T}_{(bb\overline{b}\overline{b}){0}^{++}}(19976)$. Most of the $2S$-wave states highly overlap with the high-lying $1P$-wave states. The masses for the $1D$-wave fully-charmed/bottom tetraquark states are predicted to be in the range of $\ensuremath{\sim}(6.7,7.2)/(19.5,20.0)\text{ }\text{ }\mathrm{GeV}$. The mass range for the $D$-wave tetraquark states cover most of the mass range of the $P$-wave states and the whole mass range of the $2S$-wave states. The narrow structure $X(6900)$ recently observed at LHCb in the di-$J/\ensuremath{\psi}$ invariant mass spectrum may be caused by the $1P$-, or $2S$-, or $1D$-wave ${T}_{(cc\overline{c}\overline{c})}$ states. The vague structure $X(7200)$ may be caused by the highest $2S$-wave state ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7185)$, two low-lying $3S$-wave states ${T}_{(cc\overline{c}\overline{c}){0}^{++}}(7240)$ and ${T}_{(cc\overline{c}\overline{c}){2}^{++}}(7248)$, and/or the high-lying $1D$-wave states with masses around 7.2 GeV and ${J}^{PC}={0}^{++},{1}^{++},{2}^{++},{3}^{++}$, or ${4}^{++}$. While it is apparent that the potential quark model calculations predict more states than the structures observed in the di-$J/\ensuremath{\psi}$ invariant mass spectrum, our calculations will help further understanding of the properties of these fully-heavy tetraquark states in their strong and magnetic interactions with open channels based on explicit quark model wave functions.

Co-spherical electronic configuration of the helium-like atomic systems

The properties of a special configuration of a helium-like atomic system, when both electrons are on the surface of a sphere of radius r, and angle θ characterizes their positions on sphere, are investigated. Unlike the previous studies, r is considered as a quantum mechanical variable but not a parameter. It is important that the “co-spherical” and the “collinear” configuration are coincident in two points. For θ=0 one obtains the state of the electron–electron coalescence, whereas the angle θ=π characterizes the e − n − e configuration when the electrons are located at the ends of the diameter of sphere with the nucleus at its center. The Pekeris-like method representing a fully three-body variational technique is used for the expedient calculations. Some interesting features of the expectation values representing the basic characteristics of the “co-spherical” electronic configuration are studied. The unusual properties of the expectation values of the operators associated with the kinetic and potential energy of the two-electron atom/ion possessing the “co-spherical” configuration are found. Refined formulas for calculations of the two-electron Fock expansion by the Green’s function approach are presented. The model wave functions of high accuracy describing the “co-spherical” electronic configuration are obtained. All results are illustrated in tables and figures.