State Wave Function Research Articles

Introducing Novel Materials with Diffuse Electrons for Applications in Redox Catalysis and Quantum Computing via Theoretical Calculations

Diamond-like structures, where carbon atoms have been replaced with Li+ and C–C bonds with diamines, have currently been introduced as new materials, which can host diffuse electrons in the periphery of each lithium tetra-amine center. These materials display a diverse range of properties behaving as metals or semiconductors depending on the diamine chain length. Multi-reference wavefunction and density functional theory calculations were employed to study the electronic structure of these materials. Initially, gas phase calculations are performed on isolated (NH3)3LiNH2(CH2)1–10H2NLi(NH3)3 molecular strings. One diffuse electron surrounds the periphery of each −NH2Li(NH3)3 terminus. The two terminal electrons couple into a triplet and open-shell singlet states, which are nearly degenerate for long chains and as closed shell singlets for short. At intermediate lengths, the wavefunction of the ground-state singlet state mixes both open- and closed-shell configurations raising doubts about which configuration should be considered for density functional theory calculations. Observations from gas phase calculations accurately predict properties from the condense phase density functional theory calculations carried out for proposed crystalline Li-diamine materials, offering an avenue for further development and insight. Spin-polarized and unpolarized calculations are performed for the whole range of hydrocarbon sizes reporting geometrical and electronic band structures, spin density contours, and density of states. Diffuse electrons can be used for redox reactions or can serve as qubits for quantum computing. Future work will focus on decorating the hydrocarbon backbone with functional groups and/or bulky units, in order to facilitate or block the association between neighboring electrons for more controlled quantum computing applications and propose materials for selective redox catalysis.

QCD at the amplitude level: Fock state interference in heavy quark electroproduction

Quantum chromodynamics (QCD) rigorously predicts the existence of both nonperturbative intrinsic and perturbative extrinsic heavy quark contents of nucleons. In this article we discuss the heavy quark electroproduction on protons induced by the Fock states ∣uud + g〉 of three valence quarks in the proton and a nonperturbative gluon, and the mid uud+Qoverline{Q}Bigrangle non-perturbative state of three valence quarks and a heavy quark-antiquark pair. The first one gives the perturbative contribution when the gluon produces a heavy quark pair, while the second is the intrinsic part, and they produce amplitude interference. We use nonperturbative light-front wavefunctions for these Fock states, which are computed using the color-confining light-front holographic QCD theory. Due to interference of the amplitudes corresponding to the intrinsic and extrinsic heavy quark contribution to the proton a novel Q vs. overline{Q} asymmetry emerges in the differential cross section of the electroproduction off a proton {d}^2{sigma}_{e^{-}p}/left( dxd{Q}^2right) . Our analysis proposed a novel asymmetry in QCD between intrinsic and extrinsic heavy quark content in nucleon and provides new insights into the physics of heavy quark phenomena in QCD at the amplitude level. This asymmetry is similar to the Brodsky-Gillespie asymmetry discovered before in QED case and confirmed at DESY.

Study of atomic spectroscopy and electron collision process in non-ideal classical plasmas

This manuscript presents an approach to the calculation of atomic properties and the electron collision excitation process in a non-ideal classical plasma, based on the relativistic distorted wave methodology. The method incorporating the pseudopotential obtained from a sequential solution of the Bogolyubov chain equations, that yields modification term to the calculation of the central field potential, is employed to characterize the interactions among the charged particles in plasmas. The bound/continuous state wave functions and the electron collision excitation matrix elements are determined using the aforementioned pseudopotential within a relativistic Dirac–Coulomb atomic structure framework. Systematic investigations on the effects of non-ideality of plasma on the electronic structures, radiative properties, and excitation cross sections within a selected temperature and density range are carried out in the specific cases of H atom and Ca18+ ion as they make it possible to reproduce the reference data well and thus to conclude with the reliability of the (present) method developed. Apart from its fundamental importance, this study is essential for several applications, especially for the analysis of atomic processes in non-ideal plasmas, and offers a new perspective for the calculation of atomic properties under different conditions in various astrophysical and laboratory plasmas.

Kajian Literatur Fase Adiabatik untuk mempercepat Dinamika Kuantum Adiabatik pada Osilator Harmonik

<p>This research is a theoretical research by reviewing the literature that discusses the method of accelerating quantum dynamics adiabatically. This method for accelerating quantum dynamics is so- called the fast-forward method. This method was proposed by Masuda and Nakamura in 2010. In this method, the ground state and first excited state wave function is modified by adding an additional term to the wave function which is called the adiabatic phase. This is done so that the time-dependent Schrodinger equation remains fulfilled. The accelerating process is carried out using an adiabatic parameter that goes to zero. Fast-forward method is applied first to get the adiabatic phase. Furthermore, by reviewing the wave function at the ground state and first excited state we get the adiabatic phase which ensures that the harmonic oscillator can move from the initial state to the final state in a shorter time.</p>

Dimer Rhenium Tetrafluoride with a Triple Bond Re-Re: Structure, Bond Strength.

Based on the data of the gas electron diffraction/mass spectrometry (GED/MS) experiment, the composition of the vapor over rhenium tetrafluoride at T = 471 K was established, and it was found that species of the Re2F8 is present in the gas phase. The geometric structure of the Re2F8 molecule corresponding to D4h symmetry was found, and the following geometric parameters of the rh1 configuration were determined: rh1(Re-Re) = 2.264(5) Å, rh1(Re-F) = 1.846(4) Å, α(Re-Re-F) = 99.7(0.2)°, φ(F-Re-Re-F) = 2.4 (3.6)°. Calculations by the self-consistent field in full active space approximation showed that for Re2F8, the wave function of the 1A1g ground electronic state can be described by the single closed-shell determinant. For that reason, the DFT method was used for a structural study of Re2X8 molecules. The description of the nature of the Re-Re bond was performed in the framework of Atom in Molecules and Natural Bond Orbital analysis. The difference in the experimental values of r(Re-Re) in the free Re2F8 molecule and the [Re2F8]2- dianion in the crystal corresponds to the concept of a triple σ2π4 (ReIV-ReIV) bond and a quadruple σ2π4δ2 (ReIII-ReIII) bond, respectively, which are formed between rhenium atoms due to the interaction of d-atomic orbitals. The enthalpy of dissociation of the Re2F8 molecular form in two monomers ReF4 (ΔdissH°(298) = 109.9 kcal/mol) and the bond energies E(Re-Re) and E(Re-X) in the series Re2F8→Re2Cl8→Re2Br8 molecules were estimated. It is shown that the Re-Re bond energy weakly depends on the nature of the halogen, while the symmetry of the Re2Br8 (D4d) geometric configuration differs from the symmetry of the Re2F8 and Re2Cl8 (D4h) molecules.

Fractional quantum Hall states on CP2 space

We study four-dimensional fractional quantum Hall states on CP2 geometry from microscopic approaches. While in 2d the standard Laughlin wave function, given by a power of Vandermonde determinant, admits a product representation in terms of the Jastrow factor, this is no longer true in higher dimensions. In 4d we can define two different types of Laughlin wavefunctions, the Determinant-Laughlin (Det-Laughlin) and Jastrow-Laughlin (Jas-Laughlin) states. We find that they are exactly annihilated by, respectively, two-particle and three-particle short ranged interacting Hamiltonians. We then mainly focus on the ground state, low energy excitations and the quasi-hole degeneracy of Det-Laughlin state. The quasi-hole degeneracy exhibits an anomalous counting, indicating the existence of multiple forms of quasi-hole wavefunctions. We argue that these are captured by the mathematical framework of the commutative algebra of N-points in the plane. We also generalize the pseudopotential formalism to dimensions higher than two, by considering coherent state wavefunction of bound states. The microscopic wavefunctions and Hamiltonians studied in this work pave the way for systematic study of high dimensional topological phase of matter that is potentially realizable in cold atom and optical experiments.

Weighted variation after projection method for low-lying nonyrast states* *Supported by the National Natural Science Foundation of China (11975314), the Key Laboratory of Nuclear Data foundation (JCKY2022201C158), and the Continuous Basic Scientific Research Project (WDJC-2019-13, BJ20002501)

We propose a simple algorithm to further improve the previous variation after projection (VAP) wave functions for low-lying nonyrast states. We attach a weight factor to each calculated energy; then, the sum of these weighted energies is minimized. It turns out that a low-lying nonyrast VAP wave function can be further optimized when the weight factor for the corresponding energy is far larger than the other ones. Based on the improved WVAP wave functions, the energy-variance extrapolation method is applied to estimate the exact shell model energies. The calculated results for nuclei in the and model spaces clearly show that the extrapolated energies for all the calculated states are very close to the exact shell model ones within keV.

Investigation of the tetraquark states in the improved chromomagnetic interaction model* *T. Guo is supported by the Scientific Research Foundation of Chengdu University of Technology (10912-KYQD2022-09557); J. Li and L. He are supported by the National Natural Science Foundation of China (11890712); J. Zhao is supported by the European Union's Horizon 2020 research and innovation program (824093 (STRONG-2020))

In the framework of the improved chromomagnetic interaction model, we complete a systematic study of the S-wave tetraquark states (, and ) with different quantum numbers: , , and . The mass spectra of tetraquark states are predicted, and the possible decay channels are analyzed by considering both the angular momentum and -parity conservation. The recently observed hidden-charm tetraquark states with strangeness, such as , , and , can be well explained in our model. Additionally, according to the wave function of each tetraquark state, we find that the low-lying states of each configuration have a large overlap to the and meson basis, instead of the and meson basis. This indicates that one can search these tetraquark states in future experiments via the channel of and mesons.

Do we need delocalised wavefunctions for the excited state dynamics of 1,1-difluoroethylene?

In this work, we set up a model Hamiltonian to study the excited state quantum dynamics of 1,1-difluoroethylene, a molecule that has equivalent atoms exchanged by a torsional symmetry operation leading to equivalent minima on the potential energy surface. In systems with many degrees of freedom where the minimum energy geometry is not unique, the ground state wavefunction will be delocalised among multiple minima. In this small test system, we probe the excited state dynamics considering localised (in a single minimum) and delocalised (spread over among multiple minima) wavefunctions and check whether this choice would influence the final outcome of the quantum dynamics calculations. Our molecular Hamiltonian comprises seven electronic states, including valence and Rydberg states, computed with the MS-CASPT2 method and projected onto the vibrational coordinates of the twelve normal modes of 1,1-difluoroethylene in its vibrational ground state. This Hamiltonian has been symmetrised along the torsional degree of freedom to make both minima completely equivalent and the model is supported by the excellent agreement with the experimental absorption spectrum. Quantum dynamics results show that the different initial conditions studied do not appreciably affect the excited state populations or the absorption spectrum when the dynamics is simulated assuming a delta pulse excitation.

Big Steve and the State of the Universe

I share some reminiscences of the late Steven Weinberg. Then I discuss a topic in quantum field theory that he taught me: the role of state wave functionals in deriving the iϵ term of the Feynman propagator when using functional formalism. This is perhaps a curiosity for in–out scattering amplitudes on flat-space backgrounds, but it has much greater significance for the in–in amplitudes of the Schwinger–Keldysh formalism in cosmology. It also touches on the fate, about which Weinberg wondered, of the large logarithms one sometimes finds in quantum corrections from inflationary particle production.

Information theoretic measures on the two-photon transitions of hydrogen atom embedded in weakly coupled plasma environment

The quantum information theoretic measures in terms of Shannon entropy and Fisher entropy (both in position and momentum spaces) on the ground, excited as well as virtual states arising out of the two-photon transitions (1s → nl; n = 2 − 4, l = 0, 2) of H atom embedded in classical weakly coupled plasma environment are done for the first time. Fourth order time dependent perturbation theory is adopted within a variational framework for calculating the two photon excitation energies and their respective wavefunctions from an analysis of the pole positions of the non linear response of the system. The representation of virtual state follows from an analysis of the linear response at such poles using a novel method developed by us. Ground and perturbed state wave functions of appropriate symmetries are represented by linear combination of Slater-type orbitals. The analytic form of the momentum space wave functions of ground, excited and virtual states are determined by taking Fourier transformation of the respective position space wave functions. The quantum information measures give interesting insights on the delocalization patterns of the all the real and virtual states under question w.r.t. the increase in plasma strength. The estimated data values are found to be in excellent agreement with the few existing in literature for the ground as well as excited states participating in the two-photon transitions. Such data for the virtual states are completely new and can be set as benchmark for future works in related disciplines.

Solving Schrodinger equations using a physically constrained neural network* *Supported by the National Natural Science Foundation of China (12035006, 12075098), the Natural Science Foundation of Hubei Province (2019CFB563), the Hubei Province Department of Education (D20201108), Hubei Province Department of Science and Technology (2021BLB171)

Deep neural networks (DNNs) and auto differentiation have been widely used in computational physics to solve variational problems. When a DNN is used to represent the wave function and solve quantum many-body problems using variational optimization, various physical constraints have to be injected into the neural network by construction to increase the data and learning efficiency. We build the unitary constraint to the variational wave function using a monotonic neural network to represent the cumulative distribution function (CDF) . Using this constrained neural network to represent the variational wave function, we solve Schrodinger equations using auto-differentiation and stochastic gradient descent (SGD) by minimizing the violation of the trial wave function to the Schrodinger equation. For several classical problems in quantum mechanics, we obtain their ground state wave function and energy with very low errors. The method developed in the present paper may pave a new way for solving nuclear many-body problems in the future.

Strongly Bound Dibaryon with Maximal Beauty Flavor from Lattice QCD.

We report the first lattice QCD study of the heavy dibaryons in which all six quarks have the bottom (beauty) flavor. Performing a state-of-the-art lattice QCD calculation we find clear evidence for a deeply bound Ω_{bbb}-Ω_{bbb} dibaryon in the ^{1}S_{0} channel, as a pole singularity in the S-wave Ω_{bbb}-Ω_{bbb} scattering amplitude with a binding energy -81( _{-16}^{+14}) MeV. With such a deep binding, Coulomb repulsion serves only as a perturbation on the ground state wave function of the parametrized strong potential and may shift the strong binding only by a few percent. Considering the scalar channel to be the most bound for single flavored dibaryons, we conclude this state is the heaviest possible most deeply bound dibaryon in the visible universe.

Resonance Structure of 8Be within the Two-Cluster Resonating Group Method

A microscopic two-cluster model is applied to study the elastic alpha-alpha scattering and the resonance structure of 8Be. The model is an algebraic version of the Resonating Group Method (RGM), which involves the complete set of oscillator functions to expand the wave function of a two-cluster system. The interaction of nucleons inside each cluster and the interaction between clusters are determined by the well-known semirealistic nucleon-nucleon potentials which are employed in calculations. They differ by a size of the core at small distances between nucleons and realize the strong, moderate, and weak cores. They allow us to study dependence of calculated quantities on the shape of a nucleon-nucleon potential. The detailed analysis of resonance wave functions is carried out in the oscillator, coordinate, and momentum spaces. Effects of the Pauli principle on the wave functions of the 8Be continuous spectrum states are thoroughly studied.

Spin, Charge, and η -Spin Separation in One-Dimensional Photodoped Mott Insulators

We show that effectively cold metastable states in one-dimensional photodoped Mott insulators described by the extended Hubbard model exhibit spin, charge, and η-spin separation. Their wave functions in the large on-site Coulomb interaction limit can be expressed as |Ψ⟩=|Ψ_{charge}⟩|Ψ_{spin}⟩|Ψ_{η-spin}⟩, which is analogous to the Ogata-Shiba states of the doped Hubbard model in equilibrium. Here, the η-spin represents the type of photo-generated pseudoparticles (doublon or holon). |Ψ_{charge}⟩ is determined by spinless free fermions, |Ψ_{spin}⟩ by the isotropic Heisenberg model in the squeezed spin space, and |Ψ_{η-spin}⟩ by the XXZ model in the squeezed η-spin space. In particular, the metastable η-pairing and charge-density-wave (CDW) states correspond to the gapless and gapful states of the XXZ model. The specific form of the wave function allows us to accurately determine the exponents of correlation functions. The form also suggests that the central charge of the η-pairing state is 3 and that of the CDW phase is 2, which we numerically confirm. Our study provides analytic and intuitive insights into the correlations between active degrees of freedom in photodoped strongly correlated systems.

Elastic scattering of electrons by water: An ab initio study

In this work we devise a theoretical and computational method to compute the elastic scattering of electrons from a non-spherical potential, such as in the case of molecules and molecular aggregates. Its main feature is represented by the ability of calculating accurate wave functions for continuum states of polycentric systems via the solution of the Lippmann-Schwinger equation, including both the correlation effects and multi-scattering interference terms, typically neglected in widely used approaches, such as the Mott theory. Within this framework, we calculate the purely elastic scattering matrix elements. As a test case, we apply our scheme to the modelling of electron-water elastic scattering. The Dirac-Hartree-Fock self-consistent field method is used to determine the non-spherical molecular potential projected on a functional space spanned by Gaussian basis set. By adding a number of multi-centric radially-arranged s-type Gaussian functions, whose exponents are system-dependent and optimized to reproduce the properties of the continuum electron wave function in different energy regions, we are able to achieve unprecedented access to the description of the low energy range of the spectrum (0.001 < E < 10 eV) up to keV, finding a good agreement with experimental data and previous theoretical results. To show the potential of our approach, we also compute the total elastic scattering cross section of electrons impinging on clusters of water molecules and zundel cation. Our method can be extended to deal with inelastic scattering events and heavy-charged particles.

An ab initio method on large sized molecular aggregate system: Predicting absorption spectra of crystalline organic semiconducting films.

Theoretical description of electronically excited states of molecular aggregates at an ab initio level is computationally demanding. To reduce the computational cost, we propose a model Hamiltonian approach that approximates the electronically excited state wavefunction of the molecular aggregate. We benchmark our approach on a thiophene hexamer, as well as calculate the absorption spectra of several crystalline non-fullerene acceptors, including Y6 and ITIC, which are known for their high power conversion efficiency in organic solar cells. The method qualitatively predicts the experimentally measured spectral shape, which can be further linked to the molecular arrangement in the unit cell.

The reflected entanglement spectrum for free fermions

We consider the reflected entropy and the associated entanglement spectrum for free fermions reduced to two intervals in 1 + 1 dimensions. Working directly in the continuum theory the reflected entropy can be extracted from the spectrum of a singular integral equation whose kernel is determined by the known free fermion modular evolved correlation function. We find the spectrum numerically and analytically in certain limits. For intervals that almost touch the reflected entanglement spectrum approaches the spectrum of the thermal density matrix. This suggests that the reflected entanglement spectrum is well suited to the task of extracting physical data of the theory directly from the ground state wave function.

Correlation in momentum space of Tonks–Girardeau gas

In momentum space, we investigate the correlation properties of the ground state of Tonks–Girardeau gases. With Bose–Fermi mapping method, the exact ground state wavefunction in coordinate space can be obtained based on the wavefunction of spin-polarized Fermions. By Fourier transformation we obtain the ground state wavefunction in momentum space, and therefore the pair correlation and the reduced one-body density matrix (ROBDM) in momentum space, whose diagonal part is the momentum distribution. The ROBDM in momentum space is the Fourier transformation of the ROBDM in coordinate space and the pair correlation in momentum space is the Fourier transformation of the reduced two-body density matrix in coordinate space. The correlations in momentum space display larger values only in small momentum region and vanish in most other regions. The lowest natural orbital and occupation distribution in momentum space are also obtained.

Low-lying bound and resonance states in Λ61Ca and ΛΛ62Ca

In this paper, the energy, and wavefunctions of the low-lying bound and resonance states of [Formula: see text]Ca and [Formula: see text]Ca are studied. For [Formula: see text]Ca we adopted [Formula: see text]Ca two-body cluster model while for [Formula: see text]Ca we adopted [Formula: see text]Ca three-body cluster model. Two models of potentials, namely SH: Hulthén type and WS: Woods–Saxon type potentials, each having a spin-orbit coupling term is chosen for the [Formula: see text]-nucleus pair while three-range Gaussian (TRG) Nijmegen hardcore and softcore potential models are chosen for [Formula: see text] pair. The resulting few-body (two- and three-body) Schrödinger equations are solved numerically to get the bound state energies and wavefunctions. For the three-body calculation, we used hyperspherical coordinates. The formalism of supersymmetric quantum mechanics is applied to construct a one-parameter family of isospectral potential to investigate the resonance states of the [Formula: see text]Ca ([Formula: see text]Ca) core-[Formula: see text] two-body system. To study the effect of replacement of the outer core valence nucleon(s) of [Formula: see text]Ca by [Formula: see text] hyperon(s), two- and three-body cluster model calculations for the bound states of [Formula: see text]Ca and [Formula: see text]Ca are also carried out using the same set of two-body potentials, as used for [Formula: see text]Ca and [Formula: see text]Ca respectively. And a clear enhancement in the one- and two-[Formula: see text] separation energies and a shrinking of the overall size of the nucleus is indicated. The computed results are compared with some of those found in the literature.