Effective Hamiltonian Operator Research Articles

Linearized Pair-Density Functional Theory.

Multiconfiguration pair-density functional theory (MC-PDFT) is a post-SCF multireference method that has been successful at computing ground- and excited-state energies. However, MC-PDFT is a single-state method in which the final MC-PDFT energies do not come from diagonalization of a model-space Hamiltonian matrix, and this can lead to inaccurate topologies of potential energy surfaces near locally avoided crossings and conical intersections. Therefore, in order to perform physically correct ab initio molecular dynamics with electronically excited states or to treat Jahn-Teller instabilities, it is necessary to develop a PDFT method that recovers the correct topology throughout the entire nuclear configuration space. Here we construct an effective Hamiltonian operator, called the linearized PDFT (L-PDFT) Hamiltonian, by expanding the MC-PDFT energy expression to first order in a Taylor series of the wave function density. Diagonalization of the L-PDFT Hamiltonian gives the correct potential energy surface topology near conical intersections and locally avoided crossings for a variety of challenging cases including phenol, methylamine, and the spiro cation. Furthermore, L-PDFT outperforms MC-PDFT and previous multistate PDFT methods for predicting vertical excitations from a variety of representative organic chromophores.

An operator-based approach to topological photonics

Abstract Recently, the study of topological structures in photonics has garnered significant interest, as these systems can realize robust, nonreciprocal chiral edge states and cavity-like confined states that have applications in both linear and nonlinear devices. However, current band theoretic approaches to understanding topology in photonic systems yield fundamental limitations on the classes of structures that can be studied. Here, we develop a theoretical framework for assessing a photonic structure’s topology directly from its effective Hamiltonian and position operators, as expressed in real space, and without the need to calculate the system’s Bloch eigenstates or band structure. Using this framework, we show that nontrivial topology, and associated boundary-localized chiral resonances, can manifest in photonic crystals with broken time-reversal symmetry that lack a complete band gap, a result that may have implications for new topological laser designs. Finally, we use our operator-based framework to develop a novel class of invariants for topology stemming from a system’s crystalline symmetries, which allows for the prediction of robust localized states for creating waveguides and cavities.

The NOSL-296 high resolution 14N216O line list for atmospheric applications

The Nitrous Oxide Spectroscopic Line list (NOSL-296) presented in this work is an empirical line list for the main isotopologue of nitrous oxide, 14N216O, mainly dedicated to atmospheric applications. It contains line positions and intensities at a reference temperature of 296 K calculated using the effective operator approach. The intensity cutoff is 10−30 cm/molecule. Almost 900,000 lines covering the 0.02–13,378 cm−1 spectral range are included in NOSL-296. The line list is based on the fitted non-polyad models of the effective Hamiltonian and effective dipole moment operator describing globally an exhaustive review of experimental data collected from the literature (more than 51,500 line intensities). The non-polyad model of effective Hamiltonian has been elaborated in [Tashkun SA, J Quant Spectrosc Radiat Transfer 2019;231:88–101, doi:10.1016/j.jqsrt.2019.04.023] while the non-polyad model of the effective dipole moment operator is developed in the present work. The fitted models are able to reproduce measured positions and intensities with accuracies compatible with measurement uncertainties. Comparison of NOSL-296 with HITRAN2020 and Ames-296 line lists are discussed. The NOSL-296 line list is provided as a Supplementary Material and freely accessible at https://ftp.iao.ru/pub/LTS/NOSL-296/.

Negativity Hamiltonian: An Operator Characterization of Mixed-State Entanglement.

In the context of ground states of quantum many-body systems, the locality of entanglement between connected regions of space is directly tied to the locality of the corresponding entanglement Hamiltonian: the latter is dominated by local, few-body terms. In this work, we introduce the negativity Hamiltonian as the (non-Hermitian) effective Hamiltonian operator describing the logarithm of the partial transpose of a many-body system. This allows us to address the connection between entanglement and operator locality beyond the paradigm of bipartite pure systems. As a first step in this direction, we study the structure of the negativity Hamiltonian for fermionic conformal field theories and a free-fermion chain: in both cases, we show that the negativity Hamiltonian assumes a quasilocal functional form, that is captured by simple functional relations.

Shell-model calculation of Mo100 double- β decay

For the first time, the calculation of the nuclear matrix element of the double-$\beta$ decay of $^{100}$Mo, with and without the emission of two neutrinos, is performed in the framework of the nuclear shell model. This task is accomplished starting from a realistic nucleon-nucleon potential, then the effective shell-model Hamiltonian and decay operators are derived within the many-body perturbation theory. The exotic features which characterize the structure of Mo isotopes -- such as shape coexistence and triaxiality softness -- push the shell-model computational problem beyond its present limits, making it necessary to truncate the model space. This has been done with the goal to preserve as much as possible the role of the rejected degrees of freedom in an effective approach that has been introduced and tested in previous studies. This procedure is grounded on the analysis of the effective single-particle energies of a large-scale shell-model Hamiltonian, that leads to a truncation of the number of the orbitals belonging to the model space. Then, the original Hamiltonian generates a new one by way of a unitary transformation onto the reduced model space, to retain effectively the role of the excluded single-particle orbitals. The predictivity of our calculation of the nuclear matrix element for the neutrinoless double-$\beta$ decay of $^{100}$Mo is supported by the comparison with experiment of the calculated spectra, electromagnetic transition strengths, Gamow-Teller transition strengths and the two-neutrino double-beta nuclear matrix elements.

Perturbative Approach to Effective Shell-Model Hamiltonians and Operators

The aim of this work is to present an overview of the derivation of the effective shell-model Hamiltonian and decay operators within many-body perturbation theory, and to show the results of selected shell-model studies based on their utilisation. More precisely, we report some technical details that are needed by non-experts to approach the derivation of shell-model Hamiltonians and operators starting from realistic nuclear potentials, in order to provide some guidance to shell-model calculations where the single-particle energies, two-body matrix elements of the residual interaction, effective charges and decay matrix elements, are all obtained without resorting to empirical adjustments. On the above grounds, we will present results of studies of double-beta decay of heavy-mass nuclei where shell-model ingredients are derived from theory, so to assess the reliability of such a way to shell-model investigations. Attention will be also focussed on the relevant aspects that are connected to the behavior of the perturbative expansion, whose knowledge is needed to establish limits and perspectives of this approach to nuclear structure calculations.

Probing early universe with a generalized action

Possibly, the most general action in the background of isotropic and homogeneous space–time has been considered to study the quantum evolution of the early universe, apart from a cosmological constant. The hermiticity of the effective Hamiltonian operator in the presence of curvature squared terms suggests unitary time evolution of the quantum states, assuring conservation of probability. The oscillatory behaviour of the semi-classical wavefunction around a de-Sitter solution signals that the theory is classically allowed, and the universe enters an inflationary regime just after Planck’s era. In view of a hierarchy of Hubble flow parameters, and using a redefined effective potential, the complicated classical field equations in the presence of several coupling parameters, reduce to standard general-relativistic equations with a single scalar field. As a result, inflation has been studied without considering any additional flow parameters. Inflationary parameters lie very much within the presently available Planck’s data, and the model admits graceful exit from inflation.

Calculation of the neutrinoless double- β decay matrix element within the realistic shell model

We approach the calculation of the nuclear matrix element of the neutrinoless double-beta decay process, considering the light-neutrino-exchange channel, by way of the realistic shell model. To this end, we start from a realistic nucleon-nucleon potential and then derive the effective shell-model Hamiltonian and neutrinoless double-beta decay operator within the many-body perturbation theory. We focus on investigating the perturbative properties of the effective shell-model operator of such a decay process, aiming to establish the degree of reliability of our predictions. The contributions of the so-called short-range correlations and of the correction of Pauli-principle violations to the effective shell-model operator, the latter introduced in many-valence nucleon systems, are also taken into account. The subjects of our study are a few candidates to the neutrinoless double-beta decay detection, in a mass interval ranging from A=48 up to A=136, whose spin- and spin-isospin-dependent decay properties we have studied in previous works. Our results will be finally compared with shell-model calculations for the same set of nuclei.

Renormalization of the Gamow-Teller operator within the realistic shell model

In nuclear structure calculations, the choice of a limited model space, due to computational needs, leads to the necessity to renormalize the Hamiltonian as well as any transition operator. Here, we present a study of the renormalization procedure and effects of the Gamow-Teller operator within the framework of the realistic shell model. Our effective shell-model operators are obtained, starting from a realistic nucleon-nucleon potential, by way of the many-body perturbation theory in order to take into account the degrees of freedom that are not explicitly included in the chosen model space. The theoretical effective shell-model Hamiltonian and transition operators are then employed in shell-model calculations, whose results are compared with data of Gamow-Teller transition strengths and double-beta half-lives for nuclei which are currently of interest for the detection of the neutrinoless double-beta decay process, in a mass interval ranging from A=48 up to A=136. We show that effective operators are able to reproduce quantitatively the spectroscopic and decay properties without resorting to an empirical quenching neither of the axial coupling constant gA, nor of the spin and orbital gyromagnetic factors. This should assess the reliability of applying present theoretical tools to this problematic.

Line positions and intensities in the ν2 fundamental band of sulfuryl fluoride using the C2v top data system

New experimental high-resolution Fourier-Tansform infrared spectra of the infrared active fundamental ν2 band of sulfuryl fluoride SO2F2, have been recorded at a temperature of 193 K and at resolution of 0.00102 cm−1 at the AILES (Advanced Infrared Line Exploited for Spectroscopy) beamline of the SOLEIL (Source Optimisée de Lumière d’Energie intermédiaire du LURE) Synchrotron facility. A detailed analysis has been performed both in line positions and intensities with the C2vTDS (Top Data System) program suite, based on the tensorial formalism developed in Dijon for quasi-spherical top molecules. The effective Hamiltonian was developed up to fourth order. The parameter of the effective dipole moment operator has been determined using the wavefunctions of the effective Hamiltonian operator. 2407 line positions have been measured with global root mean square deviation of about 0.19 × 10−3 cm−1. Using 71 lines intensities, we estimate the uncertainty on calculated line intensities to 10%. To the extent of our knowledge, this is the first time that an absolute intensity analysis has been carried out for sulfuryl fluoride.

Two-neutrino Double-Beta Decay within the Realistic Shell Model

We report on the calculation of double-β decay properties of 130Te and 136Xe within the framework of the realistic shell model. The effective shell-model Hamiltonian and Gamow-Teller transition operator are derived by way of many-body perturbation theory, in order to not to resort to an empirical quenching of the axial coupling constant gA. The results compare well with experimental data, paving the way to the calculation of the neutrinoless double-β decay nuclear matrix element for the nuclei that are currently the experimental target for the detection of this process. In this work we investigate about the perturbative properties of our approach, and the theoretical reliability of the realistic shell model.

Realistic shell model description of beta decay

In this paper, we extend our previous realistic shell-model study of Gamow-Teller strengths and double-β decay properties for nuclei around 132Sn to lighter mass nuclei. The effective shell-model Hamiltonian and transition operators are microscopically derived by way of many-body perturbation theory, without resorting to empirical parameters. Our main aim is to further check the reliability of our approach and verify its stability in other mass regions. Calculated energy spectra as well as electric-quadrupole and β-decay properties are presented for 76Ge and 82Se and compared with the experimental data, together with some results for 130Te and 136Xe already reported in our previous paper. Finally, some preliminary results of nuclear matrix elements responsible for the neutrinoless double beta decay, calculated by using the bare operator, are shown.

Calculation of Gamow-Teller and two-neutrino double- β decay properties for Te130 and Xe136 with a realistic nucleon-nucleon potential

We report on the calculation of Gamow-Teller and double-beta decay properties for nuclei around 132Sn within the framework of the realistic shell model. The effective shell-model Hamiltonian and Gamow-Teller transition operator are derived by way of many-body perturbation theory, without resorting to empirical effective quenching factor for the Gamow-Teller operator. The results are then compared with the available experimental data, in order to establish the reliability of our approach. This is a mandatory step, before we apply the same methodology, in forthcoming studies, to the calculation of the neutrinoless double-beta decay nuclear matrix element for nuclei that are currently considered among the best candidates for the detection of this process.

Asymptotic freedom in the Hamiltonian approach to binding of color

We derive asymptotic freedom and the SU(3) Yang-Mills β-function using the renormalization group procedure for effective particles. In this procedure, the concept of effective particles of size s is introduced. Effective particles in the Fock space build eigenstates of the effective Hamiltonian Hs, which is a matrix written in a basis that depend on the scale (or size) parameter s. The effective Hamiltonians Hs and the (regularized) canonical Hamiltonian H0 are related by a similarity transformation. We calculate the effective Hamiltonian by solving its renormalization-group equation perturbatively up to third order and calculate the running coupling from the three-gluon-vertex function in the effective Hamiltonian operator.

Quantum-statistical approach to electromagnetic wave propagation and dissipation inside dielectric media and nanophotonic and plasmonic waveguides

Quantum-statistical effects occur during the propagation of electromagnetic (EM) waves inside the dielectric media or metamaterials, which include a large class of nanophotonic and plasmonic waveguides with dissipation and noise. Exploiting the formal analogy between the Schrodinger equation and the Maxwell equations for dielectric linear media, we rigorously derive the effective Hamiltonian operator which describes such propagation. This operator turns out to be essentially non-Hermitian in general, and pseudo-Hermitian in some special cases. Using the density operator approach for general non-Hermitian Hamiltonians, we derive a master equation that describes the statistical ensembles of EM wave modes. The method also describes the quantum dissipative and decoherence processes which happen during the wave's propagation, and, among other things, it reveals the conditions that are necessary to control the energy and information loss inside the above-mentioned materials.

NOSD-1000, the high-temperature nitrous oxide spectroscopic databank

We present a high-temperature version, NOSD-1000, of the nitrous oxide spectroscopic databank. The databank contains the line parameters (positions, intensities, air- and self-broadened half-widths and coefficients of temperature dependence of air- and self-broadened half-widths) of the most abundant isotopologue 14N216O of the nitrous oxide molecule. The reference temperature is Tref=1000K and the intensity cutoff is Icut=10−25cm−1/(molecule cm−2). More than 1.4 million lines covering the 260–8310cm−1 spectral range are included in NOSD-1000. The databank has been generated within the framework of the method of effective operators and based on the global fittings of spectroscopic parameters (parameters of the effective Hamiltonian and effective dipole moment operators) to observed data collected from the literature. Line-by-line simulation of a medium-resolution high-temperature (T=873K) spectrum has been performed in order to validate the databank. NOSD-1000 is freely accessible via the Internet.

Two-photon excitation to autoionizing states of He detected via radiative cascades to the metastable states

We present a detailed theoretical study of two-photon above-threshold excitation to the lowest dipole forbidden ${}^{1}{S}^{e}$ and ${}^{1}{D}^{e}$ autoionizing states of helium with free-electron-laser pulses. We consider the case where the formation of these transient states is detected by monitoring the yield of atoms in the metastable $1s2s$ states, which are reached in the radiative cascade decays of the autoionizing states. We describe the two-photon near-resonant driving with an effective Hamiltonian operator within the density matrix formalism, and we report the relevant parameters of the model, such as the field-induced shifts, the effective Rabi frequencies, and the cascade branching ratios of both the autoionizing states and the $1sn\ensuremath{\ell}$ states, to which the autoionizing states decay. We compare the calculated metastable atom yield to the vacuum ultraviolet florescence yield and to the electron yield. We discuss the effects of the intensity of the source, admixture of higher harmonics in the incident beam, polarization of the incident light, and the pulse chirp on the metastable atom yield.

Photoluminescence and Crystal-Field Analysis of Pr3+-Doped SrMoO4 Phosphors

Abstract The phosphor SrMoO4:Pr3+ was successfully prepared by high-temperature solid-state reaction process, and characterised by X-ray diffraction (XRD), scanning electron microscope (SEM), and fluorescence spectrometer. The results show that the prepared SrMoO4:Pr3+ has a scheelite structure with pure phase and represents leaf-like shapes with good dispersity. The strong electron absorbabilities are located at 220–300 nm (charge transfer band), 448, 474, and 487 nm, respectively. The emission spectrum of the SrMoO4:Pr3+ phosphor was characterised, which peaked at 529, 545, 554, 600, 619, and 645 nm, corresponding to the f–f transitions of Pr3+. The average International Commission on Illumination (CIE) chromaticity coordinates of the phosphors are x≈0.455, and y≈0.520, and the optimum doping mole fraction of Pr3+ is 0.2 mol.%. To better understand the fluorescent behavior of as-prepared phosphors, a complete 91×91 energy matrix was built by an effective Hamiltonian operator, including free ion and crystal-field interactions. The fluorescent spectra of Pr3+ ion at the tetragonal (S 4) Sr2+ site of SrMoO4 crystal were firstly calculated from a full diagonalisation (of energy matrix) method. The fitting values are in good agreement with the experimental data.

Analysis of self-consistent extended Hückel theory (SC-EHT): a new look at the old method

We present an extensive analysis of the self-consistent extended Huckel theory (SC-EHT) and discuss the possibilities of constructing accurate and efficient semiempirical methods on its basis. We describe the mapping approach to derive a self-consistency correction to the effective 1-electron Hamiltonian (Fock) operator that is utilized in electronic structure calculations and that variationally minimizes the total energy in the SC-EHT method. We show that the SC-EHT Hamiltonian can play the role of the 1-electron operator by definition, in which case no self-consistency correction is needed. Then, the SC-EHT method can be derived from the Hartree–Fock theory by approximation of the Fock matrix. Therefore, the SC-EHT based methods have rigorous foundations that may be utilized to develop a family of successively accurate model Hamiltonians. We analyze the underlying approximation and discuss it in the light of existing formulations of the EHT method. We indicate two major deficiencies of the existing formulations of the EHT method—neglect of exchange integrals and incorrect asymptotic behavior of the Coulomb integrals. The SC-EHT is compared to the charge equilibration scheme and to the DFTB family of approximations. We show that an improved version of the SC-EHT method can be connected to both of them, indicating relation of the SC-EHT derived approximations to the fundamental DFT origins and their potential for efficient computations on large-scale systems.

Intramolecular Vibrational Spectra of Benzene and its Derivatives in CC, CH and CD Local Mode Interaction

Lie algebraic method is based on the idea of dynamic symmetry, which can be expressed in terms of U(2) Lie algebra. By applying algebraic approach, an effective Hamiltonian operator can be obtained which conveniently describes the rovibrational degrees of freedom of benzene and its derivatives. Here, every CC, CH, CD bonds of the molecule are replaced by a corresponding U(2) Lie algebra and finally the local Hamiltonian is constructed considering the invariant Casimir and Majorana operators. The fundamental modes are then calculated using this Hamiltonian to fit the results of the theoretical as well as experimental observations.