Spurious States Research Articles

Ab initio calculation of band alignment of epitaxial La<sub>2</sub>O<sub>3</sub> on Si(111) substrate

By means of plane wave pseudopotential method we have studied the electronic properties of the heterostructure formed by an high dielectric constant (k) oxide, the hexagonal La2O3 epitaxially grown with (0001)-orientation on Si (111) substrate. We found that for La2O3 both the dielectric constant along the growth direction and the band gap are larger in the epitaxial film than in the bulk. By super-cell techniques we have computed the band alignment of the junction finding a valence band offset and a conduction band offset of ~1.6 eV and ~1.7 eV respectively. We demonstrate that the band alignment can be engineered by δ-doping the interface: our simulations show that, by doping the interface with S or Se monolayer, the valence (conduction) band offset increases (decreases) of about 0.5 eV without the formation of spurious electronic states in the semiconductor band-gap. The simulation of the critical thickness of pseudomorphic Lanthana film complete the work. Our results are relevant for the realization of a new generation of devices based on ultra-scaled complementary metal oxides semiconductors (CMOS) technology.

New Possibilities of Harmonic Oscillator Basis Application for Quantum System Description. Two Particles with Coulomb Interaction

This paper is addressed to the problem of Galilei invariant basis construction for identical fermions systems. The recently introduced method for spurious state elimination from expansions in harmonic oscillator basis [1] is adopted and applied to bound states of two particles system with Coulomb potential description. Traditional expansions in this case demonstrate the extremely well-known slow convergence, and hence this is the best problem with known exact solutions for the test of the method. Obtained results demonstrate the significant simplification of the problem and fast convergence of expansions. We show that the application of this general method is very efficient in a test case of the energy spectrum calculation problem of two particles with different masses interacting with Coulomb potential.

Oscillations in Spurious States of the Associative Memory Model with Synaptic Depression

The associative memory model is a typical neural network model, which can store discretely distributed fixed-point attractors as memory patterns. When the network stores the memory patterns extensively, however, the model has other attractors besides the memory patterns. These attractors are called spurious memories. Both spurious states and memory states are equilibrium, so there is little difference between their dynamics. Recent physiological experiments have shown that short-term dynamic synapse called synaptic depression decreases its transmission efficacy to postsynaptic neurons according to the activities of presynaptic neurons. Previous studies have shown that synaptic depression induces oscillation in the network and decreases the storage capacity at finite temperature. How synaptic depression affects spurious states, however, is still unclear. We investigate the effect of synaptic depression on spurious states through Monte Carlo simulation. The results demonstrate that synaptic depression does not affect the memory states but mainly destabilizes the spurious states and induces the periodic oscillations.

Qualitatively Incorrect Features in the TDDFT Spectrum of Thiophene-Based Compounds.

Ab initio molecular electronic structure computations of thiophene-based compounds constitute an active field of research prompted by the growing interest in low-cost materials for organic electronic devices. In particular, the modeling of electronically excited states and other time-dependent phenomena has moved toward the description of more realistic albeit challenging systems. We demonstrate that due to its underlying approximations, time-dependent density functional theory predicts results that are qualitatively incorrect for thiophene and thienoacenes, although not for oligothiophene chains. The failure includes spurious state inversion and excitation characters, wrong distribution of oscillator strengths and erroneous potential energy surfaces. We briefly analyze possible origins of this behavior and identify alternative methods that alleviate these problems.

Extensive parallel processing on scale-free networks.

We adapt belief-propagation techniques to study the equilibrium behavior of a bipartite spin glass, with interactions between two sets of N and P=αN spins each having an arbitrary degree, i.e., number of interaction partners in the opposite set. An equivalent view is then of a system of N neurons storing P diluted patterns via Hebbian learning, in the high storage regime. Our method allows analysis of parallel pattern processing on a broad class of graphs, including those with pattern asymmetry and heterogeneous dilution; previous replica approaches assumed homogeneity. We show that in a large part of the parameter space of noise, dilution, and storage load, delimited by a critical surface, the network behaves as an extensive parallel processor, retrieving all P patterns in parallel without falling into spurious states due to pattern cross talk, as would be typical of the structural glassiness built into the network. Parallel extensive retrieval is more robust for homogeneous degree distributions, and is not disrupted by asymmetric pattern distributions. For scale-free pattern degree distributions, Hebbian learning induces modularity in the neural network; thus, our Letter gives the first theoretical description for extensive information processing on modular and scale-free networks.

Electroexcitation of Low-Lying Particle-Hole RPA States of 16O with WBP Interaction

The nuclear structure of 16O is studied in the framework of the particle-hole random phase approximation (ph RPA). The Hamiltonian is diagonalized within a model space with particle orbits {1d5/2,1d3/2, and 2s1/2} and the hole orbits {1p3/2 and 1p1/2} using Warburton and Brown interaction WBP. The ph RPA calculations are tested, by comparing the electron scattering form factors with the available experimental data. The results of electron scattering form factors and reduced transition strength for the states: 1−, T = 0 (7.116 MeV); 2−, T = 1 (12.968 MeV); 2−, T = 1 (20.412 MeV); and 3−, T = 0 (6.129 MeV) are interpreted in terms of the harmonic-oscillator (HO) wave functions of size parameter b. The occupation probabilities of the single particle and hole orbits are calculated. The spurious states are removed by adding the center of mass (CM) correction to the nuclear Hamiltonian. A comparison with the available experiments data is presented.

Second random-phase approximation, Thouless' theorem, and the stability condition reexamined and clarified

It has been revealed through numerical calculations that the Second Random Phase Approximation (SRPA) with the Hartree-Fock solution as its reference state results in 1) spurious states at genuinely finite energy, contrary to common expectation, and 2) unstable solutions, which within the first-order Random Phase Approximation correspond to real low-energy collective vibrations. In the present work, these shortcomings of SRPA are shown to not contradict Thouless' theorem about the energy-weighted sum rule, and their origin is traced to the violation of the stability condition. A more general theorem is proven. Formal arguments are elucidated through numerical examples. Implications for the validity of SRPA are discussed.

Structural State Dependence and Consumers' Unobserved Heterogeneity: A Case Study of the U.S. Coffee Market

In many markets of differentiated products, consumers show persistence in their consumption choices. Understanding how past consumption affects consumers' current choices and distinguishing different explanations are beneficial for price setting. In this paper, a discrete choice model is used to investigate the state dependence effect on the U.S. coffee market. Using a disaggregate data set that captures a detailed purchase history and demographic information for a massive number of consumers, I first estimate the spurious state dependence effect without assuming consumer heterogeneity. I then consider both structural state dependence and consumers' unobserved heterogeneity and distinguish those two effects by applying the discrete mass point algorithm semiparametrically. I further explore the potential correlated errors and endogeneity problem and compare the various methods to solve them. My findings show that structural state dependence and consumers' unobserved heterogeneity are the main explanations for the observed consumption persistence in the U.S. coffee market. My findings also suggest that there exist two types of consumers in the U.S. coffee market: one type treats ground coffee as normal goods and the other treats ground coffee as inferior goods. The structural state dependence is positive and significant for one type of consumers and negative for the other type of consumers.

Dual Kinetic Balance Approach to Basis-Set Expansions for axially symmetric Dirac equation

The study of the interaction of highly charged ions with laser fields requires solving the time-dependent Dirac equation. The Dual Kinetic Balance (DKB) technique enables one to eliminate the spurious states occurring in the numerical solutions of the Dirac equation obtained with finite basis set methods. Initially developed for the radial Dirac equation, here the DKB method is generalized to the three-dimensional systems with the axial symmetry. Efficiency of the method is demonstrated by calculating the spectra of hydrogenlike ions and the ionization probability of a H-like ion by a laser pulse.

Dual-kinetic-balance approach to the Dirac equation for axially symmetric systems: Application to static and time-dependent fields

Dual kinetic balance (DKB) technique was previously developed to eliminate spurious states in the finite-basis-set-based solution of the Dirac equation in central fields. In the present paper, it is extended to the Dirac equation for systems with axial symmetry. The efficiency of the method is demonstrated by the calculation of the energy spectra of hydrogenlike ions in presence of static uniform electric or magnetic fields. In addition, the DKB basis set is implemented to solve the time-dependent Dirac equation making use of the split-operator technique. The excitation and ionization probabilities for the hydrogenlike argon and tin ions exposed to laser pulses are evaluated.

Independent bases on the spatial wavefunction of four-identical-particle systems

We construct the independent bases on the spatial wavefunction of four-identical-particle systems classified under the rotational group SO(3) and the permutation group S4 with the usage of transformation coefficients that relate wavefunctions described in one set of internal coordinates with those in another. The basis functions for N ⩽ 2 are presented in the explicit expressions based on the harmonic oscillator model. Such independent bases are supposed to play a key role in the construction of the wavefunctions of the five-quark states and the variation calculation of four-body systems. Our prescription avoids the spurious states and can be programmed for arbitrary N.

30-bandk·pmodel of electron and hole states in silicon quantum wells

We modeled the electron and hole states in Si/SiO2 quantum wells within a basis of standing waves using the 30-band k.p theory. The hard-wall confinement potential is assumed, and the influence of the peculiar band structure of bulk silicon on the quantum-well sub-bands is explored. Numerous spurious solutions in the conduction-band and valence-band energy spectra are found and are identified to be of two types: (1) spurious states which have large contributions of the bulk solutions with large wave-vectors (the high-k spurious solutions) and (2) states which originate mainly from the spurious valley outside the Brillouin zone (the extra-valley spurious solutions). An algorithm to remove all those nonphysical solutions from the electron and hole energy spectra is proposed. Furthermore, slow and oscillatory convergence of the hole energy levels with the number of basis functions is found and is explained by the peculiar band mixing and the confinement in the considered quantum well. We discovered that assuming the hard-wall potential leads to numerical instability of the hole states computation. Nonetheless, allowing the envelope functions to exponentially decay in a barrier of finite height is found to improve the accuracy of the computed hole states.

Computational Studies of the Electronic Absorption Spectrum of [(2,2′;6′,2″-Terpyridine)–Pt(II)–OH] [7,7,8,8-Tetracyanoquinodimethane] Complex

The electronic excitation spectrum of the [(2,2';6',2″-terpyridine)-platinum(II)-OH] [7,7,8,8-tetracyanoquinodimethane] ([Pt(trpy)OH]TCNQ) complex has been studied at the linear-response approximate coupled-cluster singles and doubles (CC2) level using triple-ζ basis sets augmented with polarization functions (TZVP). The calculated ultraviolet-visible (UV-vis) spectrum of the [Pt(trpy)OH]TCNQ complex is compared with the UV-vis spectrum measured for [Pt(tbtrpy)OH]TCNQ (tbtrpy = 4,4',4″-(t)Bu3-2,2';6',2″-terpyridine) in dichloromethane (CH2Cl2) solution. The UV-vis spectrum is also compared with the calculated UV-vis spectra of [Pt(trpy)OH](+) and of the neutral and negatively charged TCNQ species. In contrast to previous interpretations, the CC2 calculations suggest that the [Pt(trpy)OH]TCNQ complex is dissociated into [Pt(trpy)OH](+) and TCNQ(-) when dissolved in CH2Cl2. The computed electronic excitation energies of [Pt(trpy)OH](+) provide information about the charge-transfer excitations between the Pt(II) metal center and the ligands. The UV-vis spectra were also calculated at the linear-response time-dependent density functional theory (TDDFT) level using the B3LYP, BHLYP, and CAM-B3LYP functionals in combination with TZVP quality basis sets. For the TCNQ species, the TDDFT calculations yield slightly smaller excitation energies than obtained at the CC2 level, whereas for [Pt(trpy)OH](+) the CC2 excitation energies are slightly smaller than the TDDFT ones. For the [Pt(trpy)OH]TCNQ complex, the B3LYP calculations yield spurious low-lying excited states rendering the spectral assignment using B3LYP data difficult. The low-energy part of the electronic excitation spectrum for the [Pt(trpy)OH]TCNQ complex calculated at the BHLYP and CAM-B3LYP levels is reminiscent of the CC2 one because the larger amount of Hartree-Fock exchange and the long-range correction of the potential blue shifts the excitation energies.

Magnetically defined qubits on 3D topological insulators.

We explore potentials that break time-reversal symmetry to confine the surface states of 3D topological insulators into quantum wires and quantum dots. A magnetic domain wall on a ferromagnet insulator cap layer provides interfacial states predicted to show the quantum anomalous Hall effect (QAHE). Here, we show that confinement can also occur at magnetic domain heterostructures, with states extended in the inner domain, as well as interfacial QAHE states at the surrounding domain walls. The proposed geometry allows the isolation of the wire and dot from spurious circumventing surface states. For the quantum dots, we find that highly spin-polarized quantized QAHE states at the dot edge constitute a promising candidate for quantum computing qubits.

Quantitatively Correct UV-vis Spectrum of Ferrocene with TDB3LYP.

The ultraviolet-visible light (UV-vis) absorption spectrum of ferrocene is modeled with time-dependent density functional theory employing LSDA, BLYP, B3LYP, and CAM-B3LYP functionals in combination with 6-31G*, 6-31+G*, CC-PVTZ, and aug-CC-PVTZ basis sets. With the exception of LSDA, all functionals predict a reasonable Fe-CP distance of ∼1.67 Å. Diffuse functions are essential for the strongly allowed states at high energy but of lesser consequence for the visible range of the spectrum. Dipole forbidden states are examined with vibrationally excited structures, obtained from the normal modes of the infrared (IR) spectrum. Despite earlier claims, TDB3LYP predicts the UV-vis spectrum of ferrocene quantitatively correct. TDBLYP predicts a large number of spurious charge-transfer states, TDCAM-B3LYP and TDwB97XD are correct in the low-energy region but overestimate the energy of strongest peak of the spectrum by 0.8 eV. The amount of charge transfer involved in "d-d transitions" is equal to that in "charge-transfer states".

GETTING STUCK IN THE BLUES: PERSISTENCE OF MENTAL HEALTH PROBLEMS IN AUSTRALIA

Do episodes of mental health (MH) problems cause future MH problems, and if yes, how strong are these dynamics? We quantify the degree of persistence in MH problems using nationally representative, longitudinal data from Australia and system generalized method of moments (GMM), and correlated random effects approaches are applied to separate true from spurious state dependence. Our results suggest only a moderate degree of persistence in MH problems when assuming that persistence is constant across the MH distribution once individual-specific heterogeneity is accounted for. However, individuals who fell once below a threshold that indicates an episode of depression are up to five times more likely to experience such a low score again a year later, indicating a strong element of state dependence in depression. Low income is a strong risk factor in state dependence for both men and women, which has important policy implications.

Assessment of the Performance of Long-Range-Corrected Density Functionals for Calculating the Absorption Spectra of Silver Clusters

We assess the accuracy of several long-range-corrected (LC-) density functionals for the prediction of absorption spectra of silver clusters by time-dependent density functional theory. Several types of LC-functionals, with the exact Hartree-Fock exchange at long-range, are used: those applying the long-range correction to a standard GGA-type functional (LC-BP86, LC-ωPBE) or to a local meta-GGA functional (LC-M06L) and two global hybrid functionals (CAM-B3LYP and ωB97x). The spectra calculated with those density functionals are in good agreement with the recent accurate experimental measurements. We show that CAM-B3LYP and ωB97x are some of the most accurate functionals for evaluating the electronic excitation energies, while LC-M06L is more effective in reducing the occurrence of spurious states. The long-range correction appears to be essential in describing the absorption spectra of large clusters. The description of the plasmon-like band with LC functionals as transitions associated with excitations from s orbitals to s + p orbitals is in fairly good agreement with the classical interpretation as a collective excitation of valence s electrons.

Multidimensional Supersymmetric Quantum Mechanics: Spurious States for the Tensor Sector Two Hamiltonian

We show that there exist spurious states for the sector two tensor Hamiltonian in multidimensional supersymmetric quantum mechanics. For one-dimensional supersymmetric quantum mechanics on an infinite domain, the sector one and two Hamiltonians have identical spectra with the exception of the ground state of the sector one. For tensorial multidimensional supersymmetric quantum mechanics, there exist normalizable spurious states for the sector two Hamiltonian with energy equal to the ground state energy of the sector one. These spurious states are annihilated by the adjoint charge operator, and hence, they do not correspond to physical states for the original Hamiltonian. The Hermitian property of the sector two Hamiltonian implies the orthogonality between spurious and physical states. In addition, we develop a method for construction of a specific form of the spurious states for any quantum system and also generate several spurious states for a two-dimensional anharmonic oscillator system and for the hydrogen atom.

Getting Stuck in the Blues: Persistence of Mental Health Problems in Australia

Do episodes of mental health problems cause future mental health problems, and if yes, how strong are these dynamics? We quantify the degree of persistence in mental health problems using nationally-representative, longitudinal data from Australia and system GMM-IV and correlated random effects approaches are applied to separate true from spurious state dependence. Our results suggest only a moderate degree of persistence in mental health problems when assuming that persistence is constant across the mental health distribution once individual-specific heterogeneity is accounted for. However, individuals who fell once below a threshold that indicates an episode of depression are up to five times more likely to experience such a low score again a year later, indicating a strong element of state dependence in depression. Low income is a strong risk factor in state dependence for both men and women, which has important policy implications.

Multitasking Associative Networks

We introduce a bipartite, diluted and frustrated, network as a sparse restricted Boltzmann machine and we show its thermodynamical equivalence to an associative working memory able to retrieve several patterns in parallel without falling into spurious states typical of classical neural networks. We focus on systems processing in parallel a finite (up to logarithmic growth in the volume) amount of patterns, mirroring the low-level storage of standard Amit-Gutfreund-Sompolinsky theory. Results obtained through statistical mechanics, the signal-to-noise technique, and MonteCarlo simulations are overall in perfect agreement and carry interesting biological insights. Indeed, these associative networks pave new perspectives in the understanding of multitasking features expressed by complex systems, e.g., neural and immune networks.