Relevant Wave Functions Research Articles

Generating QES potentials supporting zero energy normalizable states for an extended class of truncated Calogero Sutherland model

Motivated by recent interest in the search for generating potentials for which the underlying Schrödinger equation is solvable, we report in the recent work several situations when a zero-energy state becomes bound depending on certain restrictions on the coupling constants that define the potential. In this regard, we present evidence of the existence of regular zero-energy normalizable solutions for a system of quasi-exactly solvable (QES) potentials that correspond to the rationally extended many-body truncated Calogero–Sutherland (TCS) model. Our procedure is based upon the use of the standard potential group approach with an underlying so(2,1) structure that utilizes a point canonical transformation with three distinct types of potentials emerging having the same eigenvalues while their common properties are subjected to the evaluation of the relevant wave functions. These cases are treated individually by suitably restricting the coupling parameters.

Quantification of chirality based on electric toroidal monopole.

Chirality ubiquitously appears in nature; however, its quantification remains obscure owing to the lack of microscopic description at the quantum-mechanical level. We propose a way of evaluating chirality in terms of the electric toroidal monopole, a practical entity of time-reversal even pseudoscalar (parity-odd) objects reflecting relevant electronic wave functions. For this purpose, we analyze a twisted methane molecule at the quantum-mechanical level, showing that the electric toroidal monopoles become a quantitative indicator for chirality. In the twisted methane, we clarify that the handedness of chirality corresponds to the signof the expectation value of the electric toroidal monopole and that the most important ingredient is the modulation of the spin-dependent imaginary hopping between the hydrogen atoms, while the relativistic spin-orbit coupling within the carbon atom is irrelevant for chirality.

Quantum Circuits for the Preparation of Spin Eigenfunctions on Quantum Computers

The application of quantum algorithms to the study of many-particle quantum systems requires the ability to prepare wave functions that are relevant in the behavior of the system under study. Hamiltonian symmetries are important instruments used to classify relevant many-particle wave functions and to improve the efficiency of numerical simulations. In this work, quantum circuits for the exact and approximate preparation of total spin eigenfunctions on quantum computers are presented. Two different strategies are discussed and compared: exact recursive construction of total spin eigenfunctions based on the addition theorem of angular momentum, and heuristic approximation of total spin eigenfunctions based on the variational optimization of a suitable cost function. The construction of these quantum circuits is illustrated in detail, and the preparation of total spin eigenfunctions is demonstrated on IBM quantum devices, focusing on three- and five-spin systems on graphs with triangle connectivity.

Significance of the Chemical Environment of an Element in Nonadiabatic Molecular Dynamics: Feature Selection and Dimensionality Reduction with Machine Learning.

Using supervised and unsupervised machine learning (ML) on features generated from nonadiabatic (NA) molecular dynamics (MD) trajectories under the classical path approximation, we demonstrate that mutual information with the NA Hamiltonian can be used for feature selection and model simplification. Focusing on CsPbI3, a popular metal halide perovskite, we observe that the chemical environment of a single element is sufficient for predicting the NA Hamiltonian. The conclusion applies even to Cs, although Cs does not contribute to the relevant wave functions. Interatomic distances between Cs and I or Pb and the octahedral tilt angle are the most important features. We reduce a typical 360-parameter ML force-field model to just a 12-parameter NA Hamiltonian model, while maintaining a high NA-MD simulation quality. Because NA-MD is a valuable tool for studying excited state processes, overcoming its high computational cost through simple ML models will streamline NA-MD simulations and expand the ranges of accessible system size and simulation time.

Geometric characterization of anomalous Landau levels of isolated flat bands

According to the Onsager’s semiclassical quantization rule, the Landau levels of a band are bounded by its upper and lower band edges at zero magnetic field. However, there are two notable systems where the Landau level spectra violate this expectation, including topological bands and flat bands with singular band crossings, whose wave functions possess some singularities. Here, we introduce a distinct class of flat band systems where anomalous Landau level spreading (LLS) appears outside the zero-field energy bounds, although the relevant wave function is nonsingular. The anomalous LLS of isolated flat bands are governed by the cross-gap Berry connection that measures the wave-function geometry of multi bands. We also find that symmetry puts strong constraints on the LLS of flat bands. Our work demonstrates that an isolated flat band is an ideal system for studying the fundamental role of wave-function geometry in describing magnetic responses of solids.

Janus Pyrrolopyrrole Aza-dipyrrin: Hydrogen-Bonded Assemblies and Slow Magnetic Relaxation of the Cobalt(II) Complex in the Solid State.

A novel pyrrolopyrrole azadipyrrin (Janus-PPAD) with Janus duality was synthesized by a Schiff base-forming reaction of diketopyrrolopyrrole. The orthogonal interactions of the hydrogen-bonding ketopyrrole and metal-coordinating azadipyrrin moieties in Janus-PPAD enabled the metal ions to be arranged at regular intervals: zinc(II) and cobalt(II) coordination provided metal-coordinated Janus-PPAD dimers, which can subsequently form hydrogen-bonded one-dimensional arrays both in solution and in the solid state. The supramolecular assembly of the zinc(II) complex in solution was investigated by 1 H NMR spectroscopy based on the isodesmic model, in which a binding constant for the elongation of assemblies is constant. Owing to the tetrahedral coordination, in the solid state, the cobalt(II) complex exhibited a slow magnetic relaxation due to the negative D value of -27.1 cm-1 with an effective relaxation energy barrier Ueff of 38.0 cm-1 . The effect of magnetic dilution on the relaxation behavior is discussed. The relaxation mechanism at low temperature was analyzed by considering spin lattice interactions and quantum tunneling effects. The easy-axis magnetic anisotropy was confirmed, and the relevant wave functions were obtained by ab initio CASSCF calculations.

5D BPS quivers and KK towers

We explore BPS quivers for D = 5 theories, compactified on a circle and geometrically engineered over local Calabi-Yau 3-folds, for which many of known machineries leading to (refined) indices fail due to the fine-tuning of the superpotential. For Abelian quivers, the counting reduces to a geometric one, but the technically challenging L2 cohomology proved to be essential for sensible BPS spectra. We offer a mathematical theorem to remedy the difficulty, but for non-Abelian quivers, the cohomology approach itself fails because the relevant wavefunctions are inherently gauge-theoretical. For the Cartan part of gauge multiplets, which suffers no wall-crossing, we resort to the D0 picture and reconstruct entire KK towers. We also perform numerical checks using a multi-center Coulombic routine, with a simple hypothesis on the quiver invariants, and extend this to electric BPS states in the weak coupling chamber. We close with a comment on known Donaldson-Thomas invariants and on how L2 index might be read off from these.

Shape mixing in 0νββ candidates

Weak processes are typically observed through nuclear effects, as they mediate between different eigenstates of either one nucleus, or a pair of nuclei. Since the derivation of important parameters of the weak interaction and weakly-interacting particles, such as their masses, spin dependencies, and alike, heavily relies on nuclear theory, it must be assured that theory properly describes the relevant wave functions. A special challenge for neutrino- less double-beta decay, for example, is the location of many candidate isotopes in regions of the nuclear chart, where nuclei may exist simultaneously in different shapes, hence, different wave function components belonging to different nuclear deformations mixing into the nuclear eigenstates. In addition, isovector parameters of nuclear models are not often well constrained, posing an additional challenge. Through the measurement of properties of the nuclear scissors mode, a magnetic isovector excitation at low energies, using photon-scattering techniques, we obtain data that is relevant to constrain the structure of the nuclei and their eigenstates in question. Furthermore, our recent research program comprises the investigation of isotopes relevant for the detection of hypothetical massive weakly-interacting particles.

Characterizing the parent Hamiltonians for a complete set of orthogonal wave functions: An inverse quantum problem

We study the inverse problem of constructing an appropriate Hamiltonian from a physically reasonable set of orthogonal wave functions for a quantum spin system. Usually, we are given a local Hamiltonian and try to characterize the relevant wave functions and energies (the spectrum) of the system. Here, we take the opposite approach; starting from a collection of orthogonal wave functions, our goal is to characterize the associated parent Hamiltonian, to see how the wave functions and the energy values determine the structure of the parent Hamiltonian. Specifically, we obtain (quasi) local Hamiltonians by a complete set of (multilayer) product states and a local mapping of the energy values to the wave functions. On the other hand, a complete set of tree wave functions (having a tree structure) results to nonlocal Hamiltonians and operators which flip simultaneously all the spins in a single branch of the tree graph. We observe that even for a given set of wave functions, the energy spectrum can significantly change the nature of interactions in the Hamiltonian. These effects can be exploited in a quantum engineering problem optimizing an objective functional of the Hamiltonian.

Quantum-mechanical diffraction theory of light from a small hole: Extinction-theorem approach

In a recent paper [Phys. Rev. A 90, 043830 (2014)] it was shown that the so-called aperture response tensor is the central concept in the microscopic quantum theory of light diffraction from a small hole in a flat screen. It was further shown that the quantum mechanical theory of diffraction only requires a preknowledge of the incident field plus the electronic properties of identical screens with and without a hole. Starting from the quantum mechanical expression for the linear conductivity tensor, we study the related causal conductivity tensor paying particular attention to diamagnetic electron dynamics. Using a nonlocal-potential separation assumption, we present a calculation of the diamagnetic causal surface conductivity for a jellium quantum-well screen using a two-dimensional Hartree-Fock model. In the diamagnetic case the difference between the light-unperturbed electron densities for screens with $({n}^{0})$ and without $({n}_{\ensuremath{\infty}}^{0})$ holes are the primary quantities for the diffraction theory. In a central part (Sec. IV) of this article we determine ${n}^{0}$ via a quantum-mechanical two-dimensional extinction-theorem approach related to elastic electron scattering from a hole with an electronic selvedge. For heuristic purposes we illustrate aspects of the extinction-theorem theory by applying the approach for an infinitely high potential barrier to the vacuum hole. Finally, we calculate and discuss the aperture response tensor in the small hole limit and in the zeroth-order Born approximation. Our final result for the aperture response tensor establishes the bridge to the anisotropic electric dipole polarizability tensor of the hole. It turns out that the effective optical aperture (hole) size relates closely to the extension of the relevant electronic wave functions scattered from the hole.

A local description of dark energy in terms of classical two-component massive spin-one uncharged fields on spacetimes with torsionful affinities

Abstract It is assumed that the two-component spinor formalisms for curved spacetimes that are endowed with torsionful affine connexions can supply a local description of dark energy in terms of classical massive spin-one uncharged fields. The relevant wave functions are related to torsional affine potentials which bear invariance under the action of the generalized Weyl gauge group. Such potentials are thus taken to carry an observable character and emerge from contracted spin affinities whose patterns are chosen in a suitable way. New covariant calculational techniques are then developed towards deriving explicitly the wave equations that supposedly control the propagation in spacetime of the dark energy background. What immediately comes out of this derivation is a presumably natural display of interactions between the fields and both spin torsion and curvatures. The physical properties that may arise directly fromthe solutions to thewave equations are not brought out.

On the cluster structure of linear-chain fermionic wave functions

Using the model of cyclic polyenes $$\hbox {C}_N\hbox {H}_N$$ with a nondegenerate ground state, $$N = 4 \nu + 2 \; (\nu = 1, 2, \ldots )$$ , as a prototype of extended linear metallic-like systems we explore the cluster structure of the relevant wave functions. Based on the existing configuration interaction and coupled cluster (CC) results, as obtained with the Hubbard and Pariser–Parr–Pople Hamiltonians in the entire range of the coupling constant extending from the uncorrelated Huckel limit to the fully correlated limit, we recall the breakdown of the CCD or CCSD methods as the size of the system increases and the strongly correlated regime is approached. We introduce the concept of the indecomposable quadruply-excited clusters which arise for $$\nu > 1$$ and represent those connected quadruples that do not possess any corresponding disconnected cluster component. It is shown via explicit enumeration that the ratio of the number of these indecomposables relative to that of the decomposables depends linearly on the size of the polyene $$N$$ , so that the limit of the ratio of the number of indecomposables relative to the total number of quadruples approaches unity as $$N \rightarrow \infty $$ . We then briefly outline the implications of these results for the applicability of CC approaches to extended systems and provide a qualitative argument for an even more extreme behavior of hexa-excited, octa-excited, etc., clusters as $$N \rightarrow \infty $$ .

The control of the nonlinear optical response of semiconductor quantum dots

In the present work, we investigate the nonlinear optical properties emerged from excitonic features in an experimentally realized spherical parabolic semiconductor quantum dot (QD). The lowest exciton states together with relevant wave functions are calculated through the expansion method with direct matrix diagonalization method within the effective mass approximation. The effect of the size of QD and confinement potential in exciton state is studied in details. Results show that with increasing the size of the QD the energy of exciton decreases because of decreasing of the effect of coulomb potential. Using the compact density matrix formalism second order nonlinear optical rectification (χ(2)) are obtained. By means of the applied electric and magnetic field we manipulate the exciton states and control the nonlinear optical response in a typical GaAs, InAs, CdSe QDs. Our model system presents a way to control the performance of excitonic optoelectronic devices based on semiconductor nanostructures.

Single-particle and many-body analyses of a quasiperiodic integrable system after a quench

In general, isolated integrable quantum systems have been found to relax to an apparent equilibrium state in which the expectation values of few-body observables are described by the generalized Gibbs ensemble. However, recent work has shown that relaxation to such a generalized statistical ensemble can be precluded by localization in a quasiperiodic lattice system. Here we undertake complementary single-particle and many-body analyses of noninteracting spinless fermions and hard-core bosons within the Aubry-Andre model to gain insight into this phenomenon. Our investigations span both the localized and delocalized regimes of the quasiperiodic system, as well as the critical point separating the two. Considering first the case of spinless fermions, we study the dynamics of the momentum distribution function and characterize the effects of real-space and momentum-space localization on the relevant single-particle wave functions and correlation functions. We show that although some observables do not relax in the delocalized and localized regimes, the observables that do relax in these regimes do so in a manner consistent with a recently proposed Gaussian equilibration scenario, whereas relaxation at the critical point has a more exotic character. We also construct various statistical ensembles from the many-body eigenstates of the fermionic and bosonic Hamiltonians and study the effect of localization on their properties.

Spectrum for heavy quarkonia and mixture of the relevant wave functions within the framework of Bethe-Salpeter equation

Considering the fact that some excited states of the heavy quarkonia (charmonium and bottomonium) still missing in experimental observations and potential applications of the relevant wave functions of the bound states, we re-analyze the spectrum and the relevant wave functions of the heavy quarkonia within the framework of Bethe-Salpeter (B.S.) equation with a proper QCD-inspired kernel. Such a kernel for the heavy quarkonia, relating to potential of non-relativistic quark model, is instantaneous, so we call the corresponding B.S. equation as BS-In equation throughout the paper. Particularly, a new way to solve the B.S. equation, which is different from the traditional ones, is proposed here, and with it not only the known spectrum for the heavy quarkonia is re-generated, but also an important issue is brought in, i.e., the obtained solutions of the equation `automatically' include the 'fine', 'hyperfine' splittings and the wave function mixture, such as $S-D$ wave mixing in $J^{PC}=1^{--}$ states, $P-F$ wave mixing in $J^{PC}=2^{++}$ states for charmonium and bottomonium etc. It is pointed out that the best place to test the wave mixture probably is at $Z$-factory ($e^+e^-$ collider running at $Z$-boson pole with extremely high luminosity).

Comparison of atomistic simulations and statistical theories for variable degree of long-range order in semiconductor alloys

A direct atomistic quantum-mechanical theory is used for a comprehensive investigation on the applicability of a statistical theory based on cluster expansion to the electronic band structure of a semiconductor alloy with variable degree of long-range order. This study reveals that the applicability of the statistical theory depends on the modulation of the relevant wave function within the alloyed sublattice. This finding can be generalized beyond the prototype system\char22{}CuPt-ordered ${\text{Ga}}_{x}{\text{In}}_{1\ensuremath{-}x}\text{P}$\char22{}to other alloys or other forms of long-range order and thus establishes a framework for understanding the effect of ordering in semiconductor alloys and the limitation of the cluster expansion approach for treating the electronic structure of alloys.

EPR and optical absorption studies of Cu2+ ions in [ZnPd(CN)4(C4H12N2O2)] single crystals

A Cu2+-doped single crystal of catena-trans-bis(N-(2-hydroxyethyl)-ethylenediamine) zinc(II)-tetra-m-cyanopaladate(II) [ZnPd(CN)4(C4H12N2O2)] complex has been investigated by electron paramagnetic resonance (EPR) technique at room temperature. EPR spectra indicate that Cu2+ ions substitute for magnetically equivalent Zn2+ ions and form octahedral complexes in [ZnPd(CN)4(C4H12N2O2)] hosts. The crystal field affecting the Cu2+ ion is nearly axial. The optical absorption studies show two bands at 322 nm (30864 cm−1) and 634 nm (15337 cm−1) which confirm the axial symmetry. The spin Hamiltonian parameters and the relevant wave function are determined.

Negative differential resistance in molecular junctions: Effect of the electronic structure of the electrodes

We have carried out calculations of electron transport through a metal-molecule-metal junction with metal nanoclusters taking the part of electrodes. We show that negative differential resistance peaks could appear in the current-voltage curves. The peaks arise due to narrow features in the electron density of states of the metal clusters. The proposed analysis is based on the ab initio computations of the relevant wave functions and energies within the framework of the density functional theory using NRLMOL software package.

Inelastic resonant tunneling inC60molecular junctions

We present an ab initio theory of inelastic electron tunneling spectroscopy along with the theoretical analysis of recent experiments on inelastic transport in molecular tunneling junctions involving ${\mathrm{C}}_{60}$ molecule. We present a self-consistent procedure for calculating electron charge density and tunneling current in the presence of the electron-phonon interaction. We find that electron tunneling is significantly influenced by several specific vibrational modes. Inelastic scattering suppresses resonance transmission peak and substantially redshifts the peak position. We investigate the microscopic origin of this behavior by calculating the relevant vibrational modes and resonance wave functions under nonequilibrium transport conditions.

Two‐photon photoluminescence and exciton binding energies in single‐walled carbon nanotubes

AbstractWe compare experimental one‐ and two‐photon luminescence excitation spectra of single‐walled carbon nanotubes at room temperature to ab initio calculations. The experimental spectra reveal a Rydberg‐like series of excitonic states. The energy splitting between these states is a clear fingerprint of excitonic correlations in carbon nanotubes. From those spectra, we derive exciton binding energies of 0.3–0.4 eV for nanotubes with diameters between 6.8 Å and 9.0 Å. These energies are in quantitative agreement with our theoretical calculations, which predict the symmetries of the relevant excitonic wave functions and indicate that a low‐lying optically dark excitonic state may be responsible for the low luminescence quantum yields in nanotubes. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)