Components Of Wave Function Research Articles

Spatial Signatures of Electron Correlation in Least-Squares Tensor Hypercontraction.

Least-squares tensor hypercontraction (LS-THC) has received some attention in recent years as an approach to reduce the significant computational costs of wave function-based methods in quantum chemistry. However, previous work has demonstrated that LS-THC factorization performs disproportionately worse in the description of wave function components (e.g., cluster amplitudes T̂2) than Hamiltonian components (e.g., electron repulsion integrals (pq|rs)). This work develops novel theoretical methods to study the source of these errors in the context of the real-space T̂2 kernel, and reports, for the first time, the existence of a "correlation feature" in the errors of the LS-THC representation of the "exchange-like" correlation energy EX and T̂2 that is remarkably consistent across ten molecular species, three correlated wave functions, and four basis sets. This correlation feature portends the existence of a "pair point kernel" missing in the usual LS-THC representation of the wave function, which critically depends upon pairs of grid points situated close to atoms and with interpair distances between one and two Bohr radii. These findings point the way for future LS-THC developments to address these shortcomings.

Reinforcement learning for rotation sensing with ultracold atoms in an optical lattice

In this paper, we investigate a design approach of reinforcement learning to engineer a gyroscope in an optical lattice for the inertial sensing of rotations. Our methodology is not based on traditional atom interferometry, that is, splitting, reflecting, and recombining wavefunction components. Instead, the learning agent is assigned the task of generating lattice shaking sequences that optimize the sensitivity of the gyroscope to rotational signals in an end-to-end design philosophy. What results is an interference device that is completely distinct from the familiar Mach-Zehnder-type interferometer. For the same total interrogation time, the end-to-end design leads to a twentyfold improvement in sensitivity over traditional Bragg interferometry. Published by the American Physical Society 2024

Asymmetric intrinsic charm in the nucleon and its implications for the D0 production in the LHCb p+Ne20 fixed-target experiment

Recent results indicate that charm quarks are intrinsic components of the proton wave function, and that the charm and anticharm distributions for a given value of the Bjorken-x variable can be different. In this paper, we will investigate the impact of this asymmetric intrinsic charm on the production of D0 and D¯0 mesons for fixed target p+Ne20 collisions at the LHCb. In our calculations, we include the contribution of the gluon-gluon fusion, gluon-charm and recombination processes and assume distinct models for the treatment of the intrinsic charm component. We demonstrate that the presence of an intrinsic charm improves the description of the current data for the rapidity and transverse momentum distributions of D mesons. However, such models are not able to describe the LHCb data for the D0−D¯0 asymmetry at large transverse momentum, which point out that the description of the intrinsic charm needs to be improved and/or new effects should be taken into account in the production of heavy mesons at forward rapidities in fixed-target collisions. Published by the American Physical Society 2024

Triply charm and bottom tetraquarks in a constituent quark model

Singly, doubly, and fully charmed tetraquark candidates, e.g., Tcs¯(2900), Tcc+(3875), and X(6900) have been recently reported by the LHCb collaboration. Therefore, it is timely to implement a theoretical investigation on triply heavy tetraquark systems; herein, the S-wave triply charm and bottom tetraquarks, Q¯Qq¯Q (q=u,d,s;Q=c,b), with spin-parity JP=0+, 1+, and 2+, isospin I=0 and 12, are systematically studied in a constituent quark model. Besides, all tetraquark configurations, i.e., meson-meson, diquark-antidiquark, and K-type arrangements, along with any allowed color structure, are comprehensively considered. The Gaussian expansion method (GEM), in combination with the complex-scaling method (CSM), which is quite ingenious in dealing with either bound or resonances, is the approach adopted in solving the complex scaled Schrödinger equation. This theoretical framework has already been applied in various tetra- and pentaquark systems. In a fully coupled-channel calculation within the GEM+CSM, narrow resonances are found in each I(JP) channel of the charm and bottom sector. In particular, triply charm and bottom tetraquark resonances are obtained in 5.6–5.9 GeV and 15.3–15.7 GeV, respectively. We provide also some insights of the compositeness of these exotic states, such as the inner quark distance, magnetic moment and dominant wave function component. All this may help to distinguish them in future high energy nuclear and particle experiments. Published by the American Physical Society 2024

Persistent currents of ultrarelativistic plasma-encased endofullerene molecules entrapping a H atom

In this work, for the first time in the relevant literature, the persistent currents (PC) and induced magnetic fields (IMF) of an endofullerene molecule entrapping a hydrogen atom, under spherical confinement, are investigated. The endofullerene molecule is enclosed within a spherical region and embedded in a plasma environment. The plasma environment is depicted with the more general exponential cosine screened Coulomb potential, and its relevant effects are analyzed by considering plasma screening parameters. The relevant model for endohedral confinement is the Woods–Saxon confinement potential, which is compatible with experimental data. The effects of various forms of C n are thoroughly elucidated via the analysis of the confinement depth, spherical shell thickness, the inner radius, and the smoothing parameters. To find the bound states in the spherically confined endofullerene, the decoupling of the second-order Dirac equation for the large and small components of the radial atomic wave functions is considered. The Dirac equation with the interaction potential is solved numerically by using the Runge–Kutta–Fehlberg method via the decoupling formalism. The influence of spin orientations on the PC and IMF is also elucidated. The effects of spherical confinement, plasma shielding, and the structural properties of the fullerene on the PC and IMF are thoroughly viewed. Moreover, under given physical conditions, the optimal ranges of these effects are determined.

Coupled inhomogeneous nonlinear Schrödinger system with potential in three space diemensions

This work studies the inhomogeneous Schrödinger coupled system with potential The wave function components read for . The inhomogeneous singular term exponent is . The source term is energy sub‐critical: . Moreover, in order to avoid a singularity of the term , one assumes that . The linear Schrödinger operator reads , where is a potential satisfying some assumptions which imply that the dispersive and Strichartz estimates hold. The purpose is two‐fold. First, we develop a local well‐posedness theory in the energy space . Second, we present a dichotomy of global existence and scattering versus blow‐up of energy solutions under the ground‐state threshold in the inter‐critical focusing regime. The scattering is obtained by using the new approach of Dodson–Murphy which is based on Tao's scattering criteria and Morawetz estimates. The novelty here is the presence of the potential . The challenge is to deal with three technical problems: a coupled nonlinearity, an inhomogeneous singular term , and the presence of the potential . This note naturally extends previous works by the authors about the above problem for .

A two-dimensional string cosmology

We study two-dimensional string theory on a time-dependent background, whose worldsheet description consists of Liouville theory at central charge c = 1 and Liouville theory at central charge c = 25, together with the conformal ghosts. We compute the tree-level three-point and four-point components of the cosmological wavefunction in string perturbation theory. The latter is evaluated numerically by decomposing the Liouville four-point correlation functions into Virasoro conformal blocks and three-point function coefficients and integrating over the moduli space of the four-punctured sphere string diagram. This computation numerically confirms a surprisingly simple conjectural result for the four-point wavefunction component whose physical interpretation remains to be clarified.

Spatiotemporal Electron Beam Focusing through Parallel Interactions with Shaped Optical Fields.

The ability to modulate free electrons with light has emerged as a powerful tool to produce attosecond electron wave packets. However, research has so far aimed at the manipulation of the longitudinal wave function component, while the transverse degrees of freedom have primarily been utilized for spatial rather than temporal shaping. Here, we show that the coherent superposition of parallel light-electron interactions in transversally separate zones allows for a simultaneous spatial and temporal compression of a convergent electron wave function, enabling the formation of sub-Ångström focal spots of attosecond duration. Specifically, spots spanning just ∼3% of the light optical cycle are shown to be formed, accompanied by an increase by only a factor of 2 in spatial extension relative to an unperturbed beam. The proposed approach will facilitate the exploration of previously inaccessible ultrafast atomic-scale phenomena, in particular enabling attosecond scanning transmission electron microscopy.

Superfluidity from correlations in driven boson systems

We investigate theoretically the superfluidity of a one-dimensional boson system whose hopping energy is periodically modulated with a zero time average, which results in the suppression of first-order single-particle hopping processes. The dynamics of this Floquet-engineered flat-band system is entirely driven by correlations and described by exotic Hamiltonian and current operators. We employ exact diagonalization and compare our results with those of the conventional, undriven Bose–Hubbard system. We focus on the two main manifestations of superfluidity, the Hess-Fairbank effect and the metastability of supercurrents, with explicit inclusion of an impurity when relevant. Among the novel superfluid features, we highlight the presence of a cat-like ground state, with branches that have opposite crystal momentum but carry the same flux-dependent current, and the essential role of the interference between the collective components of the ground-state wave function. Calculation of the dynamic form factor reveals the presence of an acoustic mode that guarantees superfluidity in the thermodynamic limit.

Properties of eigenmodes and quantum-chaotic scattering in a superconducting microwave Dirac billiard with threefold rotational symmetry

We report on experimental studies that were performed with a microwave Dirac billiard (DB), that is, a flat resonator containing metallic cylinders arranged on a triangular grid, whose shape has a threefold rotational (${C}_{3}$) symmetry. Its band structure exhibits two Dirac points (DPs) that are separated by a nearly flat band. We present a procedure that we employed to identify eigenfrequencies and to separate the eigenstates according to their transformation properties under rotation by $\frac{2\ensuremath{\pi}}{3}$ into the three ${C}_{3}$ subspaces. This allows us to verify previous numerical results of Zhang and Dietz [Phys. Rev. B 104, 064310 (2021)], thus confirming that the properties of the eigenmodes coincide with those of artificial graphene around the lower DP, and they are well described by a tight-binding model for a honeycomb-kagome lattice of corresponding shape. Above all, we investigate the properties of the wave-function components in terms of the fluctuation properties of the measured scattering matrix, which are numerically not accessible. They are compared to random-matrix theory predictions for quantum-chaotic scattering systems exhibiting extended or localized states in the interaction region, that is, the DB. Even in regions where the wave functions are localized, the spectral properties coincide with those of typical quantum systems with chaotic classical counterparts.

Minimal quantum walk simulation of Dirac fermions in curved space-times

The problem of simulating through quantum walks the curved space-time propagation of Dirac fermions is revisited, taking the $$(1 + 1)$$ D case as an example. New quantum walks are introduced which encode the space-time geometry, not in the mixing operators, but in new unitary shift operators which carry out a position-dependent translation of the wave function components. These walks simulate Dirac fermions in arbitrary curved space-times and coordinates. Contrary to previously proposed general alternatives, the wave functions of the new walks have as many components as usual Dirac spinors, and not twice that number. In particular, in $$(1 + 1)$$ D space-times, only one qubit is needed at each lattice point, which makes it easier to perform quantum simulations of the Dirac dynamics on current NISQs quantum devices. Numerical simulations of the Dirac dynamics in the post Newtonian, so-called Gravitoelectromagnetism regime are presented as an illustration. The possible usefulness of the new shift operators and quantum walks in other more general contexts is also discussed.

Parameterization of Direct and Doorway Processes in R-Matrix Formalism

R-matrix formalism is extended beyond compound nuclear (CN) resonant reactions to include parameterization of direct as well as doorway processes. Direct processes in the R-matrix exterior are parameterized by a unitary matrix that introduces mixing among wave function coefficients of the incoming and outgoing wave function components at the R-matrix channel surface. Doorway processes are parameterized by separating the Hilbert space of the interior R-matrix region into its doorway and CN subspaces, from which doorway state eigenenergies, reduced width amplitudes, and the strengths of their coupling to CN levels appear as new R-matrix parameters. Parameterization of generalized as well as the conventional Reich–Moore approximation for eliminated capture channels in the presence of direct, doorway, and CN processes is presented along with a complex-valued scattering length with contributions from direct, doorway, and CN capture processes. Derivation of Brune’s alternative R-matrix parameters is extended to include doorway states. This work suggests how R-matrix formalism could be extended further by adopting the concepts from related reaction formalisms.

High order relativistic corrections on the electric field gradient within the LRESC formalism.

In this work, we present relativistic corrections to the electric field gradient (EFG) given by the Linear Response Elimination of the Small Component (LRESC) scheme at 1/c2 order and including for the first time spin-dependent (SD) corrections at 1/c4 order. We show that these new terms improve the performance of LRESC as results with this methodology are very close to those calculated at the four-component Dirac-Hartree-Fock (4c-DHF) level. We assess the new corrections in BrY and AtY di-halogen (Y = F, Cl, Br, I, and At) and XZY bi-linear molecules (Z = Zn, Cd, and Hg; X, Y = F, Cl, Br, I, and At). At the 4c-DHF level, we analyze the contributions coming from the large and small components of the relativistic 4c wave function to the electronic part of EFG and compare them with the LRESC corrections to find their electronic origin. For the HgX2 (X = Cl, Br, and I) subset, when the SDcorrecting terms are included, LRESC calculations match very well with 4c-DHF ones and those from the literature, with differences less than 1% for molecules containing up to three heavy atoms. We show that LRESC gives accurate values of EFG, allowing the analysis of the electronic origin of relativistic effects in terms of well-known nonrelativistic operators.

Phase transitions and topological properties of the 52 quantum Hall states with strong Landau-level mixing

We numerically study a $\frac{5}{2}$ fractional quantum Hall system with even number of electrons using the exact diagonalization where both the strong Landau-level (LL) mixing and a finite width of the quantum well have been considered and adapted into a screened Coulomb interaction. With the principal component analysis, we are able to recognize a compressible-incompressible phase transition in the parameter space made of the magnetic field and the quantum well width by the competition between the first two leading components of the ground-state wave functions, which is consistent with the low-lying spectral feature and previous works in the odd-electron system. In addition, the presence of the subdominant third component suggests an incompressible transition occurring as the LL mixing strength grows into a certain parameter region associated with the ZnO experiments. We further investigate the strongly LL-mixed phase in this emerging region with the Hall viscosity, wave function overlaps, and the entanglement spectra. Results show it can be well described as a particle-hole symmetrized Pfaffian state with the dual topological properties of the Pfaffian and the anti-Pfaffian states.

The four-component DFT method for the calculation of the EPR g-tensor using a restricted magnetically balanced basis and London atomic orbitals.

Four-component relativistic treatments of the electron paramagnetic resonance g-tensor have so far been based on a common gauge origin and a restricted kinetically balanced basis. The results of such calculations are prone to exhibit a dependence on the choice of the gauge origin for the vector potential associated with uniform magnetic field and a related dependence on the basis set quality. In this work, this gauge problem is addressed by a distributed-origin scheme based on the London atomic orbitals, also called gauge-including atomic orbitals (GIAOs), which have proven to be a practical approach for calculations of other magnetic properties. Furthermore, in the four-component relativistic domain, it has previously been shown that a restricted magnetically balanced (RMB) basis for the small component of the four-component wavefunctions is necessary for achieving robust convergence with regard to the basis set size. We present the implementation of a four-component density functional theory (DFT) method for calculating the g-tensor, incorporating both the GIAOs and RMB basis and based on the Dirac-Coulomb Hamiltonian. The approach utilizes the state-of-the-art noncollinear Kramers-unrestricted DFT methodology to achieve rotationally invariant results and inclusion of spin-polarization effects in the calculation. We also show that the gauge dependence of the results obtained is connected to the nonvanishing integral of the current density in a finite basis, explain why the results of cluster calculations exhibit surprisingly low gauge dependence, and demonstrate that the gauge problem disappears for systems with certain point-group symmetries.

Solutions of the Dirac equation with position-dependent mass for q-deformed Pöschl–Teller and Coulomb-like tensor potentials

We consider the Dirac equation with position-dependent mass for a q-deformed Pöschl–Teller potential plus a Coulomb-like tensor interaction in the limits of spin and pseudospin symmetries. Under the condition of spin symmetry, the bound state energy eigenvalue equation and the two radial components of the Dirac wave function in terms of the Jacobi polynomials are obtained approximately for an arbitrary shifted spin-orbit quantum number λκ = κ + H and for any value of the deformation parameter q ≥ 1. In the case of the pseudospin symmetry limit, there are no bound states. The Dirac equation describes a free physical system and the two components of the wave function are expressed in terms of the spherical Bessel functions.

Electronic densities and valence bond wave functions.

Valence bond (VB) wave functions are studied from the density point of view. The density is plotted as a difference with the quasi-state built on the same orbitals. The densities of the components of the VB wave function are also shown. The breathing orbital effect leads to small modifications of the density. It is shown that while the densities of ionic and covalent components are the same, their coupling ends-up in modifications of the electronic density.

Bright State Sensitized Triplet Energy Transfer from Quantum Dot to Molecular Acceptor Revealed by Temperature Dependent Energy Transfer Dynamics.

Quantum dot (QD) sensitized molecular triplet excited state generation has been a promising alternative for traditional triplet state harvesting schemes. However, the correlation between QD bright/dark states and QD sensitized triplet energy transfer (TET) has been unclear. Herein, we studied the bright/dark states contribution to TET with CdSe/CdS core/shell QD-oligothiophene as the model system. Equilibrium between QD bright and dark states was tuned by changing temperature, and TET dynamics were monitored with transient absorption spectroscopy. Analysis of acceptor triplet excited state growth kinetics yields rates of TET from bright and dark states as 0.492 ± 0.011 ns-1 and 0.0271 ± 0.0014 ns-1 at 5 K, suggesting significant contribution of bright states to TET. The result was rationalized by bright state wave function components with the same electron/hole spin projections leading to nonzero TET probability. The study provides new insights into QD sensitized TET mechanisms and inspiration for future TET efficiency optimization through QD exciton engineering.

Solving for the Low-Rank Tensor Components of a Scattering Wave Function

Solving for the Low-Rank Tensor Components of a Scattering Wave Function

E1 and M1 radiative transitions involving heavy-light axial, pseudoscalar, and vector quarkonia in the framework of the Bethe-Salpeter equation

This work is an extension of our previous work in \cite{bhatnagar20} to calculate M1 transitions, $0^{-+}\rightarrow 1^{--} \gamma$, and E1 transitions involving axial vector mesons such as, $1^{+-} \rightarrow 0^{-+}\gamma$, and $0^{-+}\rightarrow 1^{+-} \gamma $ for which very little data is available as of now. We make use of the general structure of the transition amplitude, $M_{fi}$ derived in our previous work \cite{bhatnagar20} as a linear superposition of terms involving all possible combinations of $++$, and $--$ components of Salpeter wave functions of final and initial hadrons. In the present work, we make use of leading Dirac structures in the hadronic Bethe-Salpeter wave functions of the involved hadrons, which makes the formulation more rigorous. We evaluate the decay widths for both the above mentioned $M1$ and $E1$ transitions. We have used algebraic forms of Salpeter wave functions obtained through analytic solutions of mass spectral equations for ground and excited states of $1^{--}$,$0^{-+}$ and $1^{+-}$ heavy-light quarkonia in approximate harmonic oscillator basis to do analytic calculations of their decay widths. We have compared our results with experimental data, where ever available, and other models.