Single-particle Wave Functions Research Articles

Observation of vortices in a dipolar supersolid.

Supersolids are states of matter that spontaneously break two continuous symmetries: translational invariance owing to the appearance of a crystal structure and phase invariance owing to phase locking of single-particle wavefunctions, responsible for superfluid phenomena. Although originally predicted to be present in solid helium1-5, ultracold quantum gases provided a first platform to observe supersolids6-10, with particular success coming from dipolar atoms8-12. Phase locking in dipolar supersolids has been investigated through, for example, measurements of the phase coherence8-10 and gapless Goldstone modes13, but quantized vortices, a hydrodynamic fingerprint of superfluidity, have not yet been observed. Here, with the prerequisite pieces at our disposal, namely a method to generate vortices in dipolar gases14,15 and supersolids with two-dimensional crystalline order11,16,17, we report on the theoretical investigation and experimental observation of vortices in the supersolid phase (SSP). Our work reveals a fundamental difference in vortex seeding dynamics between unmodulated and modulated quantum fluids. This opens the door to study the hydrodynamic properties of exotic quantum systems with numerous spontaneously broken symmetries, in disparate domains such as quantum crystals and neutron stars18.

An Implementation of Nuclear Many-Body Wave Functions by the Superposition of Localized Gaussians

Abstract We introduce a new framework for the nuclear structure calculations, which describes the single-particle wave function as a superposition of localized Gaussians. It is a hybrid of the Hartree–Fock and antisymmetrized molecular dynamics (AMD) models. In the numerical calculations of oxygen, calcium isotopes, and $^{100}{\rm Sn}$, the framework shows its potential by significantly improving upon AMD and yielding results that are consistent with or even better than Hartree–Fock(–Bogoliubov) calculations based on harmonic oscillator expansions. In addition to the basic equations, general forms of the matrix elements are also given.

Symplectic Quantization III: Non-relativistic Limit

First of all we shortly illustrate how the symplectic quantization scheme (Gradenigo and Livi, Found Phys 51(3):66, 2021) can be applied to a relativistic field theory with self-interaction. Taking inspiration from the stochastic quantization method by Parisi and Wu, this procedure is based on considering explicitly the role of an intrinsic time variable, associated with quantum fluctuations. The major part of this paper is devoted to showing how the symplectic quantization scheme can be extended to the non-relativistic limit for a Schrödinger-like field. Then we also discuss how one can obtain from this non-relativistic theory a linear Schrödinger equation for the single-particle wavefunction. This further passage is based on a suitable coarse-graining procedure, when self-interaction terms can be neglected, with respect to interactions with any external field. In the Appendix we complete our survey on symplectic quantization by discussing how this scheme applies to a non-relativistic particle under the action of a generic external potential.

Unscrambling of single-particle wave functions in systems localized through disorder and monitoring

In systems undergoing localization-delocalization quantum phase transitions due to disorder or monitoring, there is a crucial need for robust methods capable of distinguishing phases and uncovering their intrinsic properties. In this paper, we develop a process of finding a Slater determinant representation of free-fermion wave functions that accurately characterizes localized particles, a procedure we dub “unscrambling.” The central idea is to minimize the overlap between envelopes of single-particle wave functions or, equivalently, to maximize the inverse participation ratio of each orbital. This numerically efficient methodology can differentiate between distinct types of wave functions: exponentially localized, power-law localized, and conformal critical, also revealing the underlying physics of these states. The method is readily extendable to systems in higher dimensions. Furthermore, we apply this approach to a more challenging problem involving disordered monitored free fermions in one dimension, where the unscrambling process unveils the presence of a conformal critical phase and a localized area-law quantum Zeno phase. Importantly, our method can also be extended to free fermion systems without particle number conservation, which we demonstrate by estimating the phase diagram of Z2-symmetric disordered monitored free fermions. Our results unlock the potential of utilizing single-particle wave functions to gain valuable insights into the localization transition properties in systems such as monitored free fermions and disordered models. Published by the American Physical Society 2024

CHARGE CARRIERS STATES IN A MODEL OF CuO SUPERCONDUCTIVE CERAMICS

<p>The translational symmetry of the distribution of atoms (ions) of the charge carriers (electrons or holes)<br />system is broken by sputtering (doping) due to the existence of two boundary surfaces. This is a model<br />of high-temperature superconductors in which the observed symmetry breaking orthogonal to the CuO<br />plane is treated as a perturbation. Single-particle fermion wave functions and possible charge carrier<br />energies were determined. The competing existence of superconducting and normal regions in such a<br />sample is shown in agreement with experimental data. The conditions for the formation of<br />superconducting states and the limits of the current density values in the planes parallel to the<br />boundary surfaces (in the CuO planes) were obtained and discussed.</p>

A semi-analytic approximation for a single-particle continuum wavefunction

A moderately simple approximation to the radial wavefunction of an unbound particle which carries arbitrary angular momentum l( l + 1) and which scatters from any physical potential, including one with a Coulomb tail, is presented. The approximate wavefunction has the form of a linear combination of short- and long-range analytical functions that satisfies the correct boundary conditions at both the origin and at large distances. The coefficients of the short-range functions are determined by solving a matrix equation whose elements are highly suited to numerical quadrature, and which are hardly more difficult to evaluate for l ≫ 1 than for l = 0. The coefficients of the long-range functions are determined by both the nature of the interaction at large distances and the cusp condition on the wavefunction at the origin. This wavefunction has been tested by application to pure Coulomb scattering and to electron scattering from hydrogen within the 1s–2s–2p close coupling framework.

Indications for the Substantial Predominance of Short-Range Effects on Inelastic Coulomb Form Factors for Various States in the 26Mg Nucleus

Short-range effects on C2, C3, as well as C4 form factors in the 26Mg nucleus, were examined. The charge density distribution in this nucleus was also tested by means of one and two body fragments of cluster enlargement in cooperation with single-particle wave functions of harmonic potential. The correlation of Jastrow form was employed to inset the influence of short-range into the two body fragment of cluster enlargement. The nucleus of 26Mg was assumed to own a 16O-core with (A-16) nucleons dispersed over the sd-model space. The form factors in 26Mg nucleus ascend from the core-polarization and model space involvements. The form of Tassie model, subject to the charge density, was used to determine the transition density of core polarization. The one body density matrix elements required for determining the transition density of model space for various transitions in 26Mg were found via carrying out shell model computations using the OXBASH program with the universal-sd interaction of Wildenthal. The present calculations were subjected to the oscillator and correlation parameters symbolized by and respectively. These parameters are self-sufficiently generated for every specific nucleus by fitting between the calculated and observed elastic form factors. For determining the charge density, elastic form factors and inelastic Coulomb form factors for dissimilar excited states in 26Mg, one value is needed for and This study shows indications for the substantial predominance of short-range influences on current computations, where considering these influences look to be requisite for carrying out a distinguished adjustment in calculated results which ultimately leads to a remarkable explication of the data throughout all the considered momentum transfers.

INELASTIC LONGITUDINAL C6 ELECTRON SCATTERING FORM FACTORS IN Ti-50, (RESIDUAL INTERACTION CONSIDERATION)

The single orbit 1f7/2 has been adopted as a model space. The use of modern realistic M3Y effective nucleon- nucleon interaction with two sets of fitting parameters (Ried fitting (M3Y-P1), and Paris fitting (M3Y-P0)) beside the use of MSDI has been done as a residual interactions within the calculation of core polarization effects in Inelastic longitudinal electron scattering C6 form factor in Ti-50 within the framework of first order perturbation theory (microscopic theory) with 2ћω excitation energy coupling the core orbits to the higher configurations one across the model space at normal transition. Harmonic oscillator wave functions (H.O) has been adopted as a single particle wave functions in 1f7/2 and with the aid of F7MBZ model space 1f7/2 effective interaction to generate the model space wave functions. The present results have been compared with

Theory of moment propagation for quantum dynamics in single-particle description.

We present a novel theoretical formulation for performing quantum dynamics in terms of moments within the single-particle description. By expressing the quantum dynamics in terms of increasing orders of moments, instead of single-particle wave functions as generally done in time-dependent density functional theory, we describe an approach for reducing the high computational cost of simulating the quantum dynamics. The equation of motion is given for the moments by deriving analytical expressions for the first-order and second-order time derivatives of the moments, and a numerical scheme is developed for performing quantum dynamics by expanding the moments in the Taylor series as done in classical molecular dynamics simulations. We propose a few numerical approaches using this theoretical formalism on a simple one-dimensional model system, for which an analytically exact solution can be derived. The application of the approaches to an anharmonic system is also discussed to illustrate their generality. We also discuss the use of an artificial neural network model to circumvent the numerical evaluation of the second-order time derivatives of the moments, as analogously done in the context of classical molecular dynamics simulations.

Study of the Symmetry Energy and the Nuclear Equation of State for 13O -13B and 13N-13C Mirror Nuclei

In parallel with the shell model using the harmonic oscillator's single-particle wave functions, the Hartree-Fock approximation was also used to calculate the neutron skin thickness, the mirror charge radii, and the differences in proton radii for 13O-13B and 13N-13C mirror nuclei. The calculations were done for both mirror nuclei in the psdpn model space. Depending on the type of potential used, the calculated values of skin thickness are affected. The symmetry energy and the symmetry energy's slope at nuclear saturation density were also determined, and the ratio of the density to the saturation density of nuclear matter and the symmetry energy has a nearly linear correlation. The mirror energy displacement was calculated, and the findings corresponded well with the available experimental data for the binding energies of the studied mirror nuclei. The measured values of the symmetry energy coefficient for the pair of mirror nuclei agreed with the computed ones, and this coefficient's value rises exponentially as the difference in charge radius increases.

A multi-GPU implementation of Real-Time Time-Dependent Auxiliary Density Functional Theory for the investigation of nanosystems irradiations

We report a new Multi-GPU (Graphical Processor Unit) implementation of real-time time-dependent Auxiliary Density Functional Theory (DFT) for simulations of attosecond electronic dynamics in molecular systems subjected to strong perturbations. Our code relies on the Kohn-Sham formalism of DFT and has been implemented in the deMon2k Fortran code. We expand single-particle wave functions (i.e molecular orbitals) as linear combinations of Gaussian-type-orbitals centered on atoms. The density matrix propagation is carried out on GPU while the Kohn-Sham potential is operated on CPUs (Central Processor Unit) with the help of variationally fitted densities. We propose a parallelization strategy using the MAGMA/CUDA libraries to calculate the exponential of dense Hermitian matrices entering the mathematical definition of the propagator, here using Taylor expansions. We report performance benchmarks on water droplets and on fullerenes (C50 to C540). They show a clear advantage of GPU over CPU (using the Scalapack library). The benchmarks also show the benefit of using more than one GPU for systems comprised of up to more than 10,000 basis functions. There, a speed-up of almost 40 between pure 40 CPU and four 4 GPU is obtained. Attosecond electron dynamics simulation in molecular systems comprised of several thousands of electrons becomes amenable to routine simulations in our code. We assess the accuracy of the GPU implementation considering various applications, namely, the calculation of extreme UV absorption spectra with non-Hermitian dynamics, the response of C180 to an electric perturbation, and finally the irradiation of a DNA/protein complex by a 0.4 MeV proton. The results demonstrate the robustness of the implementation. This work also paves the way for future even more efficient implementations. Program SummaryProgram title: deMon2k-RT-TDDFTCPC Library link to program files: https://doi.org/10.17632/whwc5zkst5.1Developer's repository link: DOI: 10.5281/zenodo.8301468Licensing provisions: CeCILL Free Software License Agreement v2.1Programming language: FortranExternal routines/libraries: MPI, BLAS/LAPACK, CUDA, MAGMASupplementary material: User manual, installation instructions, test cases. Nature of problem: Electron dynamics within molecular systems is amenable to simulation with Real-Time Time-Dependent Density Functional Theory (RT-TD-DFT). The methodology consists in propagating on the attosecond time scale the single particle electronic wave functions on the underlying Kohn-Sham potential [1,2]. In deMon2k-RT-TDDFT, the propagation is coupled to the Auxiliary DFT framework for fast evaluation of the potential [3]. A remaining computational bottleneck is the matrix exponential calculation of the Hermitian Hamiltonian matrix. This task is achieved in deMon2k via diagolanization or expansions formulas (Taylor, Chebychev or Baker-Campbell-Hausdorff). The operation is cumbersome on central-processor-unit machines for large matrices (e.g. > 5000 × 5000), which corresponds to molecular systems comprising around 2,000 electrons. Alternatives are needed to overcome this bottleneck.Solution method: We propose to carry out the matrix exponentiation on graphical-processor-units thanks to the MAGMA[4]/CUDA libraries. The code permits a drastic reduction of the computational cost, opening the attosecond dynamic simulations of large molecular systems comprised thousands of electrons with controlled accuracy. The method is tested here for Taylor expansions. Additional comments including restrictions and unusual features: The code described in this article opens the realization of RT-TD-ADFT simulations. The code is linked to the Master version 6.1.6 of deMon2k (http://www.demon-software.com), which must be pre-installed by the user.

Spontaneous Spin and Valley Symmetry-Broken States of Interacting Massive Dirac Fermions in a Bilayer Graphene Quantum Dot.

We predict the existence of spontaneous spin and valley symmetry-broken states of interacting massive Dirac Fermions in a gated bilayer graphene quantum dot based on the exact diagonalization of the many-body Hamiltonian. The dot is defined by a vertical electric field and lateral gates, and its single-particle (SP) energies, wave functions, and Coulomb matrix elements are computed by using the atomistic tight-binding model. The effect of the Coulomb interaction is measured by the ratio of Coulomb elements to the SP level spacing. As we increase the interaction strength, we find the electrons in a series of spin and valley symmetry-broken phases with increasing valley and spin polarizations. The phase transitions result from the competition of the SP, exchange, and correlation energy scales. A phase diagram for N = 1-6 electrons is mapped out as a function of the Coulomb interaction strength.

Quench dynamics of anyon Tonks–Girardeau gases

In this paper, we investigate the quench dynamics of strongly interacting anyons triggered by the quench of harmonic trap frequency. The exact time-dependent many-body wavefunction is obtained by combing anyon-fermion mapping method with the time-dependent single-particle wavefunction. The density profiles, momentum distribution, and the reduced one-body density matrix are evaluated for different statistical parameters. It is shown that the evolution behaviours dependent on statistical parameter are displayed in the momentum distribution and the reduced one-body density matrix rather than in the density profiles in real space. As the harmonic trap is turned off suddenly, the momentum distributions exhibit the symmetric fermion-like behaviour in the long-time evolution. As the trap frequency is quenched, the momentum distribution exhibits an asymmetry breath mode during the evolution. The reduced one-body density matrix shows the dynamical symmetry broken and reproduced behaviour.

Stationary time correlations for fermions after a quench in the presence of an impurity

We consider the quench dynamics of non-interacting fermions in one dimension in the presence of a finite-size impurity at the origin. This impurity is characterized by general momentum-dependent reflection and transmission coefficients which are changed from to at time t = 0. The initial state is at equilibrium with such that the system is cut in two independent halves with , , respectively, to the right and to the left of the impurity. We obtain the exact large time limit of the multi-time correlations. These correlations become time translationally invariant, and are non-zero in two different regimes: i) for where the system reaches a non-equilibrium steady state (NESS), ii) for , i.e., the ray regime. For a repulsive impurity these correlations are independent of , , while in the presence of bound states they oscillate and memory effects persist. We show that these nontrivial relaxational properties can be retrieved in a simple manner from the large time behaviour of the single particle wave functions.

Measures of complexity and entanglement in many-fermion systems

There is no unique and widely accepted definition of the complexity measure (CM) of a many-fermion wave function in the presence of interactions. The simplest many-fermion wave function is a Slater determinant. In shell-model or configuration interaction (CI) and other related methods, the state is represented as a superposition of a large number of Slater determinants, which in case of CI calculations reaches about 20 billion terms. Although in practice this number has been used as a CM for decades, it is ill defined: it is not unique, and it depends on the particular type and the number of single-particle wave functions used to construct the Slater determinants. The canonical wave functions/natural orbitals and their corresponding occupation probabilities are intrinsic properties of any many-body wave function, irrespective of the representation, and they provide a unique solution to characterize the CM. The non-negative orbital entanglement entropy, which vanishes for a Slater determinant, provides the simplest CM, while a more complete measure of complexity is the entanglement spectrum. We illustrate these aspects in the case of a complex non-equilibrium time-dependent process, induced nuclear fission described within a real-time Density Functional Theory framework extended to superfluid systems, which can describe simultaneously the long-range and the short range correlations between fermions.

Hamiltonian sensitivity in calculating the electromagnetic moments and electroexcitation form factor for the sd nuclei using shell model with Skyrme–Hartree–Fock

In this work, the nuclear electromagnetic moments for the ground and low-lying excited states for sd shell nuclei have been calculated, resulting in a revised database with 56 magnetic dipole moments and 41 electric quadrupole moments. The shell model calculations are performed for each sd isotope chain, considering the sensitivity of changing the sd two-body effective interactions USDA, USDE, CWH and HBMUSD in the calculation of the one-body transition density matrix elements. The calculations incorporate the single-particle wave functions of the Skyrme interaction to generate a one-body potential in Hartree–Fock theory to calculate the single-particle matrix elements. For most sd shell nuclei, the experimental data are well reproduced, except for those spans near the island of inversion. In order to interpret the structure of low-lying excited states, the electric quadrupole and magnetic dipole transition form factors and the corresponding reduced transition probabilities in the sd shell nuclei have also been calculated, for which the experimental data are available. The present results demonstrate the nuclear electromagnetic moments’ sensitivity to many forms of the understanding of nucleon–nucleon interactions and provide a crucial baseline for future improvements in conceptual calculations.

A Kohn-Sham scheme based neural network for nuclear systems

A Kohn-Sham scheme based multi-task neural network is elaborated for the supervised learning of nuclear shell evolution. The training set is composed of the single-particle wave functions and occupation probabilities of 320 nuclei, calculated by the Skyrme density functional theory. It is found that the deduced density distributions, momentum distributions, and charge radii are in good agreements with the benchmarking results for the untrained nuclei. In particular, accomplishing shell evolution leads to a remarkable improvement in the extrapolation of nuclear density. After a further charge-radius-based calibration, the network evolves a stronger predictive capability. This opens the possibility to infer correlations among observables by combining experimental data for nuclear complex systems.

Orbital design of Berry curvature: pinch points and giant dipoles induced by crystal fields

The Berry curvature (BC)—a quantity encoding the geometric properties of the electronic wavefunctions in a solid—is at the heart of different Hall-like transport phenomena, including the anomalous Hall and the non-linear Hall and Nernst effects. In non-magnetic quantum materials with acentric crystalline arrangements, local concentrations of BC are generally linked to single-particle wavefunctions that are a quantum superposition of electron and hole excitations. BC-mediated effects are consequently observed in two-dimensional systems with pairs of massive Dirac cones and three-dimensional bulk crystals with quartets of Weyl cones. Here, we demonstrate that in materials equipped with orbital degrees of freedom local BC concentrations can arise even in the complete absence of hole excitations. In these solids, the crystals fields appearing in very low-symmetric structures trigger BCs characterized by hot-spots and singular pinch points. These characteristics naturally yield giant BC dipoles and large non-linear transport responses in time-reversal symmetric conditions.

Local Quantum Theory with Fluids in Space-Time

In 1948, Schwinger developed a local Lorentz-covariant formulation of relativistic quantum electrodynamics in space-time which is fundamentally inconsistent with any delocalized interpretation of quantum mechanics. An interpretation compatible with Schwinger’s theory is presented, which reproduces all of the standard empirical predictions of conventional delocalized quantum theory in configuration space. This is an explicit, unambiguous, and Lorentz-covariant “local hidden variable theory” in space-time, whose existence proves definitively that such theories are possible. This does not conflict with Bell’s theorem because it is a local many-worlds theory. Each physical system is characterized by a wave-field, which is a set of indexed piece-wise single-particle wavefunctions in space-time, each with its own coefficient, along with a memory which contains the separate local Hilbert-space quantum state at each event in space-time. Each single-particle wavefunction of a fundamental system describes the motion of a portion of a conserved fluid in space-time, with the fluid decomposing into many classical point particles, each following a world-line and recording a local memory. Local interactions between two systems take the form of local boundary conditions between the differently indexed pieces of those systems’ wave-fields, with new indexes encoding each orthogonal outcome of the interaction. The general machinery is introduced, including the local mechanisms for entanglement and interference. The experience of collapse, Born rule probability, and environmental decoherence are discussed, and a number of illustrative examples are given.

Giant dipole resonance and its fine structures in 144−152Nd,152Sm studied within the linear response theory

We present a microscopic approach for giant dipole resonance (GDR) where the linear response by the nuclear density to the dipole radiation is represented through the single-particle wavefunctions calculated with a triaxial Woods-Saxon potential. We follow a microscopic-macroscopic approach to estimate the nuclear deformation with the same potential. We explain the recent experimental data for even–even nuclei 144−152Nd and 152Sm and present a comparison with the macroscopic approach for GDR. We highlight the cases where the results from the microscopic approach are sensitive to the change in single-particle configuration despite no change in shape and mass but with a change of two protons in a mid-shell region. We also present the fine structure analysis of the GDR cross-section using the continuous wavelet transform (CWT) framework and elucidate the origin of such fine structures.