Simple Wave Function Research Articles

Excited-state positronium formation in positron–hydrogen collisions under weakly coupled plasmas

The effect of screening of weakly coupled plasma on positronium (Ps) formation in excited states in the scattering of a positron from the ground state of a hydrogen atom has been investigated using a distorted wave theory which includes screened dipole polarization potential. The effect of external plasma has been incorporated by using the Debye–Hückel screening model of the interacting charge particles. Variationally determined simple hydrogenic wave functions have been used to obtain the distorted wave scattering amplitude in a closed form. Effects of plasma screening on the differential and total cross sections have been studied in detail in the energy range 20–300 eV of incident positron. For the free atomic case, our results agree nicely with some of the most accurate results available in the literature. To the best of our knowledge, such a study on the differential and total cross sections for Ps formation in highly excited states in positron–hydrogen collisions under weakly coupled plasma is reported first time in the literature.

Transform-limited-pulse representation of excitation with natural incoherent light.

The excitation of molecular systems by natural incoherent light relevant, for example, to photosynthetic light-harvesting is examined. We show that the result of linear excitation with natural incoherent light can be obtained using incident light described in terms of transform limited pulses, as opposed to conventional classical representations with explicit random character. The derived expressions allow for computations to be done directly for any thermal light spectrum using a simple wave function formalism and provide a route to the experimental determination of natural incoherent excitation using pulsed laser techniques. Pulses associated with solar and cosmic microwave background radiation are provided as examples.

The Pion-Cloud Contribution to the Electromagnetic Nucleon Form Factors

We study the electromagnetic structure of the nucleon within a hybrid constituent-quark model that comprises, in addition to the $3q$ valence component, also a $3q$+$\pi$ non-valence component. To this aim we employ a Poincar\'e-invariant multichannel formulation based on the point-form of relativistic quantum mechanics. With a simple 3-quark wave function for the bare nucleon, i.e. the $3q$-component, we obtain reasonable results for the nucleon form factors and predict the meson-cloud contribution to be significant only below $Q^2\lesssim 0.5$\,GeV$^2$ amounting to about 10\% for $Q^2\rightarrow 0$, in accordance with the findings of other authors.

Lopsided vortex cells in rotating Bose–Einstein condensates

The amplitude of the wavefunction of a repulsive Bose–Einstein condensate in a two-dimensional axisymmetric harmonic trap decreases as we go from the center of the condensate towards its edge. Consequently the wavefunction amplitude at the edge of a vortex cell in a vortex lattice in a rotating repulsive condensate should be greater for the inner cells. Continuity of the wavefunction amplitude between neighboring cells requires then that varies along the edge of each vortex cell, so that it is greater at the points that are closer to the center of the condensate. In other words, the wavefunction amplitude is lopsided in each vortex cell. We show this explicitly via an analytic variational calculation where a simple lopsided wavefunction amplitude is used for each vortex cell. This wavefunction amplitude varies continuously as we go from one cell to the next. The results agree quite well with experimental observations.

Effect of Rashba spin–orbit interaction on the ground state energy of a D0 centre in a GaAs quantum dot with Gaussian confinement

The ground state energy of a neutral hydrogenic donor impurity (D0) trapped in a three-dimensional GaAs quantum dot with Gaussian confinement is calculated in the presence of Rashba spin–orbit interaction. The effect of the spin–orbit interaction is incorporated by performing a unitary transformation and retaining terms up to quadratic in the spin–orbit interaction coefficient. For the resulting Hamiltonian, the Rayleigh-Ritz variational method is employed with a simple wave function within the framework of effective-mass envelope function theory to determine the ground state energy and the binding energy of the donor complex. The results show that the Rashba spin–orbit interaction reduces the total GS energy of the donor impurity.

Variational Monte Carlo method in the presence of spin-orbit interaction and its application to Kitaev and Kitaev-Heisenberg models

We propose an accurate variational Monte Carlo method applicable in the presence of the strong spin-orbit interactions. The algorithm is applicable even in a wider class of Hamiltonians that do not have the spin-rotational symmetry. Our variational wave functions consist of generalized Pfaffian-Slater wave functions that involve mixtures of singlet and triplet Cooper pairs, Jastrow-Gutzwiller-type projections, and quantum number projections. The generalized wave functions allow describing states including a wide class of symmetry-broken states, ranging from magnetic and/or charge ordered states to superconducting states and their fluctuations, on equal footing without any ad hoc ansatz for variational wave functions. We detail our optimization scheme for the generalized Pfaffian-Slater wave functions with complex-number variational parameters. Generalized quantum number projections are also introduced, which imposes the conservation of not only the momentum quantum number but also Wilson loops. As a demonstration of the capability of the present variational Monte Carlo method, the accuracy and efficiency is tested for the Kitaev and Kitaev-Heisenberg models, which lack the SU(2) spin-rotational symmetry except at the Heisenberg limit. The Kitaev model serves as a critical benchmark of the present method: The exact ground state of the model is a typical gapless quantum spin liquid far beyond the reach of simple mean-field wave functions. The newly introduced quantum number projections precisely reproduce the ground state degeneracy of the Kitaev spin liquids, in addition to their ground state energy. An application to a closely related itinerant model described by a multiorbital Hubbard model with the spin-orbit interaction also shows promising benchmark results. The strong-coupling limit of the multiorbital Hubbard model is indeed described by the Kitaev model. Our framework offers accurate solutions for the systems where strong electron correlation and spin-orbit interaction coexist.

Two-body strong decay of light mesons with Gaussian expansion method

In this paper, we survey the radial and orbital excitations of I = 0 and [Formula: see text] systems anticipated up to 2.0 GeV in the framework of the chiral quark model. The Schrödinger equation is solved by using Gaussian expansion method. And using the wave functions obtained, instead of the simple harmonic oscillator wave functions, we study systematically the two-body strong decay (limited to S + S modes) of the systems. By comparing with the experimental data, we try to identify the normal states and exotic states.

Dynamical picture for the formation and decay of the exotic XYZ mesons.

We present a new dynamical picture that identifies the formation of the exotic c[over ¯]c-containing states XYZ with the confinement-induced hadronization of a rapidly separating pair of a compact diquark and antidiquark. This picture combines the advantages of diquark-based models, which can accommodate much of the known XYZ spectrum, with the experimental fact that such states are both relatively narrow and are produced promptly. It also naturally explains the preference of some of the exotic states to decay to ψ(2S), rather than J/ψ, in terms of a simple wave-function overlap effect.

Topological quasiparticles and the holographic bulk-edge relation in(2+1)-dimensional string-net models

String-net models allow us to systematically construct and classify 2+1D topologically ordered states which can have gapped boundaries. We can use a simple ideal string-net wavefunction, which is described by a set of F-matrices [or more precisely, a unitary fusion category (UFC)], to study all the universal properties of such a topological order. In this paper, we describe a finite computational method -- Q-algebra approach, that allows us to compute the non-Abelian statistics of the topological excitations [or more precisely, the unitary modular tensor category (UMTC)], from the string-net wavefunction (or the UFC). We discuss several examples, including the topological phases described by twisted gauge theory (i.e., twisted quantum double $D^\alpha(G)$). Our result can also be viewed from an angle of holographic bulk-boundary relation. The 1+1D anomalous topological orders, that can appear as edges of 2+1D topological states, are classified by UFCs which describe the fusion of quasiparticles in 1+1D. The 1+1D anomalous edge topological order uniquely determines the 2+1D bulk topological order (which are classified by UMTC). Our method allows us to compute this bulk topological order (i.e., the UMTC) from the anomalous edge topological order (i.e., the UFC).

Solvable models for unitary and nonunitary topological phases

We introduce a broad class of simple models for quantum Hall states based on the expansion of their parent Hamiltonians near the one-dimensional limit of "thin cylinders", i.e. when one dimension $L_y$ of the Hall surface becomes comparable to the magnetic length $\ell_B$. Formally, the models can be viewed as topological generalizations of the 1D Hubbard model with center-of-mass-preserving hopping of multiparticle clusters. In some cases, we show that the models can be exactly solved using elementary techniques, and yield simple wave functions for the ground states as well as the entire neutral excitation spectrum. We study a large class of Abelian and non-Abelian states in this limit, including the Read-Rezayi $\mathbb{Z}_k$ series, as well as states deriving from non-unitary conformal field theories -- the "Gaffnian", "Haffnian", Haldane-Rezayi, and the "permanent" state. We find that the thin-cylinder limit of unitary states is "classical": their effective Hamiltonians reduce to only Hartree-type terms, the ground states are trivial insulators, and excitation gaps result from simple electrostatic repulsion. In contrast, for states deriving from non-unitary conformal field theories, the thin-cylinder limit is found to be intrinsically \emph{quantum} -- it contains hopping terms that play an important role in the structure of the ground states and in the energetics of the low-lying neutral excitations.

Electromagneticρ-meson form factors in point-form relativistic quantum mechanics

The relativistic point-form formalism that we proposed for the study of the electroweak structure of few-body bound states is applied to calculate the elastic form factors of spin-1 mesons, such as the rho meson, within constituent-quark models. We treat electron-meson scattering as a Poincare-invariant coupled-channel problem for a Bakamjian-Thomas mass operator and extract the meson current from the resulting invariant 1-photon-exchange amplitude. Wrong cluster properties inherent in the Bakamjian-Thomas framework are seen to cause spurious contributions in the current. These contributions, however, can be separated unambiguously from the physical ones and we end up with a meson current with all required properties. Numerical results for the rho-meson form factors are presented assuming a simple harmonic-oscillator bound-state wave function. The comparison with other approaches reveals a remarkable agreement of our results with those obtained within the covariant light-front scheme proposed by Carbonell et al. [Phys. Rep. 300, 215 (1998)].

Compact two-electron wave function for bond dissociation and Van der Waals interactions: a natural amplitude assessment.

Electron correlations in molecules can be divided in short range dynamical correlations, long range Van der Waals type interactions, and near degeneracy static correlations. In this work, we analyze for a one-dimensional model of a two-electron system how these three types of correlations can be incorporated in a simple wave function of restricted functional form consisting of an orbital product multiplied by a single correlation function f (r12) depending on the interelectronic distance r12. Since the three types of correlations mentioned lead to different signatures in terms of the natural orbital (NO) amplitudes in two-electron systems, we make an analysis of the wave function in terms of the NO amplitudes for a model system of a diatomic molecule. In our numerical implementation, we fully optimize the orbitals and the correlation function on a spatial grid without restrictions on their functional form. Due to this particular form of the wave function, we can prove that none of the amplitudes vanishes and moreover that it displays a distinct sign pattern and a series of avoided crossings as a function of the bond distance in agreement with the exact solution. This shows that the wave function ansatz correctly incorporates the long range Van der Waals interactions. We further show that the approximate wave function gives an excellent binding curve and is able to describe static correlations. We show that in order to do this the correlation function f (r12) needs to diverge for large r12 at large internuclear distances while for shorter bond distances it increases as a function of r12 to a maximum value after which it decays exponentially. We further give a physical interpretation of this behavior.

Adaptive multiconfigurational wave functions

A method is suggested to build simple multiconfigurational wave functions specified uniquely by an energy cutoff Λ. These are constructed from a model space containing determinants with energy relative to that of the most stable determinant no greater than Λ. The resulting Λ-CI wave function is adaptive, being able to represent both single-reference and multireference electronic states. We also consider a more compact wave function parameterization (Λ+SD-CI), which is based on a small Λ-CI reference and adds a selection of all the singly and doubly excited determinants generated from it. We report two heuristic algorithms to build Λ-CI wave functions. The first is based on an approximate prescreening of the full configuration interaction space, while the second performs a breadth-first search coupled with pruning. The Λ-CI and Λ+SD-CI approaches are used to compute the dissociation curve of N2 and the potential energy curves for the first three singlet states of C2. Special attention is paid to the issue of energy discontinuities caused by changes in the size of the Λ-CI wave function along the potential energy curve. This problem is shown to be solvable by smoothing the matrix elements of the Hamiltonian. Our last example, involving the Cu2O2(2+) core, illustrates an alternative use of the Λ-CI method: as a tool to both estimate the multireference character of a wave function and to create a compact model space to be used in subsequent high-level multireference coupled cluster computations.

Effect of external magnetic field on the ground state properties of D− centres in a Gaussian quantum dot

The binding energies of a negatively charged hydrogenic donor ion (D−) trapped in a three-dimensional quantum dot with Gaussian confinement in the presence of an external magnetic field are obtained as a function of the quantum dot size and the confinement strength and also as a function of the magnetic field by a variational method with a simple wave function. A Jastrow-like factor is used to take care of the correlation effect. The results are obtained. The magnetic moment and susceptibility are also obtained for the donor complex. One of the most important objectives of this work is to study the effect of the magnetic field on the resultant dipole moment of a D− complex in a Gaussian QD. It is shown that the resultant dipole moment of a D− complex increases as the dot size increases and decreases as the magnetic field increases. The effect of the confinement strength on the resultant dipole moment is also investigated for different values of the magnetic field.

Meson-Cloud Effects in the Electromagnetic Nucleon Structure

We study how the electromagnetic structure of the nucleon is influenced by a pion cloud. To this aim we make use of a constituent-quark model with instantaneous confinement and a pion that couples directly to the quarks. To derive the invariant 1- photon-exchange electron-nucleon scattering amplitude we employ a Poincar\'e- invariant coupled-channel formulation which is based on the point-form of relativistic quantum mechanics. We argue that the electromagnetic nucleon current extracted from this amplitude can be reexpressed in terms of pure hadronic degrees of freedom with the quark substructure of the pion and the nucleon being encoded in electromagnetic and strong vertex form factors. These are form factors of bare particles, i.e. eigenstates of the pure confinement problem. First numerical results for (bare) photon-nucleon and pion-nucleon form factors, which are the basic ingredients of the further calculation, are given for a simple 3-quark wave function of the nucleon.

Generalized BF state in quantum gravity

The BF state is known as a simple wave function that satisfies three constraints in canonical quantum gravity without a cosmological constant. It is constructed from a product of the group delta functions. Applying the chiral asymmetric extension, the BF state is generalized to the state for real values of the Barbero-Immirzi parameter.

Local models of fractional quantum Hall states in lattices and physical implementation

The fractional quantum Hall effect is one of the most striking phenomena in condensed matter physics. It is described by a simple Laughlin wavefunction and has been thoroughly studied both theoretically and experimentally. In lattice systems, however, much less is currently known, and only few models and mechanisms leading to it have been identified. Here we propose a new way of constructing lattice Hamiltonians with local interactions and fractional quantum Hall like ground states. In particular, we obtain a spin 1/2 model with a bosonic Laughlin-like ground state, displaying a variety of topological features. We also demonstrate how such a model naturally emerges out of a Fermi-Hubbard-like model at half filling, in which the kinetic energy part possesses bands with non-zero Chern number, and we show how this model can be implemented in an optical lattice setup with present or planned technologies.

Visualising many-body electron dynamics using one-body densities and orbitals

As experimental techniques begin to probe electronic motions in increasing detail, the need is arising for compact and informative visualisations of simulations of such processes. The inherent challenge is that a full many-electron wavefunction is a high-dimensional object, representing the complicated correlations of strongly repulsive bodies in a small molecular volume. A general procedure is needed to distill this to a smaller amount of information that does not rely on any specific level of approximation. The result should allow for easy and intuitive interpretation while drawing out nontrivial aspects of the underlying many-body dynamics, such as the complex phase information inherent of a nonstationary state. Current visualisation schemes based on physical observables or the qualitative information contained in simple wavefunctions, such as time-dependent configuration-interaction-singles (TD-CIS) and time-dependent self-consistent-field (TD-SCF), are discussed. This information is compared to an analysis based on the one-body reduced density operator (1-RDO), which is well-defined for general wavefunctions. It is seen that the distinction between two paradigms of many-body dynamics, electron transport and energy transport, is reflected in the coherences of a difference-1-RDO, or lack thereof.

Vector meson production at low x from gauge/gravity duality

We use gauge/gravity duality to study vector meson (J/{\Psi}, {\rho}_0, {\Omega}, {\Phi}) production in electron-proton scattering, in the limit of high center of mass energy at fixed momentum transfer, corresponding to the limit of low Bjorken x, where the process is dominated by pomeron exchange. Our approach considers the pomeron at strong coupling, described by the graviton Regge trajectory in AdS space with a hard-wall to mimic confinement effects. Both the proton and vector mesons are described by simple holographic wave functions in AdS. This model agrees with HERA H1 data with a {\chi}^2 per degree of freedom below one on total cross-sections, and below two on differential cross-sections, confirming the success of previous studies that model low x DIS and DVCS using gauge/gravity duality.

One-dimensional model for the fractional quantum Hall effect

A simple one-dimensional model is proposed, in which N spinless repulsively interacting fermions occupy M>N degenerate states. It is argued that the energy spectrum and the wavefunctions of this system strongly resemble the spectrum and wavefunctions of 2D electrons in the lowest Landau level (the problem of the Fractional Quantum Hall Effect). In particular, Laughlin-type wavefunctions describe ground states at filling factors v = N/M = 1/q, q odd.. Within this model the complimentary wavefunction for v=1−1/q is found explicitly, and extremely simple ground state wavefunctions for arbitrary odd-denominator filling factors are proposed.