Simple Wave Function Research Articles

Temperature and resultant dipole moment of an off-center D- impurity in a Gaussian quantum dot

Abstract The present study investigates the variation of energy ( E ), binding energy ( E B ) and the resultant dipole moment ( D p ) of a negative donor impurity ( D − ) with on-center and off-center locations ( d ) in a GaAs three-dimensional quantum dot (3D-QD) modelled with a Gaussian confinement potential. I have performed Ritz-variational method (RVM) with a very simple wave function which contains just three-variational parameters and a Jastrow-like factor. For on-center ( D − ) impurity, it is true from [47,50] and present results that the E B is always positive and maximum at a particular size of the QD ( R c ). For off-center ( D − ) impurity especially for a large value of locations ( d ) the ( E B ) can be negative. These situations imply that the stability and instability of the system for a given range of the quantum dot size ( R ), respectively. I have obtained the temperatures of D 0 , D − impurities at which these impurities are more stable in a 3D-QD. The confinement length ( R ) and the confinement strength ( V 0 ) effects, on the resultant dipole moment ( D p ) are also investigated for various values of the impurity locations ( d ).

Variational Principles in Quantum Monte Carlo: The Troubled Story of Variance Minimization.

We investigate the use of different variational principles in quantum Monte Carlo, namely, energy and variance minimization, prompted by the interest in the robust and accurate estimation of electronic excited states. For two prototypical, challenging molecules, we readily reach the accuracy of the best available reference excitation energies using energy minimization in a state-specific or state-average fashion for states of different or equal symmetry, respectively. On the other hand, in variance minimization, where the use of suitable functionals is expected to target specific states regardless of the symmetry, we encounter severe problems for a variety of wave functions: as the variance converges, the energy drifts away from that of the selected state. This unexpected behavior is sometimes observed even when the target is the ground state and generally prevents the robust estimation of total and excitation energies. We analyze this problem using a very simple wave function and infer that the optimization finds little or no barrier to escape from a local minimum or local plateau, eventually converging to a lower-variance state instead of the target state. For the increasingly complex systems becoming in reach of quantum Monte Carlo simulations, variance minimization with current functionals appears to be an impractical route.

Non-Perturbative Treatment of Quantum Mathieu Oscillator

We study the evolution in time of the quantum Mathieu oscillator (QMO), according to the motion of a charged particle in a radio frequency Paul trap. We adopt non-perturbative treatment based on the quantized Floquet formalism together with the resonating averages method (RAM). We prove that we can develop solutions of the time-dependent Schrödinger equation of such a system, in terms of the simple harmonic oscillator wave functions. Numerical simulations of the analytical results are performed to show the coherence and the squeezed proprieties of the wave-packet of this system.

Rich Magnetic Quantization Phenomena in AA Bilayer Silicene

The rich magneto-electronic properties of AA-bottom-top (bt) bilayer silicene are investigated using a generalized tight-binding model. The electronic structure exhibits two pairs of oscillatory energy bands for which the lowest conduction and highest valence states of the low-lying pair are shifted away from the K point. The quantized Landau levels (LLs) are classified into various separated groups by the localization behaviors of their spatial distributions. The LLs in the vicinity of the Fermi energy do not present simple wave function modes. This behavior is quite different from other two-dimensional systems. The geometry symmetry, intralayer and interlayer atomic interactions, and the effect of a perpendicular magnetic field are responsible for the peculiar LL energy spectra in AA-bt bilayer silicene. This work provides a better understanding of the diverse magnetic quantization phenomena in 2D condensed-matter materials.

Tsallis entropy calculation for non-Coulombic helium

Tsallis entropy is calculated for ground state of helium that interrelate with a modified potential via a combination of Yukawa and exponential-cosine-screened-Coulomb potentials. The calculations have been done, in the position (r) space, using an explicitly correlated 3-parameter wave function. The simple wave function is used to reach intuitive and quantitative discussions. Due to the nonadditive property of our system, the modified Tsallis index Qq is proposed and calculated as a function of the screening parameter μ. Such calculations for the ground state of helium with the modified potential are carried out for the first time in the literature.

The nonadditive entropy for the ground state of helium-like ions using Hellmann potential

We are calculating the Tsallis entropy for the ground state of helium isoelectronic series that interrelates with the Yukawa and Hellmann-type potentials in the position (r) space. The calculation has been done by solving the Schrödinger equation in the Hylleraas-coordinate system and within the framework of the Ritz’s variational principle. Simple wave functions have been used in the calculation to reach informative discussions. The scaling behaviour of Tsallis entropy as a function of the nuclear charge Z, the Tsallis index , and screening parameter , is defined and discussed. Due to the nonadditive property of our system, the modified Tsallis index is proposed and calculated as a function of . The calculations for two-electron systems in Hellmann potential (HP) are carried out for the first time in the literature.

Effect of Rashba and Dresselhaus spin-orbit interactions on a D0 impurity in a two-dimensional Gaussian GaAs quantum dot in the presence of an external magnetic field

Abstract The binding energy of a hydrogenic-like donor complex D 0 placed in a two-dimensional Gaussian quantum dot GaAs semiconductor is determined incorporating the Rashba and Dresselhaus spin-orbit interactions in the presence of an externally applied magnetic field. A unitary transformation is employed to deal with the spin-orbit interactions and their effects are incorporated up to second order in the coupling coefficients. The resulting Hamiltonian is solved variationally using a simple wave function. The results indicate that the Rashba spin-orbit interaction and the confining potential reduce the energy of the donor complex whereas the magnetic field enhances it. Interestingly enough, the binding energy is enhanced by the Dresselhaus spin-orbital interaction in the presence of a magnetic field and while it is reduced in the absence of it. Finally we study the effect of magnetic field and spin-orbit interactions on the magnetic moment and susceptibility.

Spin-free wave functions for small molecules

In an earlier paper, we described a simple version of spin-free calculations of the energy of two three-electron systems, HeH and H3. Here, we extend our treatment to LiH+ and to two four-electron systems, LiH and BeH+. The necessary extensions are not trivial, but we are still able to obtain energies in atomic units consistent to at least four figures using very simple approximate wave functions. The wave functions used are given in the text, and are based on two-centre molecular orbitals consisting of exponential functions with varied exponents. Our procedures may be viewed as a convenient fusion of the classic valence-bond and molecular-orbital approaches to molecular structure.

Applications of the Variational Quantum Monte Carlo Method to the Two-Electron Atoms

The variational quantum Monte Carlo method was applied to investigate the ground states of the helium atom and helium like ions with atomic number from 1 to 10 and the first four excited states of the helium atom. Furthermore, the investigation of the ground state of helium, Li⁺, and Be²⁺ in a confined impenetrable spherical box. Moreover, the calculation of the ground state of the helium atom in a strong magnetic field using four simple trial wave functions. The trial wave functions consist of usual orbital hydrogen wave functions multiplied by correlation function. Using four different correlation wave functions, we describe the interaction of the two electrons with each other and having a small number of variational parameters.

Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz.

We perform excited-state variational Monte Carlo and diffusion Monte Carlo calculations using a simple and efficient wave function ansatz. This ansatz follows the recent variation-after-response formalism, accurately approximating a configuration interaction singles wave function as a sum of only two nonorthogonal Slater determinants and further including important orbital relaxation. The ansatz is used to perform diffusion Monte Carlo calculations with large augmented basis sets, comparing to benchmarks from near-exact quantum chemical methods. The significance of orbital optimization in excited-state diffusion Monte Carlo is demonstrated, and the excited-state optimization procedure is discussed in detail. Diffuse excited states in water and formaldehyde are studied, in addition to the formaldimine and benzonitrile molecules.

Diffusion and reptation quantum Monte Carlo study of the NaK molecule

ABSTRACTDiffusion Monte Carlo (DMC) and Reptation Monte Carlo (RMC) methods, have been applied to study some properties of the NaK molecule. Hartree–Fock (HF), Density Functional (DFT) and single and double configuration interaction (SDCI) wavefunctions with a valence quadruple zeta atomic natural orbital (VQZ/ANO) basis set were used as trial wavefunctions. Values for the potential energy curve, dissociation energy and dipole moment were calculated for all methods and compared with experimental results and previous theoretical derivations. Quantum Monte Carlo (QMC) calculations were shown to be useful methods to recover correlation in NaK, essential to obtain a reasonable description of the molecule. The equilibrium distance yield a value close to the experimental one. The dissociation energy, however, is not so good, and the minimum error is about 4% of the experimental value, except when a coupled-clusters method is used. In this case, a conventional CCSD(T) calculation with an extended aug-pc-4 basis set gives a much better agreement to experiment. However, neither the CCSD(T) nor other MO and DFT methods are able to reproduce correctly the large dipole moment of this molecule. Even DMC methods with a simple HF trial wavefunction are able to give a better agreement to experiment, although they have a larger error bar.

Molecular interactions in electron-groups embedding generalized valence bond picture

Theoretical description of molecular interactions remains a challenge for computational chemistry. In particular, systems dominated by static correlation, in which bonds are stretched or twisted, are often beyond capabilities of methods based on a single-electron approximation, being usually a method of choice. For interacting multireference systems, it is necessary to apply either high-level coupled-cluster methods (which however include multireference effects only partially) or base the theoretical description on a multireference wavefunction. Popular multireference methods like CASPT2 (complete active space perturbation theory) do not provide satisfactory results since they may suffer from problems with size consistency and poor accuracy. Recently we have shown that combining a simple multireference wavefunction, perfect-pairing generalized valence bond (GVB) with extended random phase approximation in embedding framework (EERPA) leads to a method EERPA-GVB providing accurate results for challenging multireference systems. In this paper, good performance of EERPA-GVB is confirmed by its application to van der Waals and hydrogen-bonded complexes. In addition, we show that the decomposition of the EERPA-GVB correlation energy into contributions from pairs of geminals can provide useful insight into the investigated interactions.

Solution of the logarithmic Schrödinger equation with a Coulomb potential

The nonlinear logarithmic Schrödinger equation (log SE) appears in many branches of fundamental physics, ranging from macroscopic superfluids to quantum gravity. We consider here a model problem, in which the log SE includes an attractive Coulomb interaction. We derive an analytical solution for the ground state energy and wave function as a function of the strength of the logarithmic interaction. We develop an iterative finite element method to solve the Coulombic log SE for the spherically symmetric states. The ground state results agree with the exact solution to better than one part in 1010. The excited states (n>1) are converged to better than one part in 108. We also construct a remarkably simple variational wave function, consisting of a sum of Gaussons with n free parameters. One can obtain an approximation to the energy and wave function that is in good agreement with the finite element results. Although the Coulomb problem is interesting in its own right, the iterative finite element method and the variational Gausson basis approach can be applied to any central force Hamiltonian.

Some simple solutions of Schrödinger's equation for a free particle or for an oscillator

For a non-relativistic free particle, we show that the evolution of some simple initial wave functions made up of linear segments can be expressed in terms of Fresnel integrals. Examples include the square wave function and the triangular wave function. The method is then extended to wave functions made from quadratic elements. The evolution of all these initial wave functions can also be found for the harmonic oscillator by a transformation of the free evolutions.

Fixed-Node, Importance-Sampling Diffusion Monte Carlo for Vibrational Structure with Accurate and Compact Trial States.

We present a new approach to importance sampling in diffusion Monte-Carlo (DMC) simulations of vibrational excited states whereby the trial wave functions for low-energy states are incorporated into the diffusion equations so as to enforce their orthogonality. For the model systems examined here, simple variational wave functions based on the vibrational self-consistent field (VSCF) and the simplest vibrational configuration interaction (VCI) are effective in importance sampling provided that internal coordinates used in the underlying one-particle functions have been variationally optimized. The resulting model yields results comparable in accuracy to the best unguided DMC calculations without requiring an a priori choice of coordinates to specify nodal hyperplanes.

Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo

We present a simple and efficient wave function ansatz for the treatment of excited charge-transfer states in real-space quantum Monte Carlo methods. Using the recently introduced variation-after-response method [E. Neuscamman, J. Chem. Phys. 145, 081103 (2016)], this ansatz allows a crucial orbital optimization step to be performed beyond a configuration interaction singles expansion, while only requiring calculation of two Slater determinant objects. We demonstrate this ansatz for the illustrative example of the stretched LiF molecule, for a range of excited states of formaldehyde, and finally for the more challenging ethylene-tetrafluoroethylene molecule.

Catastrophes in non-equilibrium many-particle wave functions: universality and critical scaling

As part of the quest to uncover universal features of quantum dynamics, we study catastrophes that form in simple many-particle wave functions following a quench, focusing on two-mode systems that include the two-site Bose–Hubbard model, and under some circumstances optomechanical systems and the Dicke model. When the wave function is plotted in Fock space certain characteristic shapes, that we identify as cusp catastrophes, appear under generic conditions. In the vicinity of a cusp the wave function takes on a universal structure described by the Pearcey function and obeys scaling relations which depend on the total number of particles N. In the thermodynamic limit () the cusp becomes singular, but at finite N it is decorated by an interference pattern. This pattern contains an intricate network of vortex–antivortex pairs, initiating a theory of topological structures in Fock space. In the case where the quench is a δ-kick the problem can be solved analytically and we obtain scaling exponents for the size and position of the cusp, as well as those for the amplitude and characteristic length scales of its interference pattern. Finally, we use these scalings to describe the wave function in the critical regime of a symmetry-breaking dynamical phase transition.

Numerical study of magnetization plateaus in the spin- 12 Heisenberg antiferromagnet on the checkerboard lattice

We present numerical evidence that the spin-1/2 Heisenberg model on the two-dimensional checkerboard lattice exhibits several magnetization plateaux for m=0, 1/4, 1/2 and 3/4, where m is the magnetization normalized by its saturation value. These incompressible states correspond to somehow similar valence-bond crystal phases that break lattice symmetries, though they are different from the already established plaquette phase for m=0. Our results are based on Exact Diagonalization as well as Density Matrix Renormalization Group large-scale simulations, and interpreted in terms of simple trial wavefunctions.

Pionic transition from Y(4260) to Zc(3900) in a hadronic molecular scenario

We study the pionic transition from Y(4260) to Z c(3900), where Y(4260) and Z c(3900) are regarded as the weakly bound states of D $\bar{D}_{1}$ (2420) + H.c. and D $\bar{D}^{\ast}$ + H.c., respectively. The partial width of Y(4260) $ \rightarrow$ Z c(3900) $\pi$ is estimated to be of the order of MeV with the wave functions of the bound states, where the wave functions are simulated by the simple harmonic oscillator wave functions with equivalent root-mean-square radii.

Maximal intensity higher-order Akhmediev breathers of the nonlinear Schrödinger equation and their systematic generation

It is well known that Akhmediev breathers of the nonlinear cubic Schrödinger equation can be superposed nonlinearly via the Darboux transformation to yield breathers of higher order. Surprisingly, we find that the peak height of each Akhmediev breather only adds linearly to form the peak height of the final breather. Using this peak-height formula, we show that at any given periodicity, there exists a unique high-order breather of maximal intensity. Moreover, these high-order breathers form a continuous hierarchy, growing in intensity with increasing periodicity. For any such higher-order breather, a simple initial wave function can be extracted from the Darboux transformation to dynamically generate that breather from the nonlinear Schrödinger equation.