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We have recently estimated the total energy of the BeH 2 molecule as -15.918 ± 0.015 au. One of the steps in the analysis was to estimate the difference between the SCF energies computed with a minimal basis set of Slater orbits and with the best possible single-determinant wave function, the so-called Hartree-Fock limit and was predicted to be -15.773 ± 0.007 au for BeH 2 .
Since the nowadays growing interest in Bose-Einstein condensates due to the expanded experimental evidence on various atomic systems within optical lattices in weak and strong coupling regimes, the connection with Density Functional Theory is firstly advanced within the mean field framework at three levels of comprehension: the many-body normalization condition, Thomas-Fermi limit, and the chemical hardness closure with the inter-bosonic strength and universal Hohenberg-Kohn functional. As an application the traditional Heitler-London quantum mechanical description of the chemical bonding for homopolar atomic systems is reloaded within the non-linear Schrödinger (Gross-Pitaevsky) Hamiltonian; the results show that a two-fold energetic solution is registered either for bonding and antibonding states, with the bosonic contribution being driven by the square of the order parameter for the Bose-Einstein condensate density in free (gas) motion, while the associate wave functions remain as in classical molecular orbital model.
Dissipative quantum trajectories in complex space are investigated in the framework of the logarithmic nonlinear Schrödinger equation. The logarithmic nonlinear Schrödinger equation provides a phenomenological description for dissipative quantum systems. Substituting the wave function expressed in terms of the complex action into the complex-extended logarithmic nonlinear Schrödinger equation, we derive the complex quantum Hamilton–Jacobi equation including the dissipative potential. It is shown that dissipative quantum trajectories satisfy a quantum Newtonian equation of motion in complex space with a friction force. Exact dissipative complex quantum trajectories are analyzed for the wave and solitonlike solutions to the logarithmic nonlinear Schrödinger equation for the damped harmonic oscillator. These trajectories converge to the equilibrium position as time evolves. It is indicated that dissipative complex quantum trajectories for the wave and solitonlike solutions are identical to dissipative complex classical trajectories for the damped harmonic oscillator. This study develops a theoretical framework for dissipative quantum trajectories in complex space.
The effects of weakly coupled plasmas on the dynamic dipole polarizabilities of the H{sup −} and Ps{sup −} ions are investigated using highly correlated exponential wave functions. The Debye-Hückel shielding approach of plasma modeling is used to represent weakly coupled plasma environments. In free-atomic cases, results obtained from the present study for H{sup −} are in agreement with the available calculations and results for Ps{sup −} are reported for the first time. Frequency-dependent polarizabilities of H{sup −} and Ps{sup −} as functions of screening parameter are also presented for the first time.
Particular isospin-symmetry-breaking probes including Coulomb energy differences (CED), mirror energy differences (MED), and triplet energy differences (TED) manifest anomalies in the A∼70 isovector triplets of nuclei. The structure of proton-rich nuclei in the A∼70 mass region suggests shape coexistence and competition between pairing correlations in different channels. Recent results concerning the interplay between isospin-mixing and shape-coexistence effects on exotic phenomena in A∼70 nuclei obtained within the beyond-mean-field complex Excited Vampir variational model with symmetry projection before variation using a realistic effective interaction in a relatively large model space are presented. Excited Vampir predictions concerning the Gamow-Teller β decay to the odd-odd N=Z {sup 66}As and {sup 70}Br nuclei correlated with the pair structure analysis in the T=1 and T=0 channel of the involved wave functions are discussed.
The use of variationally optimized coordinates, which minimize the vibrational self-consistent field (VSCF) ground state energy with respect to orthogonal transformations of the coordinates, has recently been shown to improve the convergence of vibrational configuration interaction (VCI) towards the exact full VCI [K. Yagi, M. Keçeli, and S. Hirata, J. Chem. Phys. 137, 204118 (2012)]. The present paper proposes an incorporation of optimized coordinates into the vibrational coupled cluster (VCC), which has in the past been shown to outperform VCI in approximate calculations where similar restricted state spaces are employed in VCI and VCC. An embarrassingly parallel algorithm for variational optimization of coordinates for VSCF is implemented and the resulting coordinates and potentials are introduced into a VCC program. The performance of VCC in optimized coordinates (denoted oc-VCC) is examined through pilot applications to water, formaldehyde, and a series of water clusters (dimer, trimer, and hexamer) by comparing the calculated vibrational energy levels with those of the conventional VCC in normal coordinates and VCI in optimized coordinates. For water clusters, in particular, oc-VCC is found to gain orders of magnitude improvement in the accuracy, exemplifying that the combination of optimized coordinates localized to each monomer with the size-extensive VCC wave function provides a supreme description of systems consisting of weakly interacting sub-systems.
The Koster–Slater and Anderson models are used to consider substitutional impurities in free-standing single-layer graphene. The density of states of graphene is described using a model (the M model). For the nitrogen and boron impurities, the occupation numbers and the parameter η which defines the fraction of delocalized electrons of the impurity are determined. In this case, experimental data are used for both determination of the model parameters and comparison with the results of theoretical estimations. The general features of the Koster–Slater and Anderson models and the differences between the two models are discussed. Specifically, it is shown that the band contributions to the occupation numbers of a nitrogen atom in both models are comparable, whereas the local contributions are substantially different: the local contributions are decisive in the Koster–Slater model and negligible in the Anderson model. The asymptotic behavior of the wave functions of a defect is considered in the Koster–Slater model, and the electron states of impurity dimers are considered in the Anderson model.
The nonthermal effects on the doubly excited resonance states of the hydrogen negative ion and helium atom are investigated in Lorentzian astrophysical plasma environments using highly correlated Hylleraas-type wave functions in the framework of the stabilization method. Resonance parameters (resonance position and width) are reported for the first time as functions of the spectral index and plasma parameter. The screening effects are more pronounced in the stronger screening region.
I will speak about Bose-Einstein condensation (BEC) in quantum magnets, in particular the compound NiCl2-4SC(NH2)2. Here a magnetic field-induced quantum phase transition to XY antiferromagnetism can be mapped onto BEC of the spins. The tuning parameter for BEC transition is the magnetic field rather than the temperature. Some interesting phenomena arise, for example the fact that the mass of the bosons that condense can be strongly renormalized by quantum fluctuations. I will discuss the utility of this mapping for both understanding the nature of the quantum magnetism and testing the thermodynamic limit of Bose-Einstein Condensation. Furthermore we can dope the system in a clean and controlled way to create the long sought-after Bose Glass transition, which is the bosonic analogy of Anderson localization. I will present experiments and simulations showing evidence for a new scaling exponent, which finally makes contact between theory and experiments. Thus we take a small step towards the difficult problem of understanding the effect of disorder on bosonic wave functions.
We report on intraband photocurrent spectroscopy of dome-shaped GeSi islands embedded in a Si matrix with n{sup +}-type bottom and top Si layers. An in-plane polarized photoresponse in the 85–160 meV energy region has been observed and ascribed to the optical excitation of electrons from states confined in the strained Si near the dome apexes to the continuum states of unstrained Si. The electron confinement is caused by a modification of the conduction band alignment induced by inhomogeneous tensile strain in Si around the buried GeSi quantum dots. Sensitivity of the device to the normal incidence radiation proves a zero-dimensional nature of confined electronic wave functions.
We present single and double particle-hole excitations in the recently revived spin-projected Hartree-Fock. Our motivation is to treat static correlation with spin-projection and recover the residual correlation, mostly dynamic in nature, with simple configuration interaction (CI). To this end, we introduce the Wick theorem for nonorthogonal determinants, which enables an efficient implementation in conjunction with the direct CI scheme. The proposed approach, termed spin-extended CI with singles and doubles, achieves a balanced treatment between dynamic and static correlations. To approximately account for the quadruple excitations, we also modify the well-known Davidson correction. We report that our approaches yield surprisingly accurate potential curves for HF, H{sub 2}O, N{sub 2}, and a hydrogen lattice, compared to traditional single reference wave function methods at the same computational scaling as regular CI.
In this paper, a quantum correction computation of the inversion layer of charge density was investigated. This study is carried out for a one-dimensional Metal–lnsulator–Semiconductor (MIS) structure with (100) oriented P-type silicon as substrate. The purpose of this paper is to point out the differences between the semiclassical and quantum-mechanical charge description at the interface Al{sub 2}O{sub 3}/Si, and to identify some electronic properties of our MIS device using different thickness of the high-k oxide and diverse temperature with different carrier statitics (Fermi–Dirak statitics and Boltzmann statitics). In particular, the calculations of capacitance voltage (C–V), sheet electron density, a relative position of subband energies and their wave functions are performed to examine qualitatively and quantitatively the electron states and charging mechanisms in our device.
In usual realistic classical dynamical systems, the Hamiltonian depends explicitly on time. In this work, a class of classical systems with time dependent nonlinear Hamiltonians is analyzed. This type of problems allows to find invariants by a family of Veronese maps. The motivation to develop this method results from the observation that the Poisson-Lie algebra of monomials in the coordinates and momenta is clearly defined in terms of its brackets and leads naturally to an infinite linear set of differential equations, under certain circumstances. To perform explicit analytic and numerical calculations, two examples are presented to estimate the trajectories, the first given by a nonlinear problem and the second by a quadratic Hamiltonian with three time dependent parameters. In the nonlinear problem, the Veronese approach using jets is shown to be equivalent to a direct procedure using elliptic functions identities, and linear invariants are constructed. For the second example, linear and quadratic invariants as well as stability conditions are given. Explicit solutions are also obtained for stepwise constant forces. For the quadratic Hamiltonian, an appropriated set of coordinates relates the geometric setting to that of the three dimensional manifold of central conic sections. It is shown further that the quantum mechanical problem of scattering in a superlattice leads to mathematically equivalent equations for the wave function, if the classical time is replaced by the space coordinate along a superlattice. The mathematical method used to compute the trajectories for stepwise constant parameters can be applied to both problems. It is the standard method in quantum scattering calculations, as known for locally periodic systems including a space dependent effective mass.
We consider acoustic wave transmission in a non-axisymmetric waveguide which consists of a cylindrical resonator of radius R and length L and two cylindrical waveguides of radius r<R whose axes are shifted relative to the axis of the resonator and relative to each other by azimuthal angle Δϕ. We find multiple bound states in the continuum (trapped modes) with nonzero orbital angular momentum under variation of L due to full destructive interference of resonant modes leaking into waveguides. For Δϕ=π∕2 we find the degenerate bound states in the continuum whose contribution into the scattering wave function is complex and supports giant vortical acoustic intensity spinning inside the resonator.
Highlights: • Foundations of quantum mechanics • Quantum decay • Non-Hermitian Hamiltonian • Unitarity • Resonant state By using an analytical exact non-Hermitian formalism for quantum tunneling decay that involves the expansion of the decaying wave function as a linear combination of resonant states and transient functions associated with the complex poles of the outgoing Green’s function to the problem, it is shown that the integrated decaying probability density in the whole space satisfies unitarity at each value of time.
We present a theoretical study of the polarization engineering in semi-polar III-nitrides heterostructures. As a case study, we investigate the influence of GaN, AlGaN, and AlInN barrier material on the performance of semi-polar (112{sup ¯}2) InGaN-based quantum wells (QWs) for blue (450 nm) and yellow (560 nm) emission. We show that the magnitude of the total built-in electric field across the QW can be controlled by the barrier material. Our results indicate that AlInN is a promising candidate to achieve (i) reduced wavelength shifts with increasing currents and (ii) strongly increased electron-hole wave function overlap, important for reduced optical recombination times.
The capping of an array of self-assembled InAs/GaAs quantum dots by an InGaAs quantum-well layer leads to an increase in their size due to indium enrichment of the region near the top of the quantum dots, which decreases the energy of the ground-state optical transition in quantum dots by 50 meV and shifts the hole wave function toward the top of the quantum dot.
We introduce an extension of the divide-and-conquer (DC) algorithmic paradigm called divide-conquer-recombine (DCR) to perform large quantum molecular dynamics (QMD) simulations on massively parallel supercomputers, in which interatomic forces are computed quantum mechanically in the framework of density functional theory (DFT). In DCR, the DC phase constructs globally informed, overlapping local-domain solutions, which in the recombine phase are synthesized into a global solution encompassing large spatiotemporal scales. For the DC phase, we design a lean divide-and-conquer (LDC) DFT algorithm, which significantly reduces the prefactor of the O(N) computational cost for N electrons by applying a density-adaptive boundary condition at the peripheries of the DC domains. Our globally scalable and locally efficient solver is based on a hybrid real-reciprocal space approach that combines: (1) a highly scalable real-space multigrid to represent the global charge density; and (2) a numerically efficient plane-wave basis for local electronic wave functions and charge density within each domain. Hybrid space-band decomposition is used to implement the LDC-DFT algorithm on parallel computers. A benchmark test on an IBM Blue Gene/Q computer exhibits an isogranular parallel efficiency of 0.984 on 786 432 cores for a 50.3 × 10{sup 6}-atom SiC system. As a test of production runs, LDC-DFT-based QMD simulation involving 16 661 atoms is performed on the Blue Gene/Q to study on-demand production of hydrogen gas from water using LiAl alloy particles. As an example of the recombine phase, LDC-DFT electronic structures are used as a basis set to describe global photoexcitation dynamics with nonadiabatic QMD (NAQMD) and kinetic Monte Carlo (KMC) methods. The NAQMD simulations are based on the linear response time-dependent density functional theory to describe electronic excited states and a surface-hopping approach to describe transitions between the excited states. A series of techniques are employed for efficiently calculating the long-range exact exchange correction and excited-state forces. The NAQMD trajectories are analyzed to extract the rates of various excitonic processes, which are then used in KMC simulation to study the dynamics of the global exciton flow network. This has allowed the study of large-scale photoexcitation dynamics in 6400-atom amorphous molecular solid, reaching the experimental time scales.