Statistical approach to the antiferromagnetic ground state problem

The statistical approach is adopted in an attempt to find the antiferromagnetic ground state. As a result an eigenstate of the Heisenberg hamiltonian is found which is not the true ground state, but which could serve as a useful starting point for other methods.The author is grateful to ing. P. Novák for valuable discussions.     

Atomic effects on α-α scattering to the8Be ground state

Theα-α scattering to the⁸Be ground state was investigated in kinematic coincidence for the angle pairs 45?/45? and 30?/60? using the crossing beams technique, with an energy resolution of 26 eV. The nuclear resonance is split into 2 structures, not the 3 structures suggested by earlier work. The atomic physics origin of the splitting, the resonance parameters of the⁸Be ground state, and astrophysical implications are discussed.     

Kinematic approach to the mixed state geometric phase in nonunitary evolution

A kinematic approach to the geometric phase for mixed quantal states in nonunitary evolution is proposed. This phase is manifestly gauge invariant and can be experimentally tested in interferometry. It leads to well-known results when the evolution is unitary.     

Variational path integral approach to the ground state energy of artificial atoms

Artificial atoms in different confinement potentials are studied using the Jensen–Feynman variational approach. The density and pair correlation function of an harmonic model with statistics are analytically calculated and used to find the variational ground state energy in two and three dimensions. The results are compared with the numerical calculations and a good correlation is found.     

A single-parameter trial wave function for the mixed valence ground state

The mixed valence trial ground state suggested by Stevens and Brandow is reconsidered in the case of two electrons per atom. The wellknown difficulties due to nonorthogonality are resolved by expanding the trial state in an orthonormal basis. The expansion coefficients are determinants composed of Bloch phase factors, as in the Gutzwiller method. Studying first the limiting case of the Kaplan-Mahanti strongly localized ground state in the Brandow formalism, we derive rules for a simplified handling of the determinants; this opens the way to the more complicated weakly localized ground state. This is handled by expressing theN variational parameters of the Brandow formalism through a single one, the hybridization temperature . The ground state energy is a well-behaved function of the hybridization matrix elementV. The valence and the shift of the Fermi level are calculated to lowest order inV. The band occupation numbers follow a Fermi distribution at temperature V. We argue that the ground state is insulating, with thed-electrons localized into large Wannier-type orbitals centered on the respectivef-holes, as envisaged by Stevens.     

A semiclassical approach to the ground state and density oscillations of quantum dots

A semiclassical Thomas–Fermi method, including a Weizsäcker gradient term, is implemented to describe ground states of two-dimensional nanostructures of arbitrary shape. Time-dependent density oscillations are addressed in the same spirit using the corresponding semiclassical time-dependent equations. The validity of the approximations is tested, both for ground state and density oscillations, compared with the available microscopic Kohn–Sham solutions.     

氦原子及类氦离子基态的二参数变分法研究

提出了一种计算氦原子及类氦离子基态能量和波函数的二参数变分法,包括试探波函数的设计和基态能量表达式的推导,并用Mathematica 5.0软件的优化计算功能方便快捷地计算出基态能量,将计算结果与实验结果和部分所列文献的结果进行对比.结果表明,本文所得精度较高,变分参数个数较少.同时强调交换对称性和量子态的交缠在双电子原子体系问题中的重要性.     

Variational approach to configuration interaction

A variational method is developed to determine configuration interaction wave functions. The method is straightforward and is applied to a pairing Hamiltonian with constant matrix elements, for which exact eigenvalues are available. Comparisons are made with the exact results. Calculations can be carried out to any desired degree of accuracy. The method is also applied to a Hamiltonian that has neutron-neutron, proton-proton, and neutron-proton pairing. No difficulties are found in extending the method to this Hamiltonian that has many collective modes. In practice, the method scales linearly with , where is the number of variational basis states.     

Atomic configuration effects in electromigration

We investigate the effects of atomic configuration on the driving force for electromigation. The validity of the pseudo-atom picture is discussed. General pseudopotential expressions are used to calculate the configuration-dependent force for lattice distortion fields around impurities as well as the force appropriate to the interstitialcy-translation-rotation mechanism for fast-diffusion. Lattice-distortion fields typically give rise to a 10–30% change in the electron-wind force. Substantial reduction in the wind-force was found to occur during the rotation phase of fast diffuser migration, in agreement with a conjecture by Hsieh et al. The effects of grain-boundary structure were considered and found to be small within the pseudoatom picture. Finally, we show how configurational effects may lead to the observed isotope separation in liquid metals (Häffner effect).     

Systematics of ground state multiplets of atomic nuclei in the delta-interaction approach

Pairing forces between nucleons in an atomic nucleus strongly influence its structure. One of the manifestations of pair interaction is the ground state multiplet (GSM) formation in the spectrum of low-lying excited states of even–even nuclei. The value of GSM splitting is determined by the value of pair interaction of nucleons; for each isotope, it can be estimated on the basis of experimental nuclear masses. The quality of this estimate is characterized by the degree of reproduction of GSM levels in the nucleus. The GSM systematics in even–even nuclei with a pair of identical nucleons in addition to the filled nuclear core is considered on the basis of delta interaction.     

Classical lattice gas model with a unique nondegenerate but unstable periodic ground state configuration

We construct a classical lattice gas model with a unique periodic ground state configuration such that the Peierls' condition is not satisfied. The ground state configuration is nondegenerate, which means that for any fixed energyE and any integern, the diameter of the support of alln-connected local excitations, with energy less thanE, is bounded. Nevertheless the configuration is not stable: it does not give rise to a low temperature phase. Any translation invariant Gibbs state of our model corresponds to quasiperiodic ground state configurations. This requires the modification of a recent hypothesis of Dobrushin and Shlosman.     

Correlated squeezed-state approach for the ground state of strongly correlated electrons coupled to local Holstein phonons

Summary In the present work we have applied the correlated squeezed-state approach to investigate the ground state of the extended Hubbard model which is coupled to local Holstein phonons. Our study begins with decoupling the electron and phonon subsystems approximately by introducing a variational correlated squeezed-state ansatz for the phonons. Then assuming the renormalized intersite electron correlation of the effective electronic Hamiltonian to be attractive and the renormalized on-site correlation repulsive, we have applied the generalized Hartree-Fock approximation to obtain the ground state of the system, which is a superconducting state with intersite pairing. With optimal values of the variational parameters the correlated squeezed-state approach will by construction yield a ground-state energy lower than those obtained in previous studies. This means that our variational ansatz is more stable as the ground state of the system. Furthermore, our variational study shows that in the correlated squeezed state the polaronic reduction effect of phonons is much more alleviated, and thus the mass enhancement inherent to the polaron effect is noticeably weakened. This weakening of the reduction effect should, in turn, significantly affect other physical properties of the system.     

Rotating Bose-Einstein condensate in an optical lattice: Formulation of vortex configuration for the ground state

We consider a rotating Bose-Einstein condensate in an optical lattice in the regime in which the system Hamiltonian can be mapped onto a Josephson junction array. In an approximate scheme where the couplings are assumed uniform, the ground state energy is formulated in terms of the vortex configuration. Application of the method for the ladder case presented and the results are compared with Monte-Carlo method.     

Prospects for the formation of ultracold ground state polar molecules from mixed alkali atom pairs

Photoassociation rates of mixed cold alkali atom pairs and formation rates of cold heteronuclear alkali dimers in their ground state are computed within an approach where the wave functions are calculated exactly, and the laser field is treated as a perturbation. These rates are predicted to have the same magnitude for all heteronuclear species involving either Rb or Cs atoms. Moreover, these rates are found slightly smaller than, or similar to, the same rates for Cs₂ molecules, which is encouraging for future experiments. We studied the specific case of the photoassociation into excited molecular states coupled with spin-orbit interaction, emphasizing the role of the so-called resonant coupling in the formation of stable ultracold molecules with low vibrational levels. The comparison with recent experimental results on RbCs photoassociation and cold molecule formation show their reasonable agreement with our calculations.Received: 2 July 2004, Published online: 23 November 2004PACS: 32.80.Pj Optical cooling of atoms; trapping - 33.20.Tp Vibrational analysis - 33.70.Ca Oscillator and band strengths, lifetimes, transition moments, and Franck-Condon factors     

A minimisation approach for computing the ground state of Gross–Pitaevskii systems

In this paper, we present a minimisation method for computing the ground state of systems of coupled Gross–Pitaevskii equations. Our approach relies on a spectral decomposition of the solution into Hermite basis functions. Inserting the spectral representation into the energy functional yields a constrained nonlinear minimisation problem for the coefficients. For its numerical solution, we employ a Newton-like method with an approximate line-search strategy. We analyse this method and prove global convergence. Appropriate starting values for the minimisation process are determined by a standard continuation strategy. Numerical examples with two- and three-component two-dimensional condensates are included. These experiments demonstrate the reliability of our method and nicely illustrate the effect of phase segregation.     

A configuration space approach to the nuclear four-body problem

The derivation of a complete orthogonal system for the nuclear four-body problem is discussed, which will be especially useful in the case of identical particles. A method for dealing with four-body bound states is proposed. Part of the orthogonal system is given explicitly.     

Two-level lasers operating on the transitions to the ground state

We analyze in detail a model of two-level lasers with a thermal production of population inversion proposed by V. A. Gerasimov et al. (Phys. Rev. Lett., 2006, 96, 123902). We show that it is possible to obtain nine new laser lines on the transitions to the ground state in atoms of rare-earth metals (REMs) with an incomplete 4f shell (Pr, Nd, Sm, Eu, and Tb–Tm). The laser line wavelengths are from the UV (Eu) to the middle IR (Tb and Er) regions of the spectrum. Based on the estimates of the specific laser energy parameters (power, power density, and efficiency), we conclude that only Sm, Eu, and Tm (among the REMs under study) are suited for the experimental prototypes of these lasers. The estimated maximum efficiency and specific power density of continuous lasing can reach the values of >40% and ~10⁷÷10⁹ W/cm², respectively.