Mott transition in anharmonic confinement

Two effects are identified that affect the visibility of the Mott transition in an atomic gas in an optical lattice confined in a power-law potential. The transition can be made more pronounced by increasing the power law, but at the same time, experimental uncertainty in the number of particles will induce corresponding fluctuations in the measured condensate fraction. Calculations in two dimensions indicate that a potential slightly more flat-bottomed than a quadratic one is to be preferred for a wide range of particle number fluctuation size.     

A law of large numbers and a central limit theorem for the Schrödinger operator with zero-range potentials

We consider the Schrödinger operator with zero-range potentials onN points of three-dimensional space, independently chosen according to a common distributionV(x). Under some assumptions we prove that, whenN goes to infinity, the sequence converges to a Schrödinger operator with an effective potential. The fluctuations around the limit operator are explicitly characterized.     

Topography of approximate molecular electrostatic potentials

A new method is described for the approximation of the molecular electrostatic potential (MESP). This method is used for the study of the topography of small molecules. The critical points of the approximate and the exact MESP are compared. It is found that most of the critical points of the exact MESP are retained, but in regions where the exact MESP changes slowly near critical points the number of critical points of the approximate MESP can be reduced.     

Ne-CH4分子间相互作用势的局域密度近似计算

利用基于密度泛函理论框架下的局域密度近似方法对Ne-CH4分子间的相互作用势进行了计算. 发现: 当Ne原子和CH4分子之间的距离约为5.8 a.u.时, 计算的势能曲线存在最小值, 对应的势阱深度约为0.053 eV. 计算结果与实验值符合较好.     

Exact solutions of a Fokker-Planck equation

Exact explicit solutions are given for a one-dimensional Fokker-Planck equation with a particular potential form involving hyperbolic functions. This potential contains four arbitrary parameters that can be chosen so that the potential is bistable. The solutions also contain parameters that can be chosen so that the initial distribution is approximately Gaussian, centered either at the unstable potential maximum or in the neighborhood of the secondary minimum. The use of the solutions to approximate solutions for other potentials is considered.     

Lifschitz tails for the Anderson model

We present, in an expository way, an elementary rigorous proof (patterned after an argument of Kirsch-Martinelli) that the Anderson model has Lifschitz tails in very great generality.Research partially supported by USNSF Grant No. MCS-81-20833.     

Ground state of liquid helium-3: off-shell effects due to non-local potentials

It is shown that by incorporating the off-shell effects through the introduction of phase equivalent nonlocal potentials, (that are essentially equivalent so far as two-body properties are concerned) one could obtain a much better agreement regarding the important properties of the ground state of liquid helium-3, in lowest order Brueckner-Goldstone theory. The binding energy, equilibruim density and the convergence character of Brueckner-Goldstone series improve drastically.     

Probing interatomic potentials by ion translational energy spectrometry: A new crossed molecular beams apparatus

This report presents details of the development of a new crossed molecular beams apparatus designed and fabricated to carry out high sensitivity ion translational energy spectrometric investigations of the potential energy surfaces of small molecular species. The translational energy spectrometer is used to carry out experimental studies of ion-neutral reactions resulting in charge stripping of CS⁺ radicals and dissociation of metastable CO²⁺ dications. These results are interpreted in the light of high-levelab initia molecular orbital calculations of the pertinent molecular potential energy functions. New results for the double ionisation energy of CS and the kinetic energy released upon dissociation of specific electronic states of CO²⁺ are presented.