Three-dimensional Hartree Research Articles

Asymptotics of the Spectrum of a Threedimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters

Asymptotics of the Spectrum of a Threedimensional Hartree Type Operator Near Upper Boundaries of Spectral Clusters

Investigating the nuclear Schiff moment of 207Pb in ferroelectric PbTiO3

A positive experimental measurement of the nuclear Schiff moment would have important implications for physics beyond the standard model. To aid in the interpretation of a proposed experiment to measure the nuclear Schiff moment of 207Pb in the ferroelectric PbTiO3, three-dimensional Hartree–Fock calculations have been performed to model the local electronic structure in the vicinity of the Pb nucleus. The energy shift due to the Schiff moment is found to be a factor of 2 smaller in comparison to existing estimates.

Inverse scattering problems for the Hartree equation whose interaction potential decays rapidly

We consider inverse scattering problems for the three-dimensional Hartree equation. We prove that if the unknown interaction potential V ( x ) of the equation satisfies some rapid decay condition, then we can uniquely determine the exact value of ∂ ξ α V ˆ ( 0 ) for any multi-index α by the knowledge of the scattering operator for the equation. Furthermore, we show some stability estimate for identifying ∂ ξ α V ˆ ( 0 ) .

Asymptotic solutions of Hartree equations concentrated near low-dimensional submanifolds. II. Localization in planar discs

We consider the eigenvalue problem for the three-dimensional Hartree equation in an external field and construct asymptotic (quasi-classical) solutions concentrated near two-dimensional planar discs. The rate of decrease of these solutions along the normal to the disc is determined by the Bogolyubov polaron, and near the edge of the disc it is defined by the Airy analogue of the polaron. To find the related series of eigenvalues, an analogue of the Bohr-Sommerfeld quantization rule is found from which is derived a simpler algebraic equation determining the main terms in the asymptotics of the eigenvalues.

Hall-conductivity sign reversal and fluctuations inYBa2Cu3O7−δfilms

We measured the longitudinal and Hall resistive transitions of ${\mathrm{YBa}}_{2}$${\mathrm{Cu}}_{3}$${\mathrm{O}}_{7\mathrm{\ensuremath{-}}\mathrm{\ensuremath{\delta}}}$ films in applied fields up to 9 T. The longitudinal fluctuation conductivities obey the scaling behavior of the three-dimensional Hartree fluctuation theory of Ullah and Dorsey. The fluctuation Hall conductivities do not scale. Our analysis shows that there are substantial contributions from the Maki-Thompson (MT) process as well as the Aslamazov-Larkin (AL) one. Using an ansatz suggested by the microscopic theory of Fukuyama et al., we separated the AL term from the total fluctuation conductivity. The AL Hall conductivity follows a scaling law, and the AL and MT terms have opposite sign. The sign of the AL term is consistent with the sign change in the flux-flow regime, as predicted by theory. At low fields and temperatures just above ${\mathrm{T}}_{\mathrm{c}}$(H), the AL term dominates the MT term, therefore causing the total Hall-conductivity sign change.

Quasiclassical soliton solutions of the Hartree equation

One considers the three-dimensional Hartree equations , ΔU=¦ψ¦2. One constructs the asymptotic (h→0) solution ψ of soliton type, localized mod 0 (h∞) in a compact domain. One finds the corresponding asymptotics of the self-consistent potential U. One obtains quantification conditions on the energy of the soliton.