Lie theory and separation of variables. 5. The equations iUt + Uxx = 0 and iUt + Uxx −c/x2 U = 0

A detailed study of the group of symmetries of the time-dependent free particle Schrödinger equation in one space dimension is presented. An orbit analysis of all first order symmetries is seen to correspond in a well-defined manner to the separation of variables of this equation. The study gives a unified treatment of the harmonic oscillator (both attractive and repulsive), Stark effect, and free particle Hamiltonians in the time dependent formalism. The case of a potential c/x2 is also discussed in the time dependent formalism. Use of representation theory for the symmetry groups permits simple derivation of expansions relating various solutions of the Schrödinger equation, several of which are new

Density functional calculations for 4He droplets

A novel density functional, which accounts correctly for the equation of state, the static response function and the phonon-roton dispersion in bulk liquid helium, is used to predict static and dynamic properties of helium droplets. The static density profile is found to exhibit significant oscillations, which are accompanied by deviations of the evaporation energy from a liquid drop behaviour in the case of small droplets. The connection between such oscillations and the structure of the static response function in the liquid is explicitly discussed. The energy and the wave function of excited states are then calculated in the framework of time dependent density functional theory. The new functional, which contains backflow-like effects, is expected to yield quantitatively correct predictions for the excitation spectrum also in the roton wave-length range.Comment: 15 pages, REVTEX, 10 figures available upon request or at http://anubis.science.unitn.it/~dalfovo/papers/papers.htm

A Theory of Ferroelectric Phase Transition in SrTiO3_3 induced by Isotope Replacement

A theory to describe the dielectric anomalies and the ferroelectric phase transition induced by oxygen isotope replacement in SrTiO$_3$ is developed. The proposed model gives consistent explanation between apparently contradictory experimental results on macroscopic dielectric measurements versus microscopic lattice dynamical measurements by neutron scattering studies. The essential feature is described by a 3-state quantum order-disorder system characterizing the degenerated excited states in addition to the ground state of TiO$_6$ cluster. The effect of isotope replacement is taken into account through the tunneling frequency between the excited states. The dielectric properties are analyzed by the mean field approximation (MFA), which gives qualitative agreements with experimental results throughout full range of the isotope concentration.The phase diagram in the temperature-tunneling frequencycoordinate is studied by a QMC method to confirm the qualitative validity of the MFA analysis.Comment: 26 pages, 8 figure

Coexistence of the "bogolons" and the one-particle spectrum of excitations with a gap in the degenerated Bose gas

Properties of the weakly non-ideal Bose gas are considered without suggestion on C-number representation of the creation and annihilation operators with zero momentum. The "density-density" correlation function and the one-particle Green function of the degenerated Bose gas are calculated on the basis of the self-consistent Hartree-Fock approximation. It is shown that the spectrum of the one-particle excitations possesses a gap whose value is connected with the density of particles in the "condensate". At the same time, the pole in the "density-density" Green function determines the phonon-roton spectrum of excitations which exactly coincides with one discovered by Bogolyubov for the collective excitations (the "bogolons").Comment: 8 pages, no figure

Structural and dynamical properties of superfluid helium: a density functional approach

We present a novel density functional for liquid 4He, properly accounting for the static response function and the phonon-roton dispersion in the uniform liquid. The functional is used to study both structural and dynamical properties of superfluid helium in various geometries. The equilibrium properties of the free surface, droplets and films at zero temperature are calculated. Our predictions agree closely to the results of ab initio Monte Carlo calculations, when available. The introduction of a phenomenological velocity dependent interaction, which accounts for backflow effects, is discussed. The spectrum of the elementary excitations of the free surface and films is studied.Comment: 37 pages, REVTeX 3.0, figures on request at [email protected]

Schottky barrier heights at polar metal/semiconductor interfaces

Using a first-principle pseudopotential approach, we have investigated the Schottky barrier heights of abrupt Al/Ge, Al/GaAs, Al/AlAs, and Al/ZnSe (100) junctions, and their dependence on the semiconductor chemical composition and surface termination. A model based on linear-response theory is developed, which provides a simple, yet accurate description of the barrier-height variations with the chemical composition of the semiconductor. The larger barrier values found for the anion- than for the cation-terminated surfaces are explained in terms of the screened charge of the polar semiconductor surface and its image charge at the metal surface. Atomic scale computations show how the classical image charge concept, valid for charges placed at large distances from the metal, extends to distances shorter than the decay length of the metal-induced-gap states.Comment: REVTeX 4, 11 pages, 6 EPS figure

The G0 Experiment: Apparatus for Parity-Violating Electron Scattering Measurements at Forward and Backward Angles

In the G0 experiment, performed at Jefferson Lab, the parity-violating elastic scattering of electrons from protons and quasi-elastic scattering from deuterons is measured in order to determine the neutral weak currents of the nucleon. Asymmetries as small as 1 part per million in the scattering of a polarized electron beam are determined using a dedicated apparatus. It consists of specialized beam-monitoring and control systems, a cryogenic hydrogen (or deuterium) target, and a superconducting, toroidal magnetic spectrometer equipped with plastic scintillation and aerogel Cerenkov detectors, as well as fast readout electronics for the measurement of individual events. The overall design and performance of this experimental system is discussed.Comment: Submitted to Nuclear Instruments and Method

Transverse Beam Spin Asymmetries in Forward-Angle Elastic Electron-Proton Scattering

We have measured the beam-normal single-spin asymmetry in elastic scattering of transversely-polarized 3 GeV electrons from unpolarized protons at Q^2 = 0.15, 0.25 (GeV/c)^2. The results are inconsistent with calculations solely using the elastic nucleon intermediate state, and generally agree with calculations with significant inelastic hadronic intermediate state contributions. A_n provides a direct probe of the imaginary component of the 2-gamma exchange amplitude, the complete description of which is important in the interpretation of data from precision electron-scattering experiments.Comment: 5 pages, 3 figures, submitted to Physical Review Letters; shortened to meet PRL length limit, clarified some text after referee's comment

Strange Quark Contributions to Parity-Violating Asymmetries in the Forward G0 Electron-Proton Scattering Experiment

We have measured parity-violating asymmetries in elastic electron-proton scattering over the range of momentum transfers 0.12 < Q^2 < 1.0 GeV^2. These asymmetries, arising from interference of the electromagnetic and neutral weak interactions, are sensitive to strange quark contributions to the currents of the proton. The measurements were made at JLab using a toroidal spectrometer to detect the recoiling protons from a liquid hydrogen target. The results indicate non-zero, Q^2 dependent, strange quark contributions and provide new information beyond that obtained in previous experiments.Comment: 5 pages, 2 figure

Black Hole Spin via Continuum Fitting and the Role of Spin in Powering Transient Jets

The spins of ten stellar black holes have been measured using the continuum-fitting method. These black holes are located in two distinct classes of X-ray binary systems, one that is persistently X-ray bright and another that is transient. Both the persistent and transient black holes remain for long periods in a state where their spectra are dominated by a thermal accretion disk component. The spin of a black hole of known mass and distance can be measured by fitting this thermal continuum spectrum to the thin-disk model of Novikov and Thorne; the key fit parameter is the radius of the inner edge of the black hole's accretion disk. Strong observational and theoretical evidence links the inner-disk radius to the radius of the innermost stable circular orbit, which is trivially related to the dimensionless spin parameter a_* of the black hole (|a_*| < 1). The ten spins that have so far been measured by this continuum-fitting method range widely from a_* \approx 0 to a_* > 0.95. The robustness of the method is demonstrated by the dozens or hundreds of independent and consistent measurements of spin that have been obtained for several black holes, and through careful consideration of many sources of systematic error. Among the results discussed is a dichotomy between the transient and persistent black holes; the latter have higher spins and larger masses. Also discussed is recently discovered evidence in the transient sources for a correlation between the power of ballistic jets and black hole spin.Comment: 30 pages. Accepted for publication in Space Science Reviews. Also to appear in hard cover in the Space Sciences Series of ISSI "The Physics of Accretion onto Black Holes" (Springer Publisher). Changes to Sections 5.2, 6.1 and 7.4. Section 7.4 responds to Russell et al. 2013 (MNRAS, 431, 405) who find no evidence for a correlation between the power of ballistic jets and black hole spi