Study of a class of non-polynomial oscillator potentials

We develop a variational method to obtain accurate bounds for the eigenenergies of H = -Delta + V in arbitrary dimensions N>1, where V(r) is the nonpolynomial oscillator potential V(r) = r^2 + lambda r^2/(1+gr^2), lambda in (-infinity,\infinity), g>0. The variational bounds are compared with results previously obtained in the literature. An infinite set of exact solutions is also obtained and used as a source of comparison eigenvalues.Comment: 16 page

Calculating the energy spectra of magnetic molecules: application of real- and spin-space symmetries

The determination of the energy spectra of small spin systems as for instance given by magnetic molecules is a demanding numerical problem. In this work we review numerical approaches to diagonalize the Heisenberg Hamiltonian that employ symmetries; in particular we focus on the spin-rotational symmetry SU(2) in combination with point-group symmetries. With these methods one is able to block-diagonalize the Hamiltonian and thus to treat spin systems of unprecedented size. In addition it provides a spectroscopic labeling by irreducible representations that is helpful when interpreting transitions induced by Electron Paramagnetic Resonance (EPR), Nuclear Magnetic Resonance (NMR) or Inelastic Neutron Scattering (INS). It is our aim to provide the reader with detailed knowledge on how to set up such a diagonalization scheme.Comment: 29 pages, many figure

Glutamine synthetase activity fuels nucleotide biosynthesis and supports growth of glutamine-restriced glioblastoma

L-Glutamine (Gln) functions physiologically to balance the carbon and nitrogen requirements of tissues. It has been proposed that in cancer cells undergoing aerobic glycolysis, accelerated anabolism is sustained by Gln-derived carbons, which replenish the tricarboxylic acid (TCA) cycle (anaplerosis). However, it is shown here that in glioblastoma (GBM) cells, almost half of the Gln-derived glutamate (Glu) is secreted and does not enter the TCA cycle, and that inhibiting glutaminolysis does not affect cell proliferation. Moreover, Gln-starved cells are not rescued by TCA cycle replenishment. Instead, the conversion of Glu to Gln by glutamine synthetase (GS; cataplerosis) confers Gln prototrophy, and fuels de novo purine biosynthesis. In both orthotopic GBM models and in patients, (13)C-glucose tracing showed that GS produces Gln from TCA-cycle-derived carbons. Finally, the Gln required for the growth of GBM tumours is contributed only marginally by the circulation, and is mainly either autonomously synthesized by GS-positive glioma cells, or supplied by astrocytes

Eigenvalues from power--series expansions: an alternative approach

An appropriate rational approximation to the eigenfunction of the Schr\"{o}dinger equation for anharmonic oscillators enables one to obtain the eigenvalue accurately as the limit of a sequence of roots of Hankel determinants. The convergence rate of this approach is greater than that for a well--established method based on a power--series expansions weighted by a Gaussian factor with an adjustable parameter (the so--called Hill--determinant method)

Effects of temperature on thick branes and the fermion (quasi-)localization

Following Campos's work [Phys. Rev. Lett. 88, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Following Campos's work [Phys. Rev. Lett. \textbf{88}, 141602 (2002)], we investigate the effects of temperature on flat, de Sitter (dS), and anti-de Sitter (AdS) thick branes in five-dimensional (5D) warped spacetime, and on the fermion (quasi-)localization. First, in the case of flat brane, when the critical temperature reaches, the solution of the background scalar field and the warp factor is not unique. So the thickness of the flat thick brane is uncertain at the critical value of the temperature parameter, which is found to be lower than the one in flat 5D spacetime. The mass spectra of the fermion Kaluza-Klein (KK) modes are continuous, and there is a series of fermion resonances. The number and lifetime of the resonances are finite and increase with the temperature parameter, but the mass of the resonances decreases with the temperature parameter. Second, in the case of dS brane, we do not find such a critical value of the temperature parameter. The mass spectra of the fermion KK modes are also continuous, and there is a series of fermion resonances. The effects of temperature on resonance number, lifetime, and mass are the same with the case of flat brane. Last, in the case of AdS brane, {the critical value of the temperature parameter can less or greater than the one in the flat 5D spacetime.} The spectra of fermion KK modes are discrete, and the mass of fermion KK modes does not decrease monotonically with increasing temperature parameter.Comment: 24 pages, 15 figures, published versio

Income Taxes, Sorting, and the Costs of Housing: Evidence from Municipal Boundaries in Switzerland

This paper provides novel evidence on the role of income taxes for residential rents and spatial sorting. Drawing on comprehensive apartment-level data, we identify the effects of tax differentials across municipal boundaries in Switzerland. The boundary discontinuity design (BDD) corrects for unobservable location characteristics such as environmental amenities or the access to public goods and thereby reduces the estimated response of housing prices by one half compared to conventional estimates: we identify an income tax elasticity of rents of about 0.26. We complement this approach with census data on local sociodemographic characteristics and show that about one third of this effect can be traced back to a sorting of high-income households into low-tax municipalities. These findings are robust to a matching approach (MBDD) which compares identical residences on opposite sides of the boundary and a number of further sensitivity checks