Unified treatment of the Coulomb and harmonic oscillator potentials in DD dimensions

Quantum mechanical models and practical calculations often rely on some exactly solvable models like the Coulomb and the harmonic oscillator potentials. The $D$ dimensional generalized Coulomb potential contains these potentials as limiting cases, thus it establishes a continuous link between the Coulomb and harmonic oscillator potentials in various dimensions. We present results which are necessary for the utilization of this potential as a model and practical reference problem for quantum mechanical calculations. We define a Hilbert space basis, the generalized Coulomb-Sturmian basis, and calculate the Green's operator on this basis and also present an SU(1,1) algebra associated with it. We formulate the problem for the one-dimensional case too, and point out that the complications arising due to the singularity of the one-dimensional Coulomb problem can be avoided with the use of the generalized Coulomb potential.Comment: 18 pages, 3 ps figures, revte

Quantum noise in a transversely pumped cavity Bose--Hubbard model

We investigate the quantum measurement noise effects on the dynamics of an atomic Bose lattice gas inside an optical resonator. We describe the dynamics by means of a hybrid model consisting of a Bose--Hubbard Hamiltonian for the atoms and a Heisenberg--Langevin equation for the lossy cavity field mode. We assume that the atoms are prepared initially in the ground state of the lattice Hamiltonian and then start to interact with the cavity mode. We show that the cavity field fluctuations originating from the dissipative outcoupling of photons from the resonator lead to vastly different effects in the different possible ground state phases, i.e., the superfluid, the supersolid, the Mott- and the charge-density-wave phases. In the former two phases with the presence of a superfluid wavefunction, the quantum measurement noise appears as a driving term leading to excess noise depletion of the ground state. The time scale for the system to leave the ground scale is determined analytically. For the latter two incompressible phases, the quantum noise results in the fluctuation of the chemical potential. We derive an analytical expression for the corresponding broadening of the quasiparticle resonances

Mapping of functionalized regions on carbon nanotubes by scanning tunneling microscopy

Scanning tunneling microscopy (STM) gives us the opportunity to map the surface of functionalized carbon nanotubes in an energy resolved manner and with atomic precision. But this potential is largely untapped, mainly due to sample stability issues which inhibit reliable measurements. Here we present a simple and straightforward solution that makes away with this difficulty, by incorporating the functionalized multiwalled carbon nanotubes (MWCNT) into a few layer graphene - nanotube composite. This enabled us to measure energy resolved tunneling conductance maps on the nanotubes, which shed light on the level of doping, charge transfer between tube and functional groups and the dependence of defect creation or functionalization on crystallographic orientation.Comment: Keywords: functionalization, carbon nanotubes, few layer graphene, STM, CITS, ST

Fe-substituted mullite powders for the in situ synthesis of carbon nanotubes by catalytic chemical vapor deposition

Powders of iron-substituted mullite were prepared by combustion and further calcination in air at different temperatures. A detailed study involving notably Mo¨ssbauer spectroscopy showed that the Fe3+ ions are distributed between the mullite phase and a corundum phase that progressively dissolves into mullite upon the increase in calcination temperature. Carbon nanotube-Fe-mullite nanocomposites were prepared for the first time by a direct method involving a reduction of these powders in H2-CH4 and without any mechanical mixing step. The carbon nanotubes formed by the catalytic decomposition of CH4 on the smallest metal particles are mostly double-walled and multiwalled, although some carbon nanofibers are also observed

Au-Rh surface structures on Rh(111): DFT insights into the formation of an ordered surface alloy

Surface alloying is an important technique to change chemical properties. In this study, by employing density functional theory (DFT) calculations, the atomic arrangements and energetics of an extensive set of Au–Rh structures in a confined (2 × 1) surface cell on a Rh(111) substrate are investigated. An ordered surface alloy layer composed of 50% Au and 50% Rh is identified as the energetically favored structure, which corresponds to a configuration proposed previously based on scanning tunneling microscopy (STM) imaging [Óvári et al. PCCP2016, 18, 25230]. Comparing this surface alloy with another candidate structure in terms of Rh and Au adsorption characteristics, the bonding preference among Rh and Au species is recovered. DFT-based simulated STM images reveal bias-voltage-dependent contrast differences among selected corrugated surface layer structures at various Au coverages. Furthermore, several new experimental results obtained by STM and low energy ion scattering (LEIS) on the thermally induced formation of the ordered Au–Rh surface alloy are also presented in this work. Our calculation approach and results are expected to contribute to the understanding of the formation of metallic surface alloys of various chemical compositions