Nanoscale atomic waveguides with suspended carbon nanotubes

We propose an experimentally viable setup for the realization of one-dimensional ultracold atom gases in a nanoscale magnetic waveguide formed by single doubly-clamped suspended carbon nanotubes. We show that all common decoherence and atom loss mechanisms are small guaranteeing a stable operation of the trap. Since the extremely large current densities in carbon nanotubes are spatially homogeneous, our proposed architecture allows to overcome the problem of fragmentation of the atom cloud. Adding a second nanowire allows to create a double-well potential with a moderate tunneling barrier which is desired for tunneling and interference experiments with the advantage of tunneling distances being in the nanometer regime.Comment: Replaced with the published version, 7 pages, 3 figure

The global abundance of tree palms

Aim: Palms are an iconic, diverse and often abundant component of tropical ecosystems that provide many ecosystem services. Being monocots, tree palms are evolutionarily, morphologically and physiologically distinct from other trees, and these differences have important consequences for ecosystem services (e.g., carbon sequestration and storage) and in terms of responses to climate change. We quantified global patterns of tree palm relative abundance to help improve understanding of tropical forests and reduce uncertainty about these ecosystems under climate change. Location: Tropical and subtropical moist forests. Time period: Current. Major taxa studied: Palms (Arecaceae). Methods: We assembled a pantropical dataset of 2,548 forest plots (covering 1,191 ha) and quantified tree palm (i.e., ≥10 cm diameter at breast height) abundance relative to co‐occurring non‐palm trees. We compared the relative abundance of tree palms across biogeographical realms and tested for associations with palaeoclimate stability, current climate, edaphic conditions and metrics of forest structure. Results: On average, the relative abundance of tree palms was more than five times larger between Neotropical locations and other biogeographical realms. Tree palms were absent in most locations outside the Neotropics but present in >80% of Neotropical locations. The relative abundance of tree palms was more strongly associated with local conditions (e.g., higher mean annual precipitation, lower soil fertility, shallower water table and lower plot mean wood density) than metrics of long‐term climate stability. Life‐form diversity also influenced the patterns; palm assemblages outside the Neotropics comprise many non‐tree (e.g., climbing) palms. Finally, we show that tree palms can influence estimates of above‐ground biomass, but the magnitude and direction of the effect require additional work. Conclusions: Tree palms are not only quintessentially tropical, but they are also overwhelmingly Neotropical. Future work to understand the contributions of tree palms to biomass estimates and carbon cycling will be particularly crucial in Neotropical forests

Phase operators of the harmonic oscillator and suppression of a number state.

The phase properties of the quantized electromagnetic field have been studied using operators P± of the harmonic oscillator whose classical analogs are exp(i) being the classical phase. P+ and P- are used to construct a unitary operator Up()=exp(P+-±*P-) and the properties of the state generated by Up from a number state are studied. It is shown that by tuning it is possible to produce a pure state 0=Up(±)0 in which a specific number-state component is suppressed. © 1989 The American Physical Society

Sum rules for odd and even states of confining potentials

Using the Green’s function associated with the one-dimensional Schroedinger equation it is possible to establish a hierarchy of sum rules involving the eigenvalues of confining potentials which have only a boundstate spectrum. For some potentials the sum rules could lead to divergences. It is shown that when this happens it is possible to examine the separate sum rules satisfied by the even and odd eigenstates of a symmetric confining potential and by subtraction cancel the divergences exactly and produce a new sum rule which is free of divergences. The procedure is illustrated by considering symmetric power law potentials and the use of several examples. One of the examples considered shows that the zeros of the Airy function and its derivative obey a sum rule and this sum rule is verified

Hierarchy of sum rules for oscillator strengths

It is shown that the well known sum rules for oscillator strengths for Hydrogen atom can be generalised to a whole class of sum rules. The sum rules have contributions from the discrete and the continuum parts of the spectrum neither of which can be calculated in closed analytical form but can be calculated numerically. The numerical calculations are carried out to check the validity of the sum rules. The procedure for constructing sum rules for general potentials is discussed. Generalisations of Kramers relations and the Virial theorem are discussed

Supersymmetric quantum mechanics and its applications

The Hamiltonian in Supersymmetric Quantum Mechanics is defined in terms of charges that obey the same algebra as that of the generators of supersymmetry in field theory. The consequences of this symmetry for the spectra of the component parts that constitute the supersymmetric system are explored. The implications of supersymmetry for the solutions of the Schrodinger equation, the Dirac equation, the inverse scattering theory and the multi-soliton solutions of the KdV equation are examined. Applications to scattering problems in Nuclear Physics with specific reference to singular potentials which arise from considerations of supersymmetry will be discussed