Symbolic-Numeric Algorithms for Computer Analysis of Spheroidal Quantum Dot Models

A computation scheme for solving elliptic boundary value problems with axially symmetric confining potentials using different sets of one-parameter basis functions is presented. The efficiency of the proposed symbolic-numerical algorithms implemented in Maple is shown by examples of spheroidal quantum dot models, for which energy spectra and eigenfunctions versus the spheroid aspect ratio were calculated within the conventional effective mass approximation. Critical values of the aspect ratio, at which the discrete spectrum of models with finite-wall potentials is transformed into a continuous one in strong dimensional quantization regime, were revealed using the exact and adiabatic classifications.Comment: 6 figures, Submitted to Proc. of The 12th International Workshop on Computer Algebra in Scientific Computing (CASC 2010) Tsakhkadzor, Armenia, September 5 - 12, 201

Simulations of the Static Friction Due to Adsorbed Molecules

The static friction between crystalline surfaces separated by a molecularly thin layer of adsorbed molecules is calculated using molecular dynamics simulations. These molecules naturally lead to a finite static friction that is consistent with macroscopic friction laws. Crystalline alignment, sliding direction, and the number of adsorbed molecules are not controlled in most experiments and are shown to have little effect on the friction. Temperature, molecular geometry and interaction potentials can have larger effects on friction. The observed trends in friction can be understood in terms of a simple hard sphere model.Comment: 13 pages, 13 figure

Electronic and thermal sequential transport in metallic and superconducting two-junction arrays

The description of transport phenomena in devices consisting of arrays of tunnel junctions, and the experimental confirmation of these predictions is one of the great successes of mesoscopic physics. The aim of this paper is to give a self-consistent review of sequential transport processes in such devices, based on the so-called "orthodox" model. We calculate numerically the current-voltage (I-V) curves, the conductance versus bias voltage (G-V) curves, and the associated thermal transport in symmetric and asymmetric two-junction arrays such as Coulomb-blockade thermometers (CBTs), superconducting-insulator-normal-insulator-superconducting (SINIS) structures, and superconducting single-electron transistors (SETs). We investigate the behavior of these systems at the singularity-matching bias points, the dependence of microrefrigeration effects on the charging energy of the island, and the effect of a finite superconducting gap on Coulomb-blockade thermometry.Comment: 23 pages, 12 figures; Berlin (ISBN: 978-3-642-12069-5

Input-output theory for fermions in an atom cavity

We generalize the quantum optical input-output theory developed for optical cavities to ultracold fermionic atoms confined in a trapping potential, which forms an "atom cavity". In order to account for the Pauli exclusion principle, quantum Langevin equations for all cavity modes are derived. The dissipative part of these multi-mode Langevin equations includes a coupling between cavity modes. We also derive a set of boundary conditions for the Fermi field that relate the output fields to the input fields and the field radiated by the cavity. Starting from a constant uniform current of fermions incident on one side of the cavity, we use the boundary conditions to calculate the occupation numbers and current density for the fermions that are reflected and transmitted by the cavity

Neutrino Masses with "Zero Sum" Condition: mν1+mν2+mν3=0m_{\nu_1} + m_{\nu_2} + m_{\nu_3} = 0

It is well known that the neutrino mass matrix contains more parameters than experimentalists can hope to measure in the foreseeable future even if we impose CP invariance. Thus, various authors have proposed ansatzes to restrict the form of the neutrino mass matrix further. Here we propose that $m_{\nu_1} + m_{\nu_2} + m_{\nu_3} = 0$; this ``zero sum'' condition can occur in certain class of models, such as models whose neutrino mass matrix can be expressed as commutator of two matrices. With this condition, the absolute neutrino mass can be obtained in terms of the mass-squared differences. When combined with the accumulated experimental data this condition predicts two types of mass hierarchies, with one of them characterized by $m_{\nu_3} \approx -2m_{\nu_1} \approx -2 m_{\nu_2} \approx 0.063$ eV, and the other by $m_{\nu_1} \approx -m_{\nu_2} \approx 0.054$ eV and $m_{\nu_3} \approx 0.0064$ eV. The mass ranges predicted is just below the cosmological upper bound of 0.23 eV from recent WMAP data and can be probed in the near future. We also point out some implications for direct laboratory measurement of neutrino masses, and the neutrino mass matrix.Comment: Latex 12 pages. No figures. New references adde

Quark phases in neutron stars and a "third family" of compact stars as a signature for phase transitions

The appearance of quark phases in the dense interior of neutron stars provides one possibility to soften the equation of state (EOS) of neutron star matter at high densities. This softening leads to more compact equilibrium configurations of neutron stars compared to pure hadronic stars of the same mass. We investigate the question to which amount the compactness of a neutron star can be attributed to the presence of a quark phase. For this purpose we employ several hadronic EOS in the framework of the relativistic mean-field (RMF) model and an extended MIT bag model to describe the quark phase. We find that - almost independent of the model parameters - the radius of a pure hadronic neutron star gets typically reduced by 20-30% if a pure quark phase in the center of the star does exist. For some EOS we furthermore find the possibility of a "third family" of compact stars which may exist besides the two known families of white dwarfs and neutron stars. We show how an experimental proof of the existence of a third family by mass and radius measurements may provide a unique signature for a phase transition inside neutron stars.Comment: 37 pages, 18 eps-figures included, LaTe

Bomb-¹⁴C analysis of ecosystem respiration reveals that peatland vegetation facilitates release of old carbon

The largest terrestrial-to-atmosphere carbon flux is respired CO<sub>2</sub>. However, the partitioning of soil and plant sources, understanding of contributory mechanisms, and their response to climate change are uncertain. A plant removal experiment was established within a peatland located in the UK uplands to quantify respiration derived from recently fixed plant carbon and that derived from decomposition of soil organic matter, using natural abundance <sup>13</sup>C and bomb-<sup>14</sup>C as tracers. Soil and plant respiration sources were found respectively to contribute ~ 36% and between 41-54% of the total ecosystem CO<sub>2</sub> flux. Respired CO<sub>2</sub> produced in the clipped (‘soil’) plots had a mean age of ~ 15 years since fixation from the atmosphere, whereas the <sup>14</sup>C content of ecosystem CO<sub>2</sub> was statistically indistinguishable from the contemporary atmosphere. Results of carbon mass balance modelling showed that, in addition to respiration from bulk soil and plant respired CO<sub>2</sub>, a third, much older source of CO<sub>2</sub> existed. This source, which we suggest is CO<sub>2</sub> derived from the catotelm constituted between ~ 10 and 23% of total ecosystem respiration and had a mean radiocarbon age of between several hundred to ~ 2000 years before present (BP). These findings show that plant-mediated transport of CO<sub>2</sub> produced in the catotelm may form a considerable component of peatland ecosystem respiration. The implication of this discovery is that current assumptions in terrestrial carbon models need to be re-evaluated to consider the climate sensitivity of this third source of peatland CO<sub>2</sub>

Statistics of the gravitational force in various dimensions of space: from Gaussian to Levy laws

We discuss the distribution of the gravitational force created by a Poissonian distribution of field sources (stars, galaxies,...) in different dimensions of space d. In d=3, it is given by a Levy law called the Holtsmark distribution. It presents an algebraic tail for large fluctuations due to the contribution of the nearest neighbor. In d=2, it is given by a marginal Gaussian distribution intermediate between Gaussian and Levy laws. In d=1, it is exactly given by the Bernouilli distribution (for any particle number N) which becomes Gaussian for N>>1. Therefore, the dimension d=2 is critical regarding the statistics of the gravitational force. We generalize these results for inhomogeneous systems with arbitrary power-law density profile and arbitrary power-law force in a d-dimensional universe

Comparison of hypoxia among four river-dominated ocean margins: The Changjiang (Yangtze), Mississippi, Pearl, and Rhône rivers

We examined the occurrence of seasonal hypoxia (O2&lt;2 mg l-1) in the bottom waters of four river-dominated ocean margins (off the Changjiang, Mississippi, Pearl and Rhône Rivers) and compared the processes leading to the depletion of oxygen. Consumption of oxygen in bottom waters is linked to biological oxygen demand fueled by organic matter from primary production in the nutrient-rich river plume and perhaps terrigenous inputs. Hypoxia occurs when this consumption exceeds replenishment by diffusion, turbulent mixing or lateral advection of oxygenated water. The margins off the Mississippi and Changjiang are affected the most by summer hypoxia, while the margins off the Rhône and the Pearl rivers systems are less affected, although nutrient concentrations in the river water are very similar in the four systems. Spring and summer primary production is high overall for the shelves adjacent to the Mississippi, Changjiang and Pearl (1-10 g C m-2 d-1), and lower off the Rhône River (<1 g C m-2 d-1), which could be one of the reasons of the absence of hypoxia on the Rhône shelf. The residence time of the bottom water is also related to the occurrence of hypoxia, with the Mississippi margin showing a long residence time and frequent occurrences of hypoxia during summer over very large spatial scales, whereas the East China Sea (ECS)/Changjiang displays hypoxia less regularly due to a shorter residence time of the bottom water. Physical stratification plays an important role with both the Changjiang and Mississippi shelf showing strong thermohaline stratification during summer over extended periods of time, whereas summer stratification is less prominent for the Pearl and Rhône partly due to the wind effect on mixing. The shape of the shelf is the last important factor since hypoxia occurs at intermediate depths (between 5 and 50 m) on broad shelves (Gulf of Mexico and ECS). Shallow estuaries with low residence time such as the Pearl River estuary during the summer wet season when mixing and flushing are dominant features, or deeper shelves, such as the Gulf of Lion off the Rhône show little or no hypoxia

Extrinsic CPT Violation in Neutrino Oscillations in Matter

We investigate matter-induced (or extrinsic) CPT violation effects in neutrino oscillations in matter. Especially, we present approximate analytical formulas for the CPT-violating probability differences for three flavor neutrino oscillations in matter with an arbitrary matter density profile. Note that we assume that the CPT invariance theorem holds, which means that the CPT violation effects arise entirely because of the presence of matter. As special cases of matter density profiles, we consider constant and step-function matter density profiles, which are relevant for neutrino oscillation physics in accelerator and reactor long baseline experiments as well as neutrino factories. Finally, the implications of extrinsic CPT violation on neutrino oscillations in matter for several past, present, and future long baseline experiments are estimated.Comment: 47 pages, 7 figures, RevTeX4. Final version to be published in Phys. Rev.