Adsorption on carbon nanotubes: quantum spin tubes, magnetization plateaus, and conformal symmetry

We formulate the problem of adsorption onto the surface of a carbon nanotube as a lattice gas on a triangular lattice wrapped around a cylinder. This model is equivalent to an XXZ Heisenberg quantum spin tube. The geometric frustration due to wrapping leads generically to four magnetization plateaus, in contrast to the two on a flat graphite sheet. We obtain analytical and numerical results for the magnetizations and transition fields for armchair, zig-zag and chiral nanotubes. The zig-zags are exceptional in that one of the plateaus has extensive zero temperature entropy in the classical limit. Quantum effects lift up the degeneracy, leaving gapless excitations which are described by a $c=1$ conformal field theory with compactification radius quantized by the tube circumference.Comment: 5 pages, 6 figure

Localized excited charge carriers generate ultrafast inhomogeneous strain in the multiferroic BiFeO3_3

We apply ultrafast X-ray diffraction with femtosecond temporal resolution to monitor the lattice dynamics in a thin film of multiferroic BiFeO$_3$ after above-bandgap photoexcitation. The sound-velocity limited evolution of the observed lattice strains indicates a quasi-instantaneous photoinduced stress which decays on a nanosecond time scale. This stress exhibits an inhomogeneous spatial profile evidenced by the broadening of the Bragg peak. These new data require substantial modification of existing models of photogenerated stresses in BiFeO$_3$: the relevant excited charge carriers must remain localized to be consistent with the data

Heterogeneous nucleation near a metastable vapour-liquid transition: the effect of wetting transitions

Phase transformations such as freezing typically start with heterogeneous nucleation. Heterogeneous nucleation near a wetting transition, of a crystalline phase is studied. The wetting transition occurs at or near a vapour-liquid transition which occurs in a metastable fluid. The fluid is metastable with respect to crystallisation, and it is the crystallisation of this fluid phase that we are interested in. At a wetting transition a thick layer of a liquid phase forms at a surface in contact with the vapour phase. The crystalline nucleus is then immersed in this liquid layer, which reduces the free energy barrier to nucleation and so dramatically increases the nucleation rate. The variation in the rate of heterogeneous nucleation close to wetting transitions is calculated for systems in which the longest-range forces are dispersion forces.Comment: 11 pages including 3 figure

Monte Carlo Study of an Extended 3-State Potts Model on the Triangular Lattice

By introducing a chiral term into the Hamiltonian of the 3-state Potts model on a triangular lattice additional symmetries are achieved between the clockwise and anticlockwise states and the ferromagnetic state. This model is investigated using Monte Carlo methods. We investigate the full phase diagram and find evidence for a line tricritical points separating the ferromagnetic and antiferromagnetic phases.Comment: 6 pages, 10 figure

U(1) Gauge Theory as Quantum Hydrodynamics

It is shown that gauge theories are most naturally studied via a polar decomposition of the field variable. Gauge transformations may be viewed as those that leave the density invariant but change the phase variable by additive amounts. The path integral approach is used to compute the partition function. When gauge fields are included, the constraint brought about by gauge invariance simply means an appropriate linear combination of the gradients of the phase variable and the gauge field is invariant. No gauge fixing is needed in this approach that is closest to the spirit of the gauge principle. We derive an exact formula for the condensate fraction and in case it is zero, an exact formula for the anomalous exponent. We also derive a formula for the vortex strength which involves computing radiation corrections.Comment: 15 pages, Plain LaTeX, final published versio

Geometric frustration and magnetization plateaus in quantum spin and Bose-Hubbard models on tubes

We study XXZ Heisenberg models on frustrated triangular lattices wrapped around a cylinder. In addition to having interesting magnetic phases, these models are equivalent to Bose-Hubbard models that describe the physical problem of adsorption of noble gases on the surface of carbon nanotubes. We find analytical results for the possible magnetization plateau values as a function of the wrapping vectors of the cylinder, which in general introduce extra geometric frustration besides the one due to the underlying triangular lattice. We show that for particular wrapping vectors $(N,0)$, which correspond to the zig-zag nanotubes, there is a macroscopically degenerate ground state in the classical Ising limit. The Hilbert space for the degenerate states can be enumerated by a mapping first into a path in a square lattice wrapped around a cylinder (a Bratteli diagram), and then to free fermions interacting with a single ${\bf Z}_N$ degree of freedom. From this model we obtain the spectrum in the anisotropic Heisenberg limit, showing that it is gapless. The continuum limit is a $c=1$ conformal field theory with compactification radius $R=N$ set by the physical tube radius. We show that the compactification radius quantization is exact in the projective $J_\perp/J_z \ll 1$ limit, and that higher order corrections reduce the value of $R$. The particular case of a $(N=2,0)$ tube, which corresponds to a 2-leg ladder with cross links, is studied separately and shown to be gapped because the fermion mapped problem contains superconducting pairing terms.Comment: 10 pages, 11 figure

Analytical and numerical study of hardcore bosons in two dimensions

We study various properties of bosons in two dimensions interacting only via onsite hardcore repulsion. In particular, we use the lattice spin-wave approximation to calculate the ground state energy, the density, the condensate density and the superfluid density in terms of the chemical potential. We also calculate the excitation spectrum, $\omega({\bf k})$. In addition, we performed high precision numerical simulations using the stochastic series expansion algorithm. We find that the spin-wave results describe extremely well the numerical results over the {\it whole} density range $0\leq \rho \leq 1$. We also compare the lattice spin-wave results with continuum results obtained by summing the ladder diagrams at low density. We find that for $\rho \leq 0.1$ there is good agreement, and that the difference between the two methods vanishes as $\rho^2$ for $\rho \to 0$. This offers the possibility of obtaining precise continuum results by taking the continuum limit of the spin-wave results for all densities. Finaly, we studied numerically the finite temperature phase transition for the entire density range and compared with low density predictions.Comment: 10 pages, 8 figures include

When Models Interact with their Subjects: The Dynamics of Model Aware Systems

A scientific model need not be a passive and static descriptor of its subject. If the subject is affected by the model, the model must be updated to explain its affected subject. In this study, two models regarding the dynamics of model aware systems are presented. The first explores the behavior of "prediction seeking" (PSP) and "prediction avoiding" (PAP) populations under the influence of a model that describes them. The second explores the publishing behavior of a group of experimentalists coupled to a model by means of confirmation bias. It is found that model aware systems can exhibit convergent random or oscillatory behavior and display universal 1/f noise. A numerical simulation of the physical experimentalists is compared with actual publications of neutron life time and {\Lambda} mass measurements and is in good quantitative agreement.Comment: Accepted for publication in PLoS-ON

Hodge Theory on Metric Spaces

Hodge theory is a beautiful synthesis of geometry, topology, and analysis, which has been developed in the setting of Riemannian manifolds. On the other hand, spaces of images, which are important in the mathematical foundations of vision and pattern recognition, do not fit this framework. This motivates us to develop a version of Hodge theory on metric spaces with a probability measure. We believe that this constitutes a step towards understanding the geometry of vision. The appendix by Anthony Baker provides a separable, compact metric space with infinite dimensional \alpha-scale homology.Comment: appendix by Anthony W. Baker, 48 pages, AMS-LaTeX. v2: final version, to appear in Foundations of Computational Mathematics. Minor changes and addition

Nonprofit governance: Improving performance in troubled economic times

Nonprofit management is currently pressured to perform effectively in a weak economy. Yet, nonprofit governance continues to suffer from unclear conceptions of the division of labor between board of directors and executive directors. This online survey of 114 executive directors aims to provide clarification and recommendations for social administration