Nonintegrability of the two-body problem in constant curvature spaces

We consider the reduced two-body problem with the Newton and the oscillator potentials on the sphere ${\bf S}^{2}$ and the hyperbolic plane ${\bf H}^{2}$. For both types of interaction we prove the nonexistence of an additional meromorphic integral for the complexified dynamic systems.Comment: 20 pages, typos correcte

Semiclassical spin liquid state of easy axis Kagome antiferromagnets

Motivated by recent experiments on Nd-langasite, we consider the effect of strong easy axis single-ion anisotropy $D$ on $S > 3/2$ spins interacting with antiferromagnetic exchange $J$ on the Kagome lattice. When $T \ll DS^2$, the collinear low energy states selected by the anisotropy map on to configurations of the classical Kagome lattice Ising antiferromagnet. However, the low temperature limit is quite different from the cooperative Ising paramagnet that obtains classically for $T \ll JS^2$. We find that sub-leading ${\mathcal O}(J^3S/D^2)$ multi-spin interactions arising from the transverse quantum dynamics result in a crossover from an intermediate temperature classical cooperative Ising paramagnet to a semiclassical spin liquid with distinct short-ranged correlations for $T \ll J^3S/D^2$.Comment: 4 pages, 3 eps figure

Bistability and oscillatory motion of natural nano-membranes appearing within monolayer graphene on silicon dioxide

The recently found material graphene is a truly two-dimensional crystal and exhibits, in addition, an extreme mechanical strength. This in combination with the high electron mobility favours graphene for electromechanical investigations down to the quantum limit. Here, we show that a monolayer of graphene on SiO2 provides natural, ultra-small membranes of diameters down to 3 nm, which are caused by the intrinsic rippling of the material. Some of these nano-membranes can be switched hysteretically between two vertical positions using the electric field of the tip of a scanning tunnelling microscope (STM). They can also be forced to oscillatory motion by a low frequency ac-field. Using the mechanical constants determined previously, we estimate a high resonance frequency up to 0.4 THz. This might be favorable for quantum-electromechanics and is prospective for single atom mass spectrometers.Comment: 9 pages, 4 figure

Numerical Linked-Cluster Approach to Quantum Lattice Models

We present a novel algorithm that allows one to obtain temperature dependent properties of quantum lattice models in the thermodynamic limit from exact diagonalization of small clusters. Our Numerical Linked Cluster (NLC) approach provides a systematic framework to assess finite-size effects and is valid for any quantum lattice model. Unlike high temperature expansions (HTE), which have a finite radius of convergence in inverse temperature, these calculations are accurate at all temperatures provided the range of correlations is finite. We illustrate the power of our approach studying spin models on {\it kagom\'e}, triangular, and square lattices.Comment: 4 pages, 5 figures, published versio

Density Matrix Renormalization Group Study of the Disorder Line in the Quantum ANNNI Model

We apply Density Matrix Renormalization Group methods to study the phase diagram of the quantum ANNNI model in the region of low frustration where the ferromagnetic coupling is larger than the next-nearest-neighbor antiferromagnetic one. By Finite Size Scaling on lattices with up to 80 sites we locate precisely the transition line from the ferromagnetic phase to a paramagnetic phase without spatial modulation. We then measure and analyze the spin-spin correlation function in order to determine the disorder transition line where a modulation appears. We give strong numerical support to the conjecture that the Peschel-Emery one-dimensional line actually coincides with the disorder line. We also show that the critical exponent governing the vanishing of the modulation parameter at the disorder transition is $\beta_q = 1/2$.Comment: 4 pages, 5 eps figure

Antiferromagnetic Quantum Spins on the Pyrochlore Lattice

The ground state of the S=1/2 Heisenberg antiferromagnet on the pyrochlore lattice is theoretically investigated. Starting from the limit of isolated tetrahedra, I include interactions between the tetrahedra and obtain an effective model for the spin-singlet ground state multiplet by third-order perturbation. I determine its ground state using the mean-field approximation and found a dimerized state with a four-sublattice structure, which agrees with the proposal by Harris et al. I also discuss chirality correlations and spin correlations for this state.Comment: 4 pages in 2-column format, 5 figures; To appear in J. Phys. Soc. Jpn. (Mar, 2001

Two-dimensional charge order in layered 2-1-4 perovskite oxides

Monte Carlo simulations are performed on the three-dimensional (3D) Ising model with the 2-1-4 layered perovskite structure as a minimal model for checkerboard charge ordering phenomena in layered perovskite oxides. Due to the interlayer frustration, only 2D long-range order emerges with a finite correlation length along the c axis. Critical exponents of the transition change continuously as a function of the interlayer coupling constant. The interlayer long-range Coulomb interaction decays exponentially and is negligible even between the second-neighbor layers. Instead, monoclinic distortion of a tetragonal unit cell lifts the macroscopic degeneracy to induce a 3D charge ordering. The dimensionality of the charge order in La$_{0.5}$Sr$_{1.5}$MnO$_4$ is discussed from this viewpoint.Comment: 5 pages including 6 figures, with major changes including discussion on charge ordering phenomena in layered perovskite oxide

Dynamical response of the nuclear pasta in neutron star crusts

The nuclear pasta -- a novel state of matter having nucleons arranged in a variety of complex shapes -- is expected to be found in the crust of neutron stars and in core-collapse supernovae at subnuclear densities of about $10^{14}$ g/cm$^3$. Due to frustration, a phenomenon that emerges from the competition between short-range nuclear attraction and long-range Coulomb repulsion, the nuclear pasta displays a preponderance of unique low-energy excitations. These excitations could have a strong impact on many transport properties, such as neutrino propagation through stellar environments. The excitation spectrum of the nuclear pasta is computed via a molecular-dynamics simulation involving up to 100,000 nucleons. The dynamic response of the pasta displays a classical plasma oscillation in the 1-2 MeV region. In addition, substantial strength is found at low energies. Yet this low-energy strength is missing from a simple ion model containing a single-representative heavy nucleus. The low-energy strength observed in the dynamic response of the pasta is likely to be a density wave involving the internal degrees of freedom of the clusters.Comment: 4 pages, 3 figures, Phys Rev C in pres

Seasonal cycle of precipitation variability in South America on intraseasonal timescales

The seasonal cycle of the intraseasonal (IS) variability of precipitation in South America is described through the analysis of bandpass filtered outgoing longwave radiation (OLR) anomalies. The analysis is discriminated between short (10--30 days) and long (30--90 days) intraseasonal timescales. The seasonal cycle of the 30--90-day IS variability can be well described by the activity of first leading pattern (EOF1) computed separately for the wet season (October--April) and the dry season (May--September). In agreement with previous works, the EOF1 spatial distribution during the wet season is that of a dipole with centers of actions in the South Atlantic Convergence Zone (SACZ) and southeastern South America (SESA), while during the dry season, only the last center is discernible. In both seasons, the pattern is highly influenced by the activity of the Madden--Julian Oscillation (MJO). Moreover, EOF1 is related with a tropical zonal-wavenumber-1 structure superposed with coherent wave trains extended along the South Pacific during the wet season, while during the dry season the wavenumber-1 structure is not observed. The 10--30-day IS variability of OLR in South America can be well represented by the activity of the EOF1 computed through considering all seasons together, a dipole but with the stronger center located over SESA. While the convection activity at the tropical band does not seem to influence its activity, there are evidences that the atmospheric variability at subtropical-extratropical regions might have a role. Subpolar wavetrains are observed in the Pacific throughout the year and less intense during DJF, while a path of wave energy dispersion along a subtropical wavetrain also characterizes the other seasons. Further work is needed to identify the sources of the 10--30-day-IS variability in South America