The nature of war: Early warfare establishes later patterns

Arms Control & Domestic and International Security (ACDIS

Scarring on invariant manifolds for perturbed quantized hyperbolic toral automorphisms

We exhibit scarring for certain nonlinear ergodic toral automorphisms. There are perturbed quantized hyperbolic toral automorphisms preserving certain co-isotropic submanifolds. The classical dynamics is ergodic, hence in the semiclassical limit almost all eigenstates converge to the volume measure of the torus. Nevertheless, we show that for each of the invariant submanifolds, there are also eigenstates which localize and converge to the volume measure of the corresponding submanifold.Comment: 17 page

Solitonic excitations in the Haldane phase of a S=1 chain

We study low-lying excitations in the 1D $S=1$ antiferromagnetic valence-bond-solid (VBS) model. In a numerical calculation on finite systems the lowest excitations are found to form a discrete triplet branch, separated from the higher-lying continuum. The dispersion of these triplet excitations can be satisfactorily reproduced by assuming approximate wave functions. These wave functions are shown to correspond to moving hidden domain walls, i.e. to one-soliton excitations.Comment: RevTex 3.0, 24 pages, 2 figures on request by fax or mai

Preschool Mathematics Performance and Executive Function: Rural-Urban Comparisons across Time

This longitudinal study examined the relationship between executive function (EF) and mathematics with rural and urban preschool children. A panel of direct and indirect EF measures were used to compare how well individual measures, as well as analytic approaches, predicted both numeracy and geometry skill. One hundred eighteen children, ages 39 to 68 months, were given EF and mathematics assessments twice, approximately six months apart, concurrent to their teachers completing an indirect assessment of EF for each child. Results suggest: (1) the child’s age determines if a panel of direct EF measures is a better predictor of numeracy and geometry skills than a single EF measure, (2) geometry and numeracy skill are influenced differently by contextual factors, and (3) the EF-geometry link may develop about six months later than the EF-numeracy connection. As the relationship between preschool age EF and mathematics is better understood, efforts can be made to improve the aspects of EF connected to mathematics skill, which may aid in performance

Quantum spin models with exact dimer ground states

Inspired by the exact solution of the Majumdar-Ghosh model, a family of one-dimensional, translationally invariant spin hamiltonians is constructed. The exchange coupling in these models is antiferromagnetic, and decreases linearly with the separation between the spins. The coupling becomes identically zero beyond a certain distance. It is rigorously proved that the dimer configuration is an exact, superstable ground state configuration of all the members of the family on a periodic chain. The ground state is two-fold degenerate, and there exists an energy gap above the ground state. The Majumdar-Ghosh hamiltonian with two-fold degenerate dimer ground state is just the first member of the family. The scheme of construction is generalized to two and three dimensions, and illustrated with the help of some concrete examples. The first member in two dimensions is the Shastry-Sutherland model. Many of these models have exponentially degenerate, exact dimer ground states.Comment: 10 pages, 8 figures, revtex, to appear in Phys. Rev.

On the multiplicativity of quantum cat maps

The quantum mechanical propagators of the linear automorphisms of the two-torus (cat maps) determine a projective unitary representation of the theta group, known as Weil's representation. We prove that there exists an appropriate choice of phases in the propagators that defines a proper representation of the theta group. We also give explicit formulae for the propagators in this representation.Comment: Revised version: proof of the main theorem simplified. 21 page

Exact ground states for a class of one-dimensional frustrated quantum spin models

We have found the exact ground state for two frustrated quantum spin-1/2 models on a linear chain. The first model describes ferromagnet- antiferromagnet transition point. The singlet state at this point has double-spiral ordering. The second model is equivalent to special case of the spin-1/2 ladder. It has non-degenerate singlet ground state with exponentially decaying spin correlations and there is an energy gap. The exact ground state wave function of these models is presented in a special recurrent form and recurrence technics of expectation value calculations is developed.Comment: 16 pages, 3 figures, RevTe

Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain:

The natural explanation of the excitation spectrum of the spin-1 antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2 ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy spectrum of the latter is calculated with fixed momentum $k$ by numerical diagonalization of finite size systems. It consists of a branch of propagating triplet pair (triplet wave) and the continuum of multiple triplet waves for weak ferromagnetic coupling. As the ferromagnetic coupling increases, the triplet wave branch is absorbed in the continuum for small $k$, reproducing the characteristics of the spin-1 antiferromagnetic Heisenberg chain.Comment: 12 Pages REVTEX, Postscript file for the figures included. SKPH-94-C00

Nuclear Magnetic Relaxation in the Haldane-Gap Antiferromagnet Ni(C_2_H_8_N_2_)_2_NO_2_(ClO_4_)

A new theory is proposed to interpret nuclear spin-lattice relaxation-time (T_1_) measurements on the spin-1 quasi-one-dimensional Heisenberg antiferromagnet Ni(C_2_H_8_N_2_)_2_NO_2_(ClO_4_) (NENP). While Sagi and Affleck pioneeringly discussed this subject in terms of field-theoretical languages, there is no theoretical attempt yet to explicitly simulate the novel observations of 1/T_1_ reported by Fujiwara et al.. By means of modified spin waves, we solve the minimum of 1/T_1_ as a function of an applied field, pending for the past decade.Comment: to be published in J. Phys. Soc. Jpn. 73, No. 4 (2004

The spectral gap for some spin chains with discrete symmetry breaking

We prove that for any finite set of generalized valence bond solid (GVBS) states of a quantum spin chain there exists a translation invariant finite-range Hamiltonian for which this set is the set of ground states. This result implies that there are GVBS models with arbitrary broken discrete symmetries that are described as combinations of lattice translations, lattice reflections, and local unitary or anti-unitary transformations. We also show that all GVBS models that satisfy some natural conditions have a spectral gap. The existence of a spectral gap is obtained by applying a simple and quite general strategy for proving lower bounds on the spectral gap of the generator of a classical or quantum spin dynamics. This general scheme is interesting in its own right and therefore, although the basic idea is not new, we present it in a system-independent setting. The results are illustrated with an number of examples.Comment: 48 pages, Plain TeX, BN26/Oct/9