557 research outputs found

    Dynamics of an ion chain in a harmonic potential

    Get PDF
    Cold ions in anisotropic harmonic potentials can form ion chains of various sizes. Here, the density of ions is not uniform, and thus the eigenmodes are not phononic-like waves. We study chains of N 1 ions and evaluate analytically the long-wavelength modes and the density of states in the short-wavelength limit. These results reproduce with good approximation the dynamics of chains consisting of dozens of ions. Moreover, they allow one to determine the critical transverse frequency required for the stability of the linear structure, which is found to be in agreement with results obtained by different theoretical methods [D. H. E. Dubin, Phys. Rev. Lett. 71, 2753 (1993)] and by numerical simulations [J. P. Schiffer, Phys. Rev. Lett. 70, 818 (1993)]. We introduce and explore the thermodynamic limit for the ion chain. The thermodynamic functions are found to exhibit deviations from extensivity

    On a class of invariant coframe operators with application to gravity

    Get PDF
    Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The paper exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the Geodesic Postulate, we find all the equations that are experimentally (by the 3 classical tests) indistinguishable from Einstein field equations. This family includes, of course, also Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the paper is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations

    Experimental identification of non-pointlike dark-matter candidates

    Get PDF
    We show that direct dark matter detection experiments can distinguish between pointlike and non-pointlike dark-matter candidates. The shape of the nuclear recoil energy spectrum from pointlike dark-matter particles, e.g., neutralinos, is determined by the velocity distribution of dark matter in the galactic halo and by nuclear form factors. In contrast, typical cross sections of non-pointlike dark matter, for example, Q-balls, have a new form factor, which decreases rapidly with the recoil energy. Therefore, a signal from non-pointlike dark matter is expected to peak near the experimental threshold and to fall off rapidly at higher energies. Although the width of the signal is practically independent of the dark matter velocity dispersion, its height is expected to exhibit an annual modulation due to the changes in the dark matter flux.Comment: 4 pages; minor changes, references adde

    A polynomial oracle-time algorithm for convex integer minimization

    Full text link
    In this paper we consider the solution of certain convex integer minimization problems via greedy augmentation procedures. We show that a greedy augmentation procedure that employs only directions from certain Graver bases needs only polynomially many augmentation steps to solve the given problem. We extend these results to convex NN-fold integer minimization problems and to convex 2-stage stochastic integer minimization problems. Finally, we present some applications of convex NN-fold integer minimization problems for which our approach provides polynomial time solution algorithms.Comment: 19 pages, 1 figur

    An Asymptotic Expansion and Recursive Inequalities for the Monomer-Dimer Problem

    Full text link
    Let (lambda_d)(p) be the p monomer-dimer entropy on the d-dimensional integer lattice Z^d, where p in [0,1] is the dimer density. We give upper and lower bounds for (lambda_d)(p) in terms of expressions involving (lambda_(d-1))(q). The upper bound is based on a conjecture claiming that the p monomer-dimer entropy of an infinite subset of Z^d is bounded above by (lambda_d)(p). We compute the first three terms in the formal asymptotic expansion of (lambda_d)(p) in powers of 1/d. We prove that the lower asymptotic matching conjecture is satisfied for (lambda_d)(p).Comment: 15 pages, much more about d=1,2,

    Relaxation and Localization in Interacting Quantum Maps

    Full text link
    We quantise and study several versions of finite multibaker maps. Classically these are exactly solvable K-systems with known exponential decay to global equilibrium. This is an attempt to construct simple models of relaxation in quantum systems. The effect of symmetries and localization on quantum transport is discussed.Comment: 32 pages. LaTex file. 9 figures, not included. For figures send mail to first author at '[email protected]

    Removing Singularities

    Get PDF
    Big bang/crunch curvature singularities in exact CFT string backgrounds can be removed by turning on gauge fields. This is described within a family of {SL(2)xSU(2)xU(1)_x}/{U(1)xU(1)} quotient CFTs. Uncharged incoming wavefunctions from the ``whiskers'' of the extended universe can be fully reflected if and only if a big bang/crunch curvature singularity, from which they are scattered, exists. Extended BTZ-like singularities remain as long as U(1)_x is compact.Comment: 21 pages, harvma
    • …
    corecore