Integer Programming: Optimization and Evaluation Are Equivalent

Link to conference publication published by Springer: http://dx.doi.org/10.1007/978-3-642-03367-4We show that if one can find the optimal value of an integer linear programming problem in polynomial time, then one can find an optimal solution in polynomial time. We also present a proper generalization to (general) integer programs and to local search problems of the well-known result that optimization and augmentation are equivalent for 0/1-integer programs. Among other things, our results imply that PLS-complete problems cannot have “near-exact” neighborhoods, unless PLS = P.United States. Office of Naval Research (ONR grant N00014-01208-1-0029

NMR relaxation in half-integer antiferromagnetic spin chains

Nuclear relaxation in half-integer spin chains at low temperatures (T << J, the antiferromagnetic exchange constant) is dominated by dissipation from a gas of thermally-excited, overdamped, spinons. The universal low temperature dependence of the relaxation rates $1/T_1$ and $1/T_{2G}$ is computed.Comment: 7 pages, 1 uuencoded postscript figure appende

Ising model with periodic pinning of mobile defects

A two-dimensional Ising model with short-range interactions and mobile defects describing the formation and thermal destruction of defect stripes is studied. In particular, the effect of a local pinning of the defects at the sites of straight equidistant lines is analysed using Monte Carlo simulations and the transfer matrix method. The pinning leads to a long-range ordered magnetic phase at low temperatures. The dependence of the phase transition temperature, at which the defect stripes are destabilized, on the pinning strength is determined. The transition seems to be of first order, with and without pinning.Comment: 7 pages, 7 figure

Superconductor coupled to two Luttinger liquids as an entangler for electron spins

We consider an s-wave superconductor (SC) which is tunnel-coupled to two spatially separated Luttinger liquid (LL) leads. We demonstrate that such a setup acts as an entangler, i.e. it creates spin-singlets of two electrons which are spatially separated, thereby providing a source of electronic Einstein-Podolsky-Rosen pairs. We show that in the presence of a bias voltage, which is smaller than the energy gap in the SC, a stationary current of spin-entangled electrons can flow from the SC to the LL leads due to Andreev tunneling events. We discuss two competing transport channels for Cooper pairs to tunnel from the SC into the LL leads. On the one hand, the coherent tunneling of two electrons into the same LL lead is shown to be suppressed by strong LL correlations compared to single-electron tunneling into a LL. On the other hand, the tunneling of two spin-entangled electrons into different leads is suppressed by the initial spatial separation of the two electrons coming from the same Cooper pair. We show that the latter suppression depends crucially on the effective dimensionality of the SC. We identify a regime of experimental interest in which the separation of two spin-entangled electrons is favored. We determine the decay of the singlet state of two electrons injected into different leads caused by the LL correlations. Although the electron is not a proper quasiparticle of the LL, the spin information can still be transported via the spin density fluctuations produced by the injected spin-entangled electrons.Comment: 15 pages, 2 figure

Quantifying the levitation picture of extended states in lattice models

The behavior of extended states is quantitatively analyzed for two dimensional lattice models. A levitation picture is established for both white-noise and correlated disorder potentials. In a continuum limit window of the lattice models we find simple quantitative expressions for the extended states levitation, suggesting an underlying universal behavior. On the other hand, these results point out that the Quantum Hall phase diagrams may be disorder dependent.Comment: 5 pages, submitted to PR

Direct Observation of a One Dimensional Static Spin Modulation in Insulating La1.95Sr0.05CuO4

We report the results of an extensive elastic neutron scattering study of the incommensurate (IC) static spin correlations in La1.95Sr0.05CuO4 which is an insulating spin glass at low temperatures. The present neutron scattering experiments on the same x=0.05 crystal employ a narrower instrumental Q-resolution and thereby have revealed that the crystal has only two orthorhombic twins at low temperatures with relative populations of 2:1. We find that, in a single twin, only two satellites are observed at (1, +/-0.064, L)(ortho) and (0, 1+/-0.064, L)(ortho), that is, the modulation vector is only along the orthorhombic b*-axis. This demonstrates unambiguously that La1.95Sr0.05CuO4 has a one-dimensional static diagonal spin modulation at low temperatures, consistent with certain stripe models. We have also reexamined the x=0.04 crystal that previously was reported to show a single commensurate peak. By mounting the sample in the (H, K, 0) zone, we have discovered that the x=0.04 sample in fact has the same IC structure as the $x=0.05$ sample. The incommensurability parameter d for x=0.04 and 0.05, where d is the distance from (1/2, 1/2) in tetragonal reciprocal lattice units, follows the linear relation d=x. These results demonstrate that the insulator to superconductor transition in the under doped regime (0.05 </= x </= 0.06) in La2-xSrxCuO4 is coincident with a transition from diagonal to collinear static stripes at low temperatures thereby evincing the intimate coupling between the one dimensional spin density modulation and the superconductivity.Comment: 9 pages 8 figure

Optimum electrode configurations for fast ion separation in microfabricated surface ion traps

For many quantum information implementations with trapped ions, effective shuttling operations are important. Here we discuss the efficient separation and recombination of ions in surface ion trap geometries. The maximum speed of separation and recombination of trapped ions for adiabatic shuttling operations depends on the secular frequencies the trapped ion experiences in the process. Higher secular frequencies during the transportation processes can be achieved by optimising trap geometries. We show how two different arrangements of segmented static potential electrodes in surface ion traps can be optimised for fast ion separation or recombination processes. We also solve the equations of motion for the ion dynamics during the separation process and illustrate important considerations that need to be taken into account to make the process adiabatic