Runtime Distributions and Criteria for Restarts

Randomized algorithms sometimes employ a restart strategy. After a certain number of steps, the current computation is aborted and restarted with a new, independent random seed. In some cases, this results in an improved overall expected runtime. This work introduces properties of the underlying runtime distribution which determine whether restarts are advantageous. The most commonly used probability distributions admit the use of a scale and a location parameter. Location parameters shift the density function to the right, while scale parameters affect the spread of the distribution. It is shown that for all distributions scale parameters do not influence the usefulness of restarts and that location parameters only have a limited influence. This result simplifies the analysis of the usefulness of restarts. The most important runtime probability distributions are the log-normal, the Weibull, and the Pareto distribution. In this work, these distributions are analyzed for the usefulness of restarts. Secondly, a condition for the optimal restart time (if it exists) is provided. The log-normal, the Weibull, and the generalized Pareto distribution are analyzed in this respect. Moreover, it is shown that the optimal restart time is also not influenced by scale parameters and that the influence of location parameters is only linear

Direct control of the tunnel splitting in a one-electron double quantum dot

Quasi-static transport measurements are employed on a laterally defined tunnel-coupled double quantum dot. A nearby quantum point contact allows us to track the charge as added to the device. If charged with only up to one electron, the low-energy spectrum of the double quantum dot is characterized by its quantum mechanical interdot tunnel splitting. We directly measure its magnitude by utilizing particular anticrossing features in the stability diagram at finite source-drain bias. By modification of gate voltages defining the confinement potential as well as by variation of a perpendicular magnetic field we demonstrate the tunability of the coherent tunnel coupling.Comment: High resolution pdf file available at http://www2.nano.physik.uni-muenchen.de/~huettel/research/anticrossing.pd

Characterization of InGaN and InAlN epilayers by microdiffraction X-Ray reciprocal space mapping

We report a study of InGaN and InAlN epilayers grown on GaN/Sapphire substrates by microfocused three-dimensional X-ray Reciprocal Space Mapping (RSM). The analysis of the full volume of reciprocal space, while probing samples on the microscale with a focused X-ray beam, allows us to gain uniquely valuable information about the microstructure of III-N alloy epilayers. It is found that “seed” InGaN mosaic nanocrystallites are twisted with respect to the ensemble average and strain free. This indicates that the growth of InGaN epilayers follows the Volmer-Weber mechanism with nucleation of “seeds” on strain fields generated by the a-type dislocations which are responsible for the twist of underlying GaN mosaic blocks. In the case of InAlN epilayer formation of composition gradient was observed at the beginning of the epitaxial growth

Entanglement verification for quantum key distribution systems with an underlying bipartite qubit-mode structure

We consider entanglement detection for quantum key distribution systems that use two signal states and continuous variable measurements. This problem can be formulated as a separability problem in a qubit-mode system. To verify entanglement, we introduce an object that combines the covariance matrix of the mode with the density matrix of the qubit. We derive necessary separability criteria for this scenario. These criteria can be readily evaluated using semidefinite programming and we apply them to the specific quantum key distribution protocol.Comment: 6 pages, 2 figures, v2: final versio

Putting competing orders in their place near the Mott transition

We describe the localization transition of superfluids on two-dimensional lattices into commensurate Mott insulators with average particle density p/q (p, q relatively prime integers) per lattice site. For bosons on the square lattice, we argue that the superfluid has at least q degenerate species of vortices which transform under a projective representation of the square lattice space group (a PSG). The formation of a single vortex condensate produces the Mott insulator, which is required by the PSG to have density wave order at wavelengths of q/n lattice sites (n integer) along the principle axes; such a second-order transition is forbidden in the Landau-Ginzburg-Wilson framework. We also discuss the superfluid-insulator transition in the direct boson representation, and find that an interpretation of the quantum criticality in terms of deconfined fractionalized bosons is only permitted at special values of q for which a permutative representation of the PSG exists. We argue (and demonstrate in detail in a companion paper: L. Balents et al., cond-mat/0409470) that our results apply essentially unchanged to electronic systems with short-range pairing, with the PSG determined by the particle density of Cooper pairs. We also describe the effect of static impurities in the superfluid: the impurities locally break the degeneracy between the q vortex species, and this induces density wave order near each vortex. We suggest that such a theory offers an appealing rationale for the local density of states modulations observed by Hoffman et al. (cond-mat/0201348) in STM studies of the vortex lattice of BSCCO, and allows a unified description of the nucleation of density wave order in zero and finite magnetic fields. We note signatures of our theory that may be tested by future STM experiments.Comment: 35 pages, 16 figures; (v2) part II is cond-mat/0409470; (v3) added new appendix and clarifying remarks; (v4) corrected typo

Anomalous expansion and phonon damping due to the Co spin-state transition in RCoO_3 with R = La, Pr, Nd and Eu

We present a combined study of the thermal expansion and the thermal conductivity of the perovskite series RCoO_3 with R = La, Nd, Pr and Eu. The well-known spin-state transition in LaCoO_3 is strongly affected by the exchange of the R ions due to their different ionic radii, i.e. chemical pressure. This can be monitored in detail by measurements of the thermal expansion, which is a highly sensitive probe for detecting spin-state transitions. The Co ions in the higher spin state act as additional scattering centers for phonons, therefore suppressing the phonon thermal conductivity. Based on the analysis of the interplay between spin-state transition and heat transport, we present a quantitative model of the thermal conductivity for the entire series. In PrCoO_3, an additional scattering effect is active at low temperatures. This effect arises from the crystal field splitting of the 4f multiplet, which allows for resonant scattering of phonons between the various 4f levels.Comment: 15 pages including 5 figure

Magnetothermal transport in the spin-1/2 chains of copper pyrazine dinitrate

We present experiments on the thermal transport in the spin-1/2 chain compound copper pyrazine dinitrate Cu(C_4 H_4 N_2)(NO_3)_2. The heat conductivity shows a surprisingly strong dependence on the applied magnetic field B, characterized at low temperatures by two main features. The first one appearing at low B is a characteristic dip located at mu_B B ~ k_B T, that may arise from Umklapp scattering. The second one is a plateau-like feature in the quantum critical regime, mu_B |B-B_c| < k_B T, where B_c is the saturation field at T=0. The latter feature clearly points towards a momentum and field independent mean free path of the spin excitations, contrary to theoretical expectations.Comment: 4 pages, 4 figure