Dressing the chopped-random-basis optimization: a bandwidth-limited access to the trap-free landscape

In quantum optimal control theory the success of an optimization algorithm is highly influenced by how the figure of merit to be optimized behaves as a function of the control field, i.e. by the control landscape. Constraints on the control field introduce local minima in the landscape --false traps-- which might prevent an efficient solution of the optimal control problem. Rabitz et al. [Science 303, 1998 (2004)] showed that local minima occur only rarely for unconstrained optimization. Here, we extend this result to the case of bandwidth-limited control pulses showing that in this case one can eliminate the false traps arising from the constraint. Based on this theoretical understanding, we modify the Chopped Random Basis (CRAB) optimal control algorithm and show that this development exploits the advantages of both (unconstrained) gradient algorithms and of truncated basis methods, allowing to always follow the gradient of the unconstrained landscape by bandwidth-limited control functions. We study the effects of additional constraints and show that for reasonable constraints the convergence properties are still maintained. Finally, we numerically show that this approach saturates the theoretical bound on the minimal bandwidth of the control needed to optimally drive the system.Comment: 8 pages, 6 figure

Charge fluctuations in nonlinear heat transport

We show that charge fluctuation processes are crucial for the nonlinear heat conductance through an interacting nanostructure, even far from a resonance. We illustrate this for an Anderson quantum dot accounting for the first two leading orders of the tunneling in a master equation. The often made assumption that off-resonant transport proceeds entirely by virtual occupation of charge states, underlying exchange-scattering models, can fail dramatically for heat transport. The identified energy-transport resonances in the Coulomb blockade regime provide new qualitative information about relaxation processes, for instance by strong negative differential heat conductance relative to the heat current. These can go unnoticed in the charge current, making nonlinear heat-transport spectroscopy with energy-level control a promising experimental tool

Significant Subgraph Mining with Multiple Testing Correction

The problem of finding itemsets that are statistically significantly enriched in a class of transactions is complicated by the need to correct for multiple hypothesis testing. Pruning untestable hypotheses was recently proposed as a strategy for this task of significant itemset mining. It was shown to lead to greater statistical power, the discovery of more truly significant itemsets, than the standard Bonferroni correction on real-world datasets. An open question, however, is whether this strategy of excluding untestable hypotheses also leads to greater statistical power in subgraph mining, in which the number of hypotheses is much larger than in itemset mining. Here we answer this question by an empirical investigation on eight popular graph benchmark datasets. We propose a new efficient search strategy, which always returns the same solution as the state-of-the-art approach and is approximately two orders of magnitude faster. Moreover, we exploit the dependence between subgraphs by considering the effective number of tests and thereby further increase the statistical power.Comment: 18 pages, 5 figure, accepted to the 2015 SIAM International Conference on Data Mining (SDM15

Supercontinuum generation in media with sign-alternated dispersion

When an ultrafast optical pulse with high intensity is propagating through transparent material a supercontinuum can be coherently generated by self-phase modulation, which is essential to many photonic applications in fibers and integrated waveguides. However, the presence of dispersion causes stagnation of spectral broadening past a certain propagation length, requiring an increased input peak power for further broadening. We present a concept to drive supercontinuum generation with significantly lower input power by counteracting spectral stagnation via alternating the sign of group velocity dispersion along the propagation. We demonstrate the effect experimentally in dispersion alternating fiber in excellent agreement with modeling, revealing almost an order of magnitude reduced peak power compared to uniform dispersion. Calculations reveal a similar power reduction also with integrated optical waveguides, simultaneously with a significant increase of flat bandwidth, which is important for on-chip broadband photonics.Comment: Main text and supplementary informatio

Holograms of Conformal Chern-Simons Gravity

We show that conformal Chern-Simons gravity in three dimensions has various holographic descriptions. They depend on the boundary conditions on the conformal equivalence class and the Weyl factor, even when the former is restricted to asymptotic Anti-deSitter behavior. For constant or fixed Weyl factor our results agree with a suitable scaling limit of topologically massive gravity results. For varying Weyl factor we find an enhancement of the asymptotic symmetry group, the details of which depend on certain choices. We focus on a particular example where an affine u(1) algebra related to holomorphic Weyl rescalings shifts one of the central charges by 1. The Weyl factor then behaves as a free chiral boson in the dual conformal field theory.Comment: 5