Fractional Power-Law Spectral Response of CaCu3Ti4O12 Dielectric: Many-Body Effects

Spectral character of dielectric response in CaCu3Ti4O12 across 0.5Hz-4MHz over 45-200K corresponding to neither the Debyean nor the KWW relaxation patterns rather indicates a random-walk like diffusive dynamics of moments. Non-linear relaxation here is due to the many body dipole-interactions, as confirmed by spectral-fits of our measured permittivity to the Dissado-Hill behaviour. Fractional power-laws observed in {\epsilon}*({\omega}) macroscopically reflect the fractal microscopic configurations. Below ~100K, the power-law exponent m (n) steeply decreases (increases), indicating finite length-scale collective response of moment-bearing entities. At higher temperatures, m gradually approaches 1 and n falls to low values, reflecting tendency towards the single-particle/Debyean relaxation.Comment: 10 pages, 3 figures, 22 reference

Discovery of Strange Kinetics in Bulk Material: Correlated Dipoles in CaCu3Ti4O12

Dielectric spectroscopy of CaCu3Ti4O12 was performed spanning broad ranges of temperature (10-300K) and frequency (0.5Hz-2MHz). We attribute the permittivity step-fall to the evolution of Kirkwood-Fr\"oehlich dipole-correlations; reducing the moment-density due to anti-parallel orienting dipoles, with decreasing temperature. Unambiguous sub-Arrhenic dispersion of the associated loss-peak reveals the prime role of strange kinetics; used to describe nonlinearity-governed meso-confined/fractal systems, witnessed here for the first time in a bulk material. Effective energy-scale is seen to follow thermal evolution of the moment density, and the maidenly estimated correlation-length achieves mesoscopic scale below 100K. Temperature dependence of correlations reveals emergence of a new, parallel-dipole-orientation branch below 85K. Novel features observed define a crossover temperature window connecting the single-dipoles regime and the correlated moments. Conciling known results, we suggest a fractal-like self-similar configuration of Ca/Cu-rich sub-phases; resultant heterogeneity endowing CaCu3Ti4O12 its peculiar electrical behaviour.Comment: 19 pages, 5 figures, 44 reference

Reentrant Adhesion Behavior in Nanocluster Deposition

We simulate the collision of atomic clusters with a weakly attractive surface using molecular dynamics in a regime between soft-landing and fragmentation, where the cluster undergoes large deformation but remains intact. As a function of incident kinetic energy, we find a transition from adhesion to reflection at low kinetic energies. We also identify a second adhesive regime at intermediate kinetic energies, where strong deformation of the cluster leads to an increase in contact area and adhesive energy.Comment: 7 pages, 6 figure

t-SURFF: Fully Differential Two-Electron Photo-Emission Spectra

The time dependent surface flux (t-SURFF) method is extended to single and double ionization of two electron systems. Fully differential double emission spectra by strong pulses at extreme UV and infrared wave length are calculated using simulation volumes that only accommodate the effective range of the atomic binding potential and the quiver radius of free electrons in the external field. For a model system we find pronounced dependence of shake-up and non-sequential double ionization on phase and duration of the laser pulse. Extension to fully three-dimensional calculations is discussed

Label optimal regret bounds for online local learning

We resolve an open question from (Christiano, 2014b) posed in COLT'14 regarding the optimal dependency of the regret achievable for online local learning on the size of the label set. In this framework the algorithm is shown a pair of items at each step, chosen from a set of $n$ items. The learner then predicts a label for each item, from a label set of size $L$ and receives a real valued payoff. This is a natural framework which captures many interesting scenarios such as collaborative filtering, online gambling, and online max cut among others. (Christiano, 2014a) designed an efficient online learning algorithm for this problem achieving a regret of $O(\sqrt{nL^3T})$, where $T$ is the number of rounds. Information theoretically, one can achieve a regret of $O(\sqrt{n \log L T})$. One of the main open questions left in this framework concerns closing the above gap. In this work, we provide a complete answer to the question above via two main results. We show, via a tighter analysis, that the semi-definite programming based algorithm of (Christiano, 2014a), in fact achieves a regret of $O(\sqrt{nLT})$. Second, we show a matching computational lower bound. Namely, we show that a polynomial time algorithm for online local learning with lower regret would imply a polynomial time algorithm for the planted clique problem which is widely believed to be hard. We prove a similar hardness result under a related conjecture concerning planted dense subgraphs that we put forth. Unlike planted clique, the planted dense subgraph problem does not have any known quasi-polynomial time algorithms. Computational lower bounds for online learning are relatively rare, and we hope that the ideas developed in this work will lead to lower bounds for other online learning scenarios as well.Comment: 13 pages; Changes from previous version: small changes to proofs of Theorems 1 & 2, a small rewrite of introduction as well (this version is the same as camera-ready copy in COLT '15