Using molecular similarity to construct accurate semiempirical electron structure theories

Ab initio electronic structure methods give accurate results for small systems, but do not scale well to large systems. Chemical insight tells us that molecular functional groups will behave approximately the same way in all molecules, large or small. This molecular similarity is exploited in semiempirical methods, which couple simple electronic structure theories with parameters for the transferable characteristics of functional groups. We propse that high-level calculations on small molecules provide a rich source of parametrization data. In principle, we can select a functional group, generate a large amount of ab initio data on the group in various small-molecule environments, and "mine" this data to build a sophisticated model for the group's behavior in large molecules. This work details such a model for electron correlation: a semiempirical, subsystem-based correlation functional that predicts a subsystem's two-electron density as a functional of its one-electron density. This model is demonstrated on two small systems: chains of linear, minimal-basis (H-H)5, treated as a sum of four overlapping (H-H)2 subsystems; and the aldehyde group of a set of HOC-R molecules. The results provide an initial demonstration of the feasibility of this approach.Comment: The following article appeared in the Journal of Chemical Physics, 121 (12), 5635-5645 (2004) and may be found at http://jcp.aip.org

Ghost imaging with a single detector

We experimentally demonstrate pseudothermal ghost imaging and ghost diffraction using only a single single-pixel detector. We achieve this by replacing the high resolution detector of the reference beam with a computation of the propagating field, following a recent proposal by Shapiro [J. H. Shapiro, arXiv:0807.2614 (2008)]. Since only a single detector is used, this provides an experimental evidence that pseudothermal ghost imaging does not rely on non-local quantum correlations. In addition, we show the depth-resolving capability of this ghost imaging technique.Comment: See video at http://www.weizmann.ac.il/home/feori/Misc.html Comments are welcom

Nonlinear interactions with an ultrahigh flux of broadband entangled photons

We experimentally demonstrate sum-frequency generation (SFG) with entangled photon-pairs, generating as many as 40,000 SFG photons per second, visible even to the naked eye. The nonclassical nature of the interaction is exhibited by a linear intensity-dependence of the nonlinear process. The key element in our scheme is the generation of an ultrahigh flux of entangled photons while maintaining their nonclassical properties. This is made possible by generating the down-converted photons as broadband as possible, orders of magnitude wider than the pump. This approach is readily applicable for other nonlinear interactions, and may be applicable for various quantum-measurement tasks.Comment: 4 pages, 2 figures, Accepted to Phys. Rev. Let

Hydrodynamics and the Detection of the QCD Axial Anomaly in Heavy Ion Collisions

We consider the experimental implications of the axial current triangle diagram anomaly in a hydrodynamic description of high density QCD. We propose a signal of an enhanced production of spin-excited hadrons in the direction of the rotation axis in off-central heavy ion collisions.Comment: 15 pages, 19 figures; v2: refs added, minor changes to the plots; v3, comments adde

Shocks and Universal Statistics in (1+1)-Dimensional Relativistic Turbulence

We propose that statistical averages in relativistic turbulence exhibit universal properties. We consider analytically the velocity and temperature differences structure functions in the (1+1)-dimensional relativistic turbulence in which shock waves provide the main contribution to the structure functions in the inertial range. We study shock scattering, demonstrate the stability of the shock waves, and calculate the anomalous exponents. We comment on the possibility of finite time blowup singularities.Comment: 37 pages, 7 figure

Constant Size Molecular Descriptors For Use With Machine Learning

A set of molecular descriptors whose length is independent of molecular size is developed for machine learning models that target thermodynamic and electronic properties of molecules. These features are evaluated by monitoring performance of kernel ridge regression models on well-studied data sets of small organic molecules. The features include connectivity counts, which require only the bonding pattern of the molecule, and encoded distances, which summarize distances between both bonded and non-bonded atoms and so require the full molecular geometry. In addition to having constant size, these features summarize information regarding the local environment of atoms and bonds, such that models can take advantage of similarities resulting from the presence of similar chemical fragments across molecules. Combining these two types of features leads to models whose performance is comparable to or better than the current state of the art. The features introduced here have the advantage of leading to models that may be trained on smaller molecules and then used successfully on larger molecules.Comment: 18 pages, 5 figure

Localization of Multi-Dimensional Wigner Distributions

A well known result of P. Flandrin states that a Gaussian uniquely maximizes the integral of the Wigner distribution over every centered disc in the phase plane. While there is no difficulty in generalizing this result to higher-dimensional poly-discs, the generalization to balls is less obvious. In this note we provide such a generalization.Comment: Minor corrections, to appear in the Journal of Mathematical Physic