Resolving the notorious case of conical intersections for coupled cluster dynamics

The motion of electrons and nuclei in photochemical events often involve conical intersections, degeneracies between electronic states. They serve as funnels for nuclear relaxation - on the femtosecond scale - in processes where the electrons and nuclei couple nonadiabatically. Accurate ab initio quantum chemical models are essential for interpreting experimental measurements of such phenomena. In this paper we resolve a long-standing problem in coupled cluster theory, presenting the first formulation of the theory that correctly describes conical intersections between excited electronic states of the same symmetry. This new development demonstrates that the highly accurate coupled cluster theory can be applied to describe dynamics on excited electronic states involving conical intersections.Comment: 8 pages and 3 figures and including supporting information (with corrections and improved notation

Separable states can be used to distribute entanglement

We show that no entanglement is necessary to distribute entanglement; that is, two distant particles can be entangled by sending a third particle that is never entangled with the other two. Similarly, two particles can become entangled by continuous interaction with a highly mixed mediating particle that never itself becomes entangled. We also consider analogous properties of completely positive maps, in which the composition of two separable maps can create entanglement.Comment: 4 pages, 2 figures. Slight modification

Space-Time Approach to Scattering from Many Body Systems

We present scattering from many body systems in a new light. In place of the usual van Hove treatment, (applicable to a wide range of scattering processes using both photons and massive particles) based on plane waves, we calculate the scattering amplitude as a space-time integral over the scattering sample for an incident wave characterized by its correlation function which results from the shaping of the wave field by the apparatus. Instrument resolution effects - seen as due to the loss of correlation caused by the path differences in the different arms of the instrument are automatically included and analytic forms of the resolution function for different instruments are obtained. The intersection of the moving correlation volumes (those regions where the correlation functions are significant) associated with the different elements of the apparatus determines the maximum correlation lengths (times) that can be observed in a sample, and hence, the momentum (energy) resolution of the measurement. This geometrical picture of moving correlation volumes derived by our technique shows how the interaction of the scatterer with the wave field shaped by the apparatus proceeds in space and time. Matching of the correlation volumes so as to maximize the intersection region yields a transparent, graphical method of instrument design. PACS: 03.65.Nk, 3.80 +r, 03.75, 61.12.BComment: Latex document with 6 fig

Improved detection of small atom numbers through image processing

We demonstrate improved detection of small trapped atomic ensembles through advanced post-processing and optimal analysis of absorption images. A fringe removal algorithm reduces imaging noise to the fundamental photon-shot-noise level and proves beneficial even in the absence of fringes. A maximum-likelihood estimator is then derived for optimal atom-number estimation and is applied to real experimental data to measure the population differences and intrinsic atom shot-noise between spatially separated ensembles each comprising between 10 and 2000 atoms. The combined techniques improve our signal-to-noise by a factor of 3, to a minimum resolvable population difference of 17 atoms, close to our ultimate detection limit.Comment: 4 pages, 3 figure

An Efficient Approximate kNN Graph Method for Diffusion on Image Retrieval

The application of the diffusion in many computer vision and artificial intelligence projects has been shown to give excellent improvements in performance. One of the main bottlenecks of this technique is the quadratic growth of the kNN graph size due to the high-quantity of new connections between nodes in the graph, resulting in long computation times. Several strategies have been proposed to address this, but none are effective and efficient. Our novel technique, based on LSH projections, obtains the same performance as the exact kNN graph after diffusion, but in less time (approximately 18 times faster on a dataset of a hundred thousand images). The proposed method was validated and compared with other state-of-the-art on several public image datasets, including Oxford5k, Paris6k, and Oxford105k

UCN Upscattering rates in a molecular deuterium crystal

A calculation of ultra-cold neutron (UCN) upscattering rates in molecular deuterium solids has been carried out, taking into account intra-molecular exictations and phonons. The different moelcular species ortho-D2 (with even rotational quantum number J) and para-D2 (with odd J) exhibit significantly different UCN-phonon annihilation cross-sections. Para- to ortho-D2 conversion, furthermore, couples UCN to an energy bath of excited rotational states without mediating phonons. This anomalous upscattering mechanism restricts the UCN lifetime to 4.6 msec in a normal-D2 solid with 33% para content.Comment: 3 pages, one figur

Random copying in space

Random copying is a simple model for population dynamics in the absence of selection, and has been applied to both biological and cultural evolution. In this work, we investigate the effect that spatial structure has on the dynamics. We focus in particular on how a measure of the diversity in the population changes over time. We show that even when the vast majority of a population's history may be well-described by a spatially-unstructured model, spatial structure may nevertheless affect the expected level of diversity seen at a local scale. We demonstrate this phenomenon explicitly by examining the random copying process on small-world networks, and use our results to comment on the use of simple random-copying models in an empirical context.Comment: 26 pages, 11 figures. Based on invited talk at AHRC CECD Conference on "Cultural Evolution in Spatially Structured Populations" at UCL, September 2010. To appear in ACS - Advances in Complex System

Matrix Pencils and Entanglement Classification

In this paper, we study pure state entanglement in systems of dimension $2\otimes m\otimes n$. Two states are considered equivalent if they can be reversibly converted from one to the other with a nonzero probability using only local quantum resources and classical communication (SLOCC). We introduce a connection between entanglement manipulations in these systems and the well-studied theory of matrix pencils. All previous attempts to study general SLOCC equivalence in such systems have relied on somewhat contrived techniques which fail to reveal the elegant structure of the problem that can be seen from the matrix pencil approach. Based on this method, we report the first polynomial-time algorithm for deciding when two $2\otimes m\otimes n$ states are SLOCC equivalent. Besides recovering the previously known 26 distinct SLOCC equivalence classes in $2\otimes 3\otimes n$ systems, we also determine the hierarchy between these classes