First-principles quantum dynamics for fermions: Application to molecular dissociation

We demonstrate that the quantum dynamics of a many-body Fermi-Bose system can be simulated using a Gaussian phase-space representation method. In particular, we consider the application of the mixed fermion-boson model to ultracold quantum gases and simulate the dynamics of dissociation of a Bose-Einstein condensate of bosonic dimers into pairs of fermionic atoms. We quantify deviations of atom-atom pair correlations from Wick's factorization scheme, and show that atom-molecule and molecule-molecule correlations grow with time, in clear departures from pairing mean-field theories. As a first-principles approach, the method provides benchmarking of approximate approaches and can be used to validate dynamical probes for characterizing strongly correlated phases of fermionic systems.Comment: Final published versio

Validation of purdue engineering shape benchmark clusters by crowdsourcing

The effective organization of CAD data archives is central to PLM and consequently content based retrieval of 2D drawings and 3D models is often seen as a "holy grail" for the industry. Given this context, it is not surprising that the vision of a "Google for shape", which enables engineers to search databases of 3D models for components similar in shape to a query part, has motivated numerous researchers to investigate algorithms for computing geometric similarity. Measuring the effectiveness of the many approaches proposed has in turn lead to the creation of benchmark datasets against which researchers can compare the performance of their search engines. However to be useful the datasets used to measure the effectiveness of 3D retrieval algorithms must not only define a collection of models, but also provide a canonical specification of their relative similarity. Because the objective of shape retrieval algorithms is (typically) to retrieve groups of objects that humans perceive as "similar" these benchmark similarity relationships have (by definition) to be manually determined through inspection

Improving the efficiency of remanufacture through enhanced pre-processing inspection–a comprehensive study of over 2000 engines at Caterpillar remanufacturing, U.K.

Remanufacture, an industrial process to return used product to an “as-new” condition, is a key strategy in environmentally conscious manufacturing and waste management. However strategies to improve the efficiency of the process are hampered by a lack of remanufacturing-specific knowledge and tools. This paper presents the results of quantitative research, conducted in a Caterpillar Remanufacturing UK facility, to establish the relationship between pre-processing inspection levels and the subsequent remanufacturing process time for returned used products known as cores. It concludes that for components (i.e. cores) having either complex geometry (such as internal ports), a large number of sub-components or that are constructed from, or comprising of, multiple materials the remanufacturing process is shortened by increased inspection prior to processing. However, these benefits are currently limited by the amount of information that can be gained from the inspection methods used. The paper describes the practical use of these factors in a decision-making methodology for inspection and in a refined cost assessment tool

Geometric reasoning via internet crowdsourcing

The ability to interpret and reason about shapes is a peculiarly human capability that has proven difficult to reproduce algorithmically. So despite the fact that geometric modeling technology has made significant advances in the representation, display and modification of shapes, there have only been incremental advances in geometric reasoning. For example, although today's CAD systems can confidently identify isolated cylindrical holes, they struggle with more ambiguous tasks such as the identification of partial symmetries or similarities in arbitrary geometries. Even well defined problems such as 2D shape nesting or 3D packing generally resist elegant solution and rely instead on brute force explorations of a subset of the many possible solutions. Identifying economic ways to solving such problems would result in significant productivity gains across a wide range of industrial applications. The authors hypothesize that Internet Crowdsourcing might provide a pragmatic way of removing many geometric reasoning bottlenecks.This paper reports the results of experiments conducted with Amazon's mTurk site and designed to determine the feasibility of using Internet Crowdsourcing to carry out geometric reasoning tasks as well as establish some benchmark data for the quality, speed and costs of using this approach.After describing the general architecture and terminology of the mTurk Crowdsourcing system, the paper details the implementation and results of the following three investigations; 1) the identification of "Canonical" viewpoints for individual shapes, 2) the quantification of "similarity" relationships with-in collections of 3D models and 3) the efficient packing of 2D Strips into rectangular areas. The paper concludes with a discussion of the possibilities and limitations of the approach

Gaussian phase-space representations for fermions

We introduce a positive phase-space representation for fermions, using the most general possible multi-mode Gaussian operator basis. The representation generalizes previous bosonic quantum phase-space methods to Fermi systems. We derive equivalences between quantum and stochastic moments, as well as operator correspondences that map quantum operator evolution onto stochastic processes in phase space. The representation thus enables first-principles quantum dynamical or equilibrium calculations in many-body Fermi systems. Potential applications are to strongly interacting and correlated Fermi gases, including coherent behaviour in open systems and nanostructures described by master equations. Examples of an ideal gas and the Hubbard model are given, as well as a generic open system, in order to illustrate these ideas.Comment: More references and examples. Much less mathematical materia

Simulations and Experiments on Polarisation Squeezing in Optical Fibre

We investigate polarisation squeezing of ultrashort pulses in optical fibre, over a wide range of input energies and fibre lengths. Comparisons are made between experimental data and quantum dynamical simulations, to find good quantitative agreement. The numerical calculations, performed using both truncated Wigner and exact $+P$ phase-space methods, include nonlinear and stochastic Raman effects, through coupling to phonons variables. The simulations reveal that excess phase noise, such as from depolarising GAWBS, affects squeezing at low input energies, while Raman effects cause a marked deterioration of squeezing at higher energies and longer fibre lengths. The optimum fibre length for maximum squeezing is also calculated.Comment: 19 pages, lots of figure

Quantum Dynamics of Three Coupled Atomic Bose-Einstein Condensates

The simplest model of three coupled Bose-Einstein Condensates (BEC) is investigated using a group theoretical method. The stationary solutions are determined using the SU(3) group under the mean field approximation. This semiclassical analysis using the system symmetries shows a transition in the dynamics of the system from self trapping to delocalization at a critical value for the coupling between the condensates. The global dynamics are investigated by examination of the stable points and our analysis shows the structure of the stable points depends on the ratio of the condensate coupling to the particle-particle interaction, undergoes bifurcations as this ratio is varied. This semiclassical model is compared to a full quantum treatment, which also displays the dynamical transition. The quantum case has collapse and revival sequences superposed on the semiclassical dynamics reflecting the underlying discreteness of the spectrum. Non-zero circular current states are also demonstrated as one of the higher dimensional effects displayed in this system.Comment: Accepted to PR

Precision study of 6p 2Pj - 8s 2S1/2 relative transition matrix elements in atomic Cs

A combined experimental and theoretical study of transition matrix elements of the 6p 2Pj - 8s 2S1/2 transition in atomic Cs is reported. Measurements of the polarization-dependent two-photon excitation spectrum associated with the transition were made in an approximately 200 cm-1 range on the low frequency side of the 6s 2S1/2 - 6p 2P3/2 resonance. The measurements depend parametrically on the relative transition matrix elements, but also are sensitive to far-off-resonance 6s 2S1/2 - np 2Pj - 8s 2S1/2 transitions. In the past, this dependence has yielded a generalized sum rule, the value of which is dependent on sums of relative two-photon transition matrix elements. In the present case, best available determinations from other experiments are combined with theoretical matrix elements to extract the ratio of transition matrix elements for the 6p 2Pj - 8s 2S1/2 (j = 1/2,3/2) transition. The resulting experimental value of 1.423(2) is in excellent agreement with the theoretical value, calculated using a relativistic all-order method, of 1.425(2)

Quantum many-body simulations using Gaussian phase-space representations

Phase-space representations are of increasing importance as a viable and successful means to study exponentially complex quantum many-body systems from first principles. This review traces the background of these methods, starting from the early work of Wigner, Glauber and Sudarshan. We focus on modern phase-space approaches using non-classical phase-space representations. These lead to the Gaussian representation, which unifies bosonic and fermionic phase-space. Examples treated include quantum solitons in optical fibers, colliding Bose-Einstein condensates, and strongly correlated fermions on lattices.Comment: Short Review (10 pages); Corrected typo in eq (14); Added a few more reference

Quantum dynamics in ultra-cold atomic physics

We review recent developments in the theory of quantum dynamics in ultra-cold atomic physics, including exact techniques, but focusing on methods based on phase-space mappings that are appli- cable when the complexity becomes exponentially large. These phase-space representations include the truncated Wigner, positive-P and general Gaussian operator representations which can treat both bosons and fermions. These phase-space methods include both traditional approaches using a phase-space of classical dimension, and more recent methods that use a non-classical phase-space of increased dimensionality. Examples used include quantum EPR entanglement of a four-mode BEC, time-reversal tests of dephasing in single-mode traps, BEC quantum collisions with up to 106 modes and 105 interacting particles, quantum interferometry in a multi-mode trap with nonlinear absorp- tion, and the theory of quantum entropy in phase-space. We also treat the approach of variational optimization of the sampling error, giving an elementary example of a nonlinear oscillator