Uniform Density Theorem for the Hubbard Model

A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov-Kimball model. For the half-filled band, the single-particle density matrix \uprho (x,y) in the ground state and in the canonical and grand canonical ensembles is shown to be constant on the diagonal $x=y$, and to vanish if $x \not=y$ and if $x$ and $y$ are on the same sublattice. For free electron hopping models, it is shown in addition that there are no correlations between sites of the same sublattice in any higher order density matrix. Physical implications are discussed.Comment: 15 pages, plaintex, EHLMLRJM-22/Feb/9

On orbit validation of solar sailing control laws with thin-film spacecraft

Many innovative approaches to solar sail mission and trajectory design have been proposed over the years, but very few ever have the opportunity to be validated on orbit with real spacecraft. Thin- Film Spacecraft/Lander/Rovers (TF-SL Rs) are a new class of very low cost, low mass space vehicle which are ideal for inexpensively and quickly testing in flight new approaches to solar sailing. This paper describes using TF- SLR based micro solar sails to implement a generic solar sail test bed on orbit. TF -SLRs are high area- to-mass ratio (A/m) spacecraft developed for very low cost consumer and scientific deep space missions. Typically based on a 5 μm or thinner metalised substrate, they include an integrated avionics and payload system -on-chip (SoC) die bonded to the substrate with passive components and solar cells printed or deposited by Metal Organic Chemical Vapour Deposition (MOCVD). The avionics include UHF/S- band transceivers, processors, storage, sensors and attitude control provided by integrated magnetorquers and reflectivity control devices. Resulting spacecraft have a typical thickness of less than 50 μm, are 80 mm in diameter, and have a mass of less than 100 mg resulting in sail loads of less than 20 g/m 2 . TF -SLRs are currently designed for direct dispensing in swarms from free flying 0.5U Interplanetary CubeSats or dispensers attached to launch vehicles. Larger 160 mm, 320 mm and 640 mm diameter TF -SLRs utilizing a CubeSat compatible TWIST deployment mechanism that maintains the high A/m ratio are also under development. We are developing a mission to demonstrate the utility of these devices as a test bed for experimenting with a variety of mission designs and control laws. Batches of up to one hundred TF- SLRs will be released on earth escape trajectories, with each batch executing a heterogeneous or homogenous mixture of control laws and experiments. Up to four releases at different points in orbit are currently envisaged with experiments currently being studied in MATLAB and GMA T including managing the rate of separation of individual spacecraft, station keeping and single deployment/substantially divergent trajectory development. It is also hoped to be able to demonstrate uploading new experiment designs while in orbit and to make this capability available to researchers around the world. A suitable earth escape mission is currently being sought and it is hoped the test bed could be on orbit in 2017/18

Distributed Optimization in Energy Harvesting Sensor Networks with Dynamic In-network Data Processing

Energy Harvesting Wireless Sensor Networks (EH- WSNs) have been attracting increasing interest in recent years. Most current EH-WSN approaches focus on sensing and net- working algorithm design, and therefore only consider the energy consumed by sensors and wireless transceivers for sensing and data transmissions respectively. In this paper, we incorporate CPU-intensive edge operations that constitute in-network data processing (e.g. data aggregation/fusion/compression) with sens- ing and networking; to jointly optimize their performance, while ensuring sustainable network operation (i.e. no sensor node runs out of energy). Based on realistic energy and network models, we formulate a stochastic optimization problem, and propose a lightweight on-line algorithm, namely Recycling Wasted Energy (RWE), to solve it. Through rigorous theoretical analysis, we prove that RWE achieves asymptotical optimality, bounded data queue size, and sustainable network operation. We implement RWE on a popular IoT operating system, Contiki OS, and eval- uate its performance using both real-world experiments based on the FIT IoT-LAB testbed, and extensive trace-driven simulations using Cooja. The evaluation results verify our theoretical analysis, and demonstrate that RWE can recycle more than 90% wasted energy caused by battery overflow, and achieve around 300% network utility gain in practical EH-WSNs

Universality in escape from a modulated potential well

We show that the rate of activated escape $W$ from a periodically modulated potential displays scaling behavior versus modulation amplitude $A$. For adiabatic modulation of an optically trapped Brownian particle, measurements yield $\ln W\propto (A_{\rm c} - A)^{\mu}$ with $\mu = 1.5$. The theory gives $\mu=3/2$ in the adiabatic limit and predicts a crossover to $\mu=2$ scaling as $A$ approaches the bifurcation point where the metastable state disappears.Comment: 4 pages, 3 figure

Ultracold, radiative charge transfer in hybrid Yb ion - Rb atom traps

Ultracold hybrid ion-atom traps offer the possibility of microscopic manipulation of quantum coherences in the gas using the ion as a probe. However, inelastic processes, particularly charge transfer can be a significant process of ion loss and has been measured experimentally for the Yb$^{+}$ ion immersed in a Rb vapour. We use first-principles quantum chemistry codes to obtain the potential energy curves and dipole moments for the lowest-lying energy states of this complex. Calculations for the radiative decay processes cross sections and rate coefficients are presented for the total decay processes. Comparing the semi-classical Langevin approximation with the quantum approach, we find it provides a very good estimate of the background at higher energies. The results demonstrate that radiative decay mechanisms are important over the energy and temperature region considered. In fact, the Langevin process of ion-atom collisions dominates cold ion-atom collisions. For spin dependent processes \cite{kohl13} the anisotropic magnetic dipole-dipole interaction and the second-order spin-orbit coupling can play important roles, inducing couplingbetween the spin and the orbital motion. They measured the spin-relaxing collision rate to be approximately 5 orders of magnitude higher than the charge-exchange collision rate \cite{kohl13}. Regarding the measured radiative charge transfer collision rate, we find that our calculation is in very good agreement with experiment and with previous calculations. Nonetheless, we find no broad resonances features that might underly a strong isotope effect. In conclusion, we find, in agreement with previous theory that the isotope anomaly observed in experiment remains an open question.Comment: 7 figures, 1 table accepted for publication in J. Phys. B: At. Mol. Opt. Phys. arXiv admin note: text overlap with arXiv:1107.114

Electron release of rare gas atom clusters under an intense laser pulse

Calculating the energy absorption of atomic clusters as a function of the laser pulse length $T$ we find a maximum for a critical $T^*$. We show that $T^*$ can be linked to an optimal cluster radius $R^*$. The existence of this radius can be attributed to the enhanced ionization mechanism originally discovered for diatomic molecules. Our findings indicate that enhanced ionization should be operative for a wide class of rare gas clusters. From a simple Coulomb explosion ansatz, we derive an analytical expression relating the maximum energy release to a suitably scaled expansion time which can be expressed with the pulse length $T^*$.Comment: 4 pages, 5 figure

Active financial analysis: stimulating engagement using Bloomberg for introductory finance students

There is increasing interest in the adoption of real-world interactive and participative learning techniques within economics and finance teaching through the use of trading room software. Previous research suggests that the integration of trading room software can improve knowledge development and performance. However, the time constraints of providing software training and requirements for foundation knowledge of basic maths and economics has restricted the adoption of trading room software to advanced courses. This paper outlines how the Bloomberg Professional Software was used in an introductory finance course and analyses student engagement, learning and attainment using feedback and performance data. We find that students valued the novelty of Bloomberg as part of a mix of different learning activities which facilitated the practical application of theory. Results also indicate that the alignment of teaching, learning and assessment promotes deeper engagement, and is associated with higher attainment. We demonstrate that trading room software can be effectively used in introductory courses to enhance the student experience and deepen understanding

Overcoming barriers to effective early parenting interventions for attention-deficit hyperactivity disorder (ADHD): parent and practitioner views

BackgroundThe importance of early intervention approaches for the treatment of attention-deficit hyperactivity disorder (ADHD) has been increasingly acknowledged. Parenting programmes (PPs) are recommended for use with preschool children with ADHD. However, low take-up' and high drop-out' rates compromise the effectiveness of such programmes within the community. MethodsThis qualitative study examined the views of 25 parents and 18 practitioners regarding currently available PPs for preschool children with ADHD-type problems in the UK. Semi-structured interviews were undertaken to identify both barriers and facilitators associated with programme access, programme effectiveness, and continued engagement. Results and conclusionsMany of the themes mirrored previous accounts relating to generic PPs for disruptive behaviour problems. There were also a number of ADHD-specific themes. Enhancing parental motivation to change parenting practice and providing an intervention that addresses the parents' own needs (e.g. in relation to self-confidence, depression or parental ADHD), in addition to those of the child, were considered of particular importance. Comparisons between the views of parents and practitioners highlighted a need to increase awareness of parental psychological barriers among practitioners and for better programme advertising generally. Clinical implications and specific recommendations drawn from these findings are discussed and presented