Transport, atom blockade and output coupling in a Tonks-Girardeau gas

Recent experiments have demonstrated how quantum-mechanical impurities can be created within strongly correlated quantum gases and used to probe the coherence properties of these systems [S. Palzer, C. Zipkes, C. Sias, and M. K\"ohl, Phys. Rev. Lett. 103, 150601 (2009).]. Here we present a phenomenological model to simulate such an output coupler for a Tonks-Girardeau gas that shows qualitative agreement with the experimental results for atom transport and output coupling. Our model allows us to explore nonequilibrium transport phenomena in ultracold quantum gases and leads us to predict a regime of atom blockade, where the impurity component becomes localized in the parent cloud despite the presence of gravity. We show that this provides a stable mixed-species quantum gas in the strongly correlated limit

Postbuckling behaviour of beams with discrete nonlinear restraints

A beam with nonlinearly ‐ elastic lateral restraints attached at discrete points along its span is investigated via analytical and numerical methods. Previous results for the critical moment and the deflected shape based on an eigenvalue analysis of a similar beam with linearly ‐ elastic restraints are discussed, along with a validation of these results against an equivalent finite element model and results from numerical continuation. A beam with nonlinearly ‐ elastic restraints is then analysed with treatments for both quadratic and cubic restraint force–displacement relationships being provided. After formulation of the potential energy functionals, the governing differential equations of the system are derived via the calculus of variations and appropriate boundary conditions are applied. The equations are then solved using the numerical continuation software AUTO ‐ 07p for a standard I ‐ section beam. The variation in elastic critical buckling moment with the linear component of the restraint stiffness is tracked via a two ‐ parameter numerical continuation, allowing determination of the stiffness values at which the critical buckling modes changes qualitatively. Using these stiffness values, subsequent analyses are conducted to examine the influence of the nonlinear component of the restraint stiffness, from which post ‐ buckling equilibrium paths and deformation modes are extracted. The results of these analyses are then compared with an equivalent Rayleigh–Ritz formulation whereby the displacement components are represented by Fourier series. Equilibrium equations are derived by minimizing the potential energy functional with respect to the amplitudes of the constituent harmonics of the Fourier series. The amplitudes are solved for in the post ‐ buckling range by AUTO ‐ O7p and equilibrium paths are produced and compared to the equivalent solutions of the differential equations, with good agreement observed

Gate-tunable bandgap in bilayer graphene

The tight-binding model of bilayer graphene is used to find the gap between the conduction and valence bands, as a function of both the gate voltage and as the doping by donors or acceptors. The total Hartree energy is minimized and the equation for the gap is obtained. This equation for the ratio of the gap to the chemical potential is determined only by the screening constant. Thus the gap is strictly proportional to the gate voltage or the carrier concentration in the absence of donors or acceptors. In the opposite case, where the donors or acceptors are present, the gap demonstrates the asymmetrical behavior on the electron and hole sides of the gate bias. A comparison with experimental data obtained by Kuzmenko et al demonstrates the good agreement.Comment: 6 pages, 5 figure

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

Strategies for the Parallel Training of Simple Recurrent Neural Networks

Two concurrent implementations of the method of conjugate gradients for training Elman networks are discussed. The parallelism is obtained in the computation of the error gradient and the method is therefore applicable to any gradient descent training technique for this form of network. The experimental results were obtained on a Sun Sparc Center 2000 multiprocessor. The Sparc 2000 is a shared memory machine well suited to coarse-grained distributed computations, but the concurrency could be extended to other architectures as well

Doppler cooling of gallium atoms: 2. Simulation in complex multilevel systems

This paper derives a general procedure for the numerical solution of the Lindblad equations that govern the coherences arising from multicoloured light interacting with a multilevel system. A systematic approach to finding the conservative and dissipative terms is derived and applied to the laser cooling of gallium. An improved numerical method is developed to solve the time-dependent master equation and results are presented for transient cooling processes. The method is significantly more robust, efficient and accurate than the standard method and can be applied to a broad range of atomic and molecular systems. Radiation pressure forces and the formation of dynamic dark-states are studied in the gallium isotope 66Ga.Comment: 15 pages, 8 figure

Efficient Processing Node Proximity via Random Walk with Restart

Graph is a useful tool to model complicated data structures. One important task in graph analysis is assessing node proximity based on graph topology. Recently, Random Walk with Restart (RWR) tends to pop up as a promising measure of node proximity, due to its proliferative applications in e.g. recommender systems, and image segmentation. However, the best-known algorithm for computing RWR resorts to a large LU matrix factorization on an entire graph, which is cost-inhibitive. In this paper, we propose hybrid techniques to efficiently compute RWR. First, a novel divide-and-conquer paradigm is designed, aiming to convert the large LU decomposition into small triangular matrix operations recursively on several partitioned subgraphs. Then, on every subgraph, a “sparse accelerator” is devised to further reduce the time of RWR without any sacrifice in accuracy. Our experimental results on real and synthetic datasets show that our approach outperforms the baseline algorithms by at least one constant factor without loss of exactness

A glimpse into the differential topology and geometry of optimal transport

This note exposes the differential topology and geometry underlying some of the basic phenomena of optimal transportation. It surveys basic questions concerning Monge maps and Kantorovich measures: existence and regularity of the former, uniqueness of the latter, and estimates for the dimension of its support, as well as the associated linear programming duality. It shows the answers to these questions concern the differential geometry and topology of the chosen transportation cost. It also establishes new connections --- some heuristic and others rigorous --- based on the properties of the cross-difference of this cost, and its Taylor expansion at the diagonal.Comment: 27 page