Behaviour of the energy gap in a model of Josephson coupled Bose-Einstein condensates

In this work we investigate the energy gap between the ground state and the first excited state in a model of two single-mode Bose-Einstein condensates coupled via Josephson tunnelling. The ene:rgy gap is never zero when the tunnelling interaction is non-zero. The gap exhibits no local minimum below a threshold coupling which separates a delocalized phase from a self-trapping phase that occurs in the absence of the external potential. Above this threshold point one minimum occurs close to the Josephson regime, and a set of minima and maxima appear in the Fock regime. Expressions for the position of these minima and maxima are obtained. The connection between these minima and maxima and the dynamics for the expectation value of the relative number of particles is analysed in detail. We find that the dynamics of the system changes as the coupling crosses these points.

Anomalous Excitation Spectra of Frustrated Quantum Antiferromagnets

We use series expansions to study the excitation spectra of spin-1/2 antiferromagnets on anisotropic triangular lattices. For the isotropic triangular lattice model (TLM), the high-energy spectra show several anomalous features that differ strongly from linear spin-wave theory (LSWT). Even in the Neel phase, the deviations from LSWT increase sharply with frustration, leading to rotonlike minima at special wave vectors. We argue that these results can be interpreted naturally in a spinon language and provide an explanation for the previously observed anomalous finite-temperature properties of the TLM. In the coupled-chains limit, quantum renormalizations strongly enhance the one-dimensionality of the spectra, in agreement with experiments on Cs2CuCl4.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.

Excitation spectra of the spin-1/2 triangular-lattice Heisenberg antiferromagnet

We use series expansion methods to calculate the dispersion relation of the one-magnon excitations for the spin-(1)/(2) triangular-lattice nearest-neighbor Heisenberg antiferromagnet above a three-sublattice ordered ground state. Several striking features are observed compared to the classical (large-S) spin-wave spectra. Whereas, at low energies the dispersion is only weakly renormalized by quantum fluctuations, significant anomalies are observed at high energies. In particular, we find rotonlike minima at special wave vectors and strong downward renormalization in large parts of the Brillouin zone, leading to very flat or dispersionless modes. We present detailed comparison of our calculated excitation energies in the Brillouin zone with the spin-wave dispersion to order 1/S calculated recently by Starykh, Chubukov, and Abanov [Phys. Rev. B74, 180403(R) (2006)]. We find many common features but also some quantitative and qualitative differences. We show that at temperatures as low as 0.1J the thermally excited rotons make a significant contribution to the entropy. Consequently, unlike for the square lattice model, a nonlinear sigma model description of the finite-temperature properties is only applicable at temperatures < 0.1J. Finally, we review recent NMR measurements on the organic compound kappa-(BEDT-TTF)(2)Cu-2(CN)(3). We argue that these are inconsistent with long-range order and a description of the low-energy excitations in terms of interacting magnons, and that therefore a Heisenberg model with only nearest-neighbor exchange does not offer an adequate description of this material.

Description and training of neural network dynamics

Attractor properties of a popular discrete-time neural network model are illustrated through numerical simulations. The most complex dynamics is found to occur within particular ranges of parameters controlling the symmetry and magnitude of the weight matrix. A small network model is observed to produce fixed points, limit cycles, mode-locking, the Ruelle-Takens route to chaos, and the period-doubling route to chaos. Training algorithms for tuning this dynamical behaviour are discussed. Training can be an easy or difficult task, depending whether the problem requires the use of temporal information distributed over long time intervals. Such problems require training algorithms which can handle hidden nodes. The most prominent of these algorithms, back propagation through time, solves the temporal credit assignment problem in a way which can work only if the relevant information is distributed locally in time. The Moving Targets algorithm works for the more general case, but is computationally intensive, and prone to local minima.

The dynamics of a genetic algorithm under stabilizing selection

A formalism recently introduced by Prugel-Bennett and Shapiro uses the methods of statistical mechanics to model the dynamics of genetic algorithms. To be of more general interest than the test cases they consider. In this paper, the technique is applied to the subset sum problem, which is a combinatorial optimization problem with a strongly non-linear energy (fitness) function and many local minima under single spin flip dynamics. It is a problem which exhibits an interesting dynamics, reminiscent of stabilizing selection in population biology. The dynamics are solved under certain simplifying assumptions and are reduced to a set of difference equations for a small number of relevant quantities. The quantities used are the population's cumulants, which describe its shape, and the mean correlation within the population, which measures the microscopic similarity of population members. Including the mean correlation allows a better description of the population than the cumulants alone would provide and represents a new and important extension of the technique. The formalism includes finite population effects and describes problems of realistic size. The theory is shown to agree closely to simulations of a real genetic algorithm and the mean best energy is accurately predicted.

Using generative models for handwritten digit recognition

We describe a method of recognizing handwritten digits by fitting generative models that are built from deformable B-splines with Gaussian ``ink generators'' spaced along the length of the spline. The splines are adjusted using a novel elastic matching procedure based on the Expectation Maximization (EM) algorithm that maximizes the likelihood of the model generating the data. This approach has many advantages. (1) After identifying the model most likely to have generated the data, the system not only produces a classification of the digit but also a rich description of the instantiation parameters which can yield information such as the writing style. (2) During the process of explaining the image, generative models can perform recognition driven segmentation. (3) The method involves a relatively small number of parameters and hence training is relatively easy and fast. (4) Unlike many other recognition schemes it does not rely on some form of pre-normalization of input images, but can handle arbitrary scalings, translations and a limited degree of image rotation. We have demonstrated our method of fitting models to images does not get trapped in poor local minima. The main disadvantage of the method is it requires much more computation than more standard OCR techniques.