Experimental study of the quantum driven pendulum and its classical analog in atom optics

We present experimental results for the dynamics of cold atoms in a far detuned amplitude-modulated optical standing wave. Phase-space resonances constitute distinct peaks in the atomic momentum distribution containing up to 65% of all atoms resulting from a mixed quantum chaotic phase space. We characterize the atomic behavior in classical and quantum regimes and we present the applicable quantum and classical theory, which we have developed and refined. We show experimental proof that the size and the position of the resonances in phase space can be controlled by varying several parameters, such as the modulation frequency, the scaled well depth, the modulation amplitude, and the scaled Planck’s constant of the system. We have found a surprising stability against amplitude noise. We present methods to accurately control the momentum of an ensemble of atoms using these phase-space resonances which could be used for efficient phase-space state preparation.

Entanglement in a simple quantum phase transition

What entanglement is present in naturally occurring physical systems at thermal equilibrium? Most such systems are intractable and it is desirable to study simple but realistic systems that can be solved. An example of such a system is the one-dimensional infinite-lattice anisotropic XY model. This model is exactly solvable using the Jordan-Wigner transform, and it is possible to calculate the two-site reduced density matrix for all pairs of sites. Using the two-site density matrix, the entanglement of formation between any two sites is calculated for all parameter values and temperatures. We also study the entanglement in the transverse Ising model, a special case of the XY model, which exhibits a quantum phase transition. It is found that the next-nearest-neighbor entanglement (though not the nearest-neighbor entanglement) is a maximum at the critical point. Furthermore, we show that the critical point in the transverse Ising model corresponds to a transition in the behavior of the entanglement between a single site and the remainder of the lattice.

A scheme for efficient quantum computation wtih linear optics

Quantum computers promise to increase greatly the efficiency of solving problems such as factoring large integers, combinatorial optimization and quantum physics simulation. One of the greatest challenges now is to implement the basic quantum-computational elements in a physical system and to demonstrate that they can be reliably and scalably controlled. One of the earliest proposals for quantum computation is based on implementing a quantum bit with two optical modes containing one photon. The proposal is appealing because of the ease with which photon interference can be observed. Until now, it suffered from the requirement for non-linear couplings between optical modes containing few photons. Here we show that efficient quantum computation is possible using only beam splitters, phase shifters, single photon sources and photo-detectors. Our methods exploit feedback from photo-detectors and are robust against errors from photon loss and detector inefficiency. The basic elements are accessible to experimental investigation with current technology.

Achromatic optical phase shifter/modulator

We propose and demonstrate, theoretically and experimentally, a novel achromatic optical phase shifter modulator based on a frequency-domain optical delay line configured to maintain zero group delay as variable phase delay is generated by means of tilting a mirror. Compared with previously reported phase shifter modulators, e.g., based on the Pancharatnam (geometric) phase, our device is high speed and polarization insensitive and produces a large, bounded phase delay that, uniquely, is one-to-one mapped to a measurable parameter, the tilt angle.

Calculation of line integrals in boundary integral methods

We propose quadrature rules for the approximation of line integrals possessing logarithmic singularities and show their convergence. In some instances a superconvergence rate is demonstrated.

Hamiltonian mappings and circle packing phase spaces.

We introduce three area preserving maps with phase space structures which resemble circle packings. Each mapping is derived from a kicked Hamiltonian system with one of the three different phase space geometries (planar, hyperbolic or spherical) and exhibits an infinite number of coexisting stable periodic orbits which appear to ‘pack’ the phase space with circular resonances.

A two-phase strategy for detecting recombination in nucleotide sequences

Genetic recombination can produce heterogeneous phylogenetic histories within a set of homologous genes. Delineating recombination events is important in the study of molecular evolution, as inference of such events provides a clearer picture of the phylogenetic relationships among different gene sequences or genomes. Nevertheless, detecting recombination events can be a daunting task, as the performance of different recombination-detecting approaches can vary, depending on evolutionary events that take place after recombination. We previously evaluated the effects of post-recombination events on the prediction accuracy of recombination-detecting approaches using simulated nucleotide sequence data. The main conclusion, supported by other studies, is that one should not depend on a single method when searching for recombination events. In this paper, we introduce a two-phase strategy, applying three statistical measures to detect the occurrence of recombination events, and a Bayesian phylogenetic approach to delineate breakpoints of such events in nucleotide sequences. We evaluate the performance of these approaches using simulated data, and demonstrate the applicability of this strategy to empirical data. The two-phase strategy proves to be time-efficient when applied to large datasets, and yields high-confidence results.

Review of recent results on excursion set models

Many images consist of two or more 'phases', where a phase is a collection of homogeneous zones. For example, the phases may represent the presence of different sulphides in an ore sample. Frequently, these phases exhibit very little structure, though all connected components of a given phase may be similar in some sense. As a consequence, random set models are commonly used to model such images. The Boolean model and models derived from the Boolean model are often chosen. An alternative approach to modelling such images is to use the excursion sets of random fields to model each phase. In this paper, the properties of excursion sets will be firstly discussed in terms of modelling binary images. Ways of extending these models to multi-phase images will then be explored. A desirable feature of any model is to be able to fit it to data reasonably well. Different methods for fitting random set models based on excursion sets will be presented and some of the difficulties with these methods will be discussed.

A framework for electricity price spike analysis with advanced data mining methods

There are many techniques for electricity market price forecasting. However, most of them are designed for expected price analysis rather than price spike forecasting. An effective method of predicting the occurrence of spikes has not yet been observed in the literature so far. In this paper, a data mining based approach is presented to give a reliable forecast of the occurrence of price spikes. Combined with the spike value prediction techniques developed by the same authors, the proposed approach aims at providing a comprehensive tool for price spike forecasting. In this paper, feature selection techniques are firstly described to identify the attributes relevant to the occurrence of spikes. A simple introduction to the classification techniques is given for completeness. Two algorithms: support vector machine and probability classifier are chosen to be the spike occurrence predictors and are discussed in details. Realistic market data are used to test the proposed model with promising results.

A demonstration of artificial dissipation effects in some finite volume solution methods for the Navier-Stokes equations

The artificial dissipation effects in some solutions obtained with a Navier-Stokes flow solver are demonstrated. The solvers were used to calculate the flow of an artificially dissipative fluid, which is a fluid having dissipative properties which arise entirely from the solution method itself. This was done by setting the viscosity and heat conduction coefficients in the Navier-Stokes solvers to zero everywhere inside the flow, while at the same time applying the usual no-slip and thermal conducting boundary conditions at solid boundaries. An artificially dissipative flow solution is found where the dissipation depends entirely on the solver itself. If the difference between the solutions obtained with the viscosity and thermal conductivity set to zero and their correct values is small, it is clear that the artificial dissipation is dominating and the solutions are unreliable.