de Hans Raedt

Integral-geometry morphological image analysis

Abstract This paper reviews a general method to characterize the morphology of two- and three-dimensional patterns in terms of geometrical and topological descriptors. Based on concepts of integral geometry, it involves the calculation of the Minkowski functionals of black-and-white images representing the patterns. The result of this approach is an objective, numerical characterization of a given pattern. We briefly review the basic elements of morphological image processing, a technique to transform images to patterns that are amenable to further morphological image analysis. The image processing technique is applied to electron microscope images of nano-ceramic particles and metal-oxide precipitates. The emphasis of this review is on the practical aspects of the integral-geometry-based morphological image analysis but we discuss its mathematical foundations as well. Applications to simple lattice structures, triply periodic minimal surfaces, and the Klein bottle serve to illustrate the basic steps of the approach. More advanced applications include random point sets, percolation and complex structures found in block copolymers.

Massively parallel quantum computer simulator

We describe portable software to simulate universal quantum computers on massive parallel computers. We illustrate the use of the simulation software by running various quantum algorithms on different computer architectures, such as a IBM BlueGene/L, a IBM Regatta p690+, a Hitachi SR11000/J1, a Cray X1E, a SGI Altix 3700 and clusters of PCs running Windows XP. We study the performance of the software by simulating quantum computers containing up to 36 qubits, using up to 4096 processors and up to 1 TB of memory. Our results demonstrate that the simulator exhibits nearly ideal scaling as a function of the number of processors and suggest that the simulation software described in this paper may also serve as benchmark for testing high-end parallel computers.

New Unconditionally Stable Algorithms to Solve the Time-Dependent Maxwell Equations

For the recently introduced algorithms to solve the time-dependent Maxwell equations [J. S. Kole, M. T. Figge, and H. De Raedt, Phys. Rev. E 64, 066705 (2001)], we construct a variable grid implementation and an improved spatial discretization implementation that preserve the exceptional property of the algorithms to be unconditionally stable by construction. We find that the performance and accuracy of the corresponding algorithms are significant and illustrate their practical relevance by simulating various physical model systems.

Solving the Maxwell equations by the Chebyshev method: a one-step finite-difference time-domain algorithm

We present a one-step algorithm that solves the Maxwell equations for systems with spatially varying permittivity and permeability by the Chebyshev method. We demonstrate that this algorithm may be orders of magnitude more efficient than current finite-difference time-domain (FDTD) algorithms.

Efficient scheme for numerical simulations of the spin-bath decoherence.

We demonstrate that the Chebyshev expansion method is a very efficient numerical tool for studying spin-bath decoherence of quantum systems. We consider two typical problems arising in studying decoherence of quantum systems consisting of a few coupled spins: (i) determining the pointer states of the system and (ii) determining the temporal decay of quantum oscillations. As our results demonstrate, for determining the pointer states, the Chebyshev-based scheme is at least a factor of 8 faster than existing algorithms based on the Suzuki-Trotter decomposition. For problems of the second type, the Chebyshev-based approach is 3-4 times faster than the Suzuki-Trotter-based schemes. This conclusion holds qualitatively for a wide spectrum of systems, with different spin baths and different Hamiltonians.

Deterministic event-based simulation of quantum phenomena

We propose and analyse simple deterministic algorithms that can be used to construct machines that have primitive learning capabilities. We demonstrate that locally connected networks of these machines can be used to perform blind classification on an event-by-event basis, without storing the information of the individual events. We also demonstrate that properly designed networks of these machines exhibit behavior that is usually only attributed to quantum systems. We present networks that simulate quantum interference on an event-by-event basis. In particular we show that by using simple geometry and the learning capabilities of the machines it is possible to simulate single-photon interference in a Mach–Zehnder interferometer. The interference pattern generated by the network of deterministic learning machines is in perfect agreement with the quantum theoretical result for the single-photon Mach–Zehnder interferometer. To illustrate that networks of these machines are indeed capable of simulating quantum interference we simulate, event-by-event, a setup involving two chained Mach–Zehnder interferometers, and demonstrate that also in this case the simulation results agree with quantum theory.  2005 Elsevier B.V. All rights reserved.

A computer program to simulate Einstein-Podolsky-Rosen-Bohm experiments with photons

Starting from the data gathering and analysis procedures used in Einstein–Podolsky–Rosen–Bohm experiments with photons, we construct a simulation algorithm that satisfies Einstein’s criteria of local causality and realism and generates the same type of data as recorded in these idealized experiments. The simulation data is analyzed according to the experimental procedure to count coincidences, that is by using an expression for the coincidence counts that, besides depending on the settings of the variable polarizers, explicitly depends on the difference of the time tags of the detection signals in both observation stations and on an adjustable time window. We demonstrate that the simulation algorithm produces data that agrees with the two-particle correlation for the singlet state.

Optical conductivity of disordered graphene beyond the Dirac cone approximation

In this paper we systemically study the optical conductivity and density of states of disordered graphene beyond the Dirac cone approximation. The optical conductivity of graphene is computed by using the Kubo formula, within the framework of a full p-band tight-binding model. Different types of noncorrelated and correlated disorder are considered, such as random or Gaussian potentials, random or Gaussian nearest-neighbor hopping parameters, randomly distributed vacancies or their clusters, and randomly adsorbed hydrogen atoms or their clusters. For a large enough concentration of resonant impurities, an additional peak in the optical conductivity is found, associated with transitions between the midgap states and the Van Hove singularities of the main pi band. We further discuss the effect of doping on the spectrum, and find that small amounts of resonant impurities are enough to obtain a background contribution to the conductivity in the infrared part of the spectrum, in agreement with recent experiments.

On the theory of layered high-temperature superconductors

Assuming that charge carriers form a Fermi liquid state, we study a model for layered high-temperature superconductors with unretarded intralayer and interlayer pairing. Guided by band structure calculations and inverse photoemission experiments, we adopt a tight binding band with nearest and next-nearest neighbors hopping within the sheets and weak interlayer hopping. The gap equations are solved numerically, without imposing a cutoff energy, characteristic to phonon mediated superconductivity. On this basis we calculate the gap parameters,Tc, the tunneling conductance, infrared absorption and the coherence length for various band fillings ρ=1/2−x by introducing excess holes of concentrationx. Assuming the interlayer coupling strength to be smaller than the intralayer one, our main results are as follows:Tc is dominated by the intralayer properties, reaching a maximum atx≈0.3, where strong coupling features appear. In the presence of interlayer pairing, the gap becomes anisotropic perpendicular to the layers, and standard BCS-behavior is modified. In particular the BCS-square root singularity in the density of states and in the tunneling conductance is replaced by van Hove singularities characterizing the anisotropic gap. In particular, we investigate the anisotropy of the tunneling conductance for specular and diffuse tunneling for a junction parallel or perpendicular to the layers, infrared absorption, as well as the coherence length, parallel and perpendicular to the layers.

Decoherence by a chaotic many-spin bath

We numerically investigate decoherence of a two-spin system (central system) by a bath of many spins 1/2. By carefully adjusting parameters, the dynamical regime of the bath has been varied from quantum chaos to regular, while all other dynamical characteristics have been kept practically intact. We explicitly demonstrate that for a many-body quantum bath, the onset of quantum chaos leads to significantly faster and stronger decoherence compared to an equivalent non-chaotic bath. Moreover, the non-diagonal elements of the systems density matrix, the linear entropy, and the fidelity of the central system decay differently for chaotic and non-chaotic baths. Therefore, knowledge of the basic parameters of the bath (strength of the system-bath interaction, and the baths spectral density of states) is not always sufficient, and much finer details of the baths dynamics can strongly affect the decoherence process.