The brochure of the John von Neumann Institute for Computing is available in English and in German. It can be ordered at the NIC secretariat (nic@fz-juelich.de).

deutsche Broschüre (pdf)   |  English brochure (pdf)

Intro- duction	Scientific Computing	Astro- physics	Elementary Particles	Multi- particles	Polymers	Chemistry	Earth, En- vironment	Other Fields

    Multiparticle Physics

• "Multiparticle Physics"
• Molecular Dynamical Simulation of Silicates
• Rodlike Liquid Crystalline Molecules
• Theory of High-Temperature Superconductivity
• Reactions in Biological Systems
• Quantum Monte Carlo Studies of Correlated Systems
• Microscopic Properties of Gold Surfaces
• Properties of Nanowires

"Multiparticle Physics"

Multiparticle physics is primarily concerned with explaining the macroscopic structure and dynamics of condensed matter from its atomic constituents. In doing so, one either starts from the correct fundamental forces ("ab initio" calculations), or one uses a simplified heuristic ansatz. In many cases the latter is sufficient, especially for critical phenomena but also for many complex systems where a realistic ab initio strategy would not be feasible today. This holds in particular for biological problems, including, for instance, the folding of proteins or of RNA, or the structure and functioning of molecular motors. Heuristic ansatzes for the interaction are, of course, also needed when the "atomic" constituents are indeed mesoscopic or even macroscopic. Examples of the latter which are today treated by means of statistical physics methods are the flow of sand and the development of traffic jams on a highway.

It is obvious that quantum mechanics plays no part in the latter problems. But the same is also true for molecular problems, if one is interested in structural properties and if one uses a coarse-grained description with phenomenological forces. Such problems can be treated by directly integrating Newton's equations of motion ("molecular dynamics") or by means of Monte Carlo methods. Examples are found in the contributions by J. Horbach and G. Germano et al. in this brochure.

In contrast, there are problems like superconductivity where quantum mechanics plays an essential role. This requires a much bigger computational effort, in particular if fermions are involved (which is practically always the case), and if they are strongly correlated (as in high-T_c superconductivity). The contributions by W. Hanke et al., J. Akola et al., C. Lavalle et al., and by W. Schattke belong to this category. They illustrate very clearly the enormous progress made in this field by combining fast and big hardware with efficient algorithms.

There is a last class of problems where it is impossible, on the one hand, to treat the entire system fully quantum mechanically, but where, on the other hand, a purely classical description would not be adequate. Hybrid methods can be used here where some of the degrees of freedom are treated quantum mechanically and the rest classically. An example is provided by the contribution of M. Dreher et al.

The contributions to this brochure illustrate perfectly the wide and interdisciplinary range of problems to which many-body methods have been applied. They also illustrate that the phenomena treated here cannot be understood by bigger computers alone, nor by brute force attacks using existing algorithms. It is only the interplay between fast computers, on the one hand, and innovative efficient algorithms, on the other, which has made the present achievements possible and which will allow the field to continue to grow in the future.

(Peter Grassberger, NIC Research Group "Complex Systems", Jülich)

Molecular Dynamical Simulation of Silicates

Amorphous silica (SiO₂) is the base material for many technological glasses. Every silicon atom sits in the center of a tetrahedron with four oxygen atoms at the corners, whereby the oxygen atoms connect the tetrahedra to each other. This results in a disordered tetrahedral network structure. If one mixes SiO₂ with an alkali oxide such as Li₂O, Na₂O, or K₂O, the Si-O network is partially disrupted due to the alkali ions (Li, Na, K). Interestingly, alkali silicates are ion-conducting materials in which the alkali ions have a much higher mobility than the Si and O atoms. The high mobility of the alkali ions can be understood in terms of the channel structures that they form. This is illustrated in the figures. The pictures show snapshots from molecular dynamics simulations of potassium disilicate [(K₂O)(2 · SiO₂)], lithium disilicate [(Li₂O)(2 · SiO₂)], and a mixture of SiO₂, Li₂O und K₂O [(0.5 · K₂O)(0.5 · Li₂O) (20.5 · SiO₂)] at a temperature T = 1000 K.

The big green and silver spheres that are connected to each other represent the K and Li atoms, respectively. The Si-O network is indicated by small yellow (Si) and red (O) spheres that are connected to each other by covalent bonds shown as rods between Si and O spheres. The snapshots show that Li and K ions form different channel structures, which is due to the fact that the coordination of Li ions with oxygen atoms is smaller and also that the Li-O distance is significantly smaller than the K-O distance. From the snapshot of the mixture of SiO₂ with the two alkali components one can infer that in each case Li and K form their own separate channel structure.

(Jürgen Horbach, Institute of Physics, University of Mainz)

Rodlike Liquid Crystalline Molecules

Rodlike liquid crystalline molecules as found in displays and electronic devices can be modeled with ellipsoids. Here they are colored according to their orientation. The figure on the left shows a sheared multiphase system with over 100,000 molecules, where an isotropic, disordered region (dominated by blue and green) is sandwiched between two nematic, ordered regions (dominated by yellow). The figure on the right shows a detail of the interface where in the upper, nematic part the molecules are clearly aligned preferentially from left to right along the flow direction. This system was simulated with a domain decomposition molecular dynamics program on 128 nodes. Each node processed only a small cube, whose edges were 1/4 of the horizontal edges and 1/8 of the vertical edge of the whole box.

(Guido Germano, Philipps-University of Marburg; Friederike Schmid, University of Bielefeld)

Theory of High-Temperature Superconductivity

High-temperature superconductivity is one of the most fascinating phenomena of modern solid state physics. This fascination is motivated, on the one hand, by the wide range of possible technical innovations connected with high-temperature superconductivity, such as loss-free energy storage, faster computer chips or simply loss-free electricity transport. On the other hand, a consistent theoretical description of high-temperature superconductivity is still not available. However, such an understanding is a necessary condition for the specific further development of high-temperature superconductors. The reason for the difficulty in obtaining a microscopic understanding of this phenomenon, which would allow high-temperature superconductors (HTSC) to be synthesized with enhanced material properties, is an unusually strong entanglement of the many-body wave function. This strong entanglement of about 10²³ electrons within typically a cubic centimeter is the reason why one can observe "quantum mechanical behavior" on a macroscopic level, but it is also responsible for the failure of the standard analytical approach in theoretical solid state physics, where one attempts to describe the interaction between two particles by a small perturbation of the non-interacting system. Obviously, this attempt fails if the interaction plays a major role and substantially affects the physics of the system under consideration. Therefore numerical simulations on supercomputers provide one of the most powerful tools for achieving a detailed understanding of the microscopic physics of high-temperature superconductors.

The upper figure shows a generic temperature versus chemical potential phase diagram of the cuprate HTSC. The temperature is plotted against the chemical potential µ. In real HTSC crystals, the chemical potential µ can be varied by various hole doping concentrations.

The lower figure depicts the result of a simulation of an effective model for the high- temperature superconductors. The plot shows the phase boundaries close to the bicritical point, where the antiferromagnetic and the superconducting phases meet. The results obtained using high-performance computing offer sufficient precision to determine even the critical exponents of the phase transition lines. "SC" marks the superconducting phase.

(Werner Hanke, Martin Jöstingmeier, Theoretical Physics I, University of Würzburg)

Reactions in Biological Systems

The density functional formalism provides a method for calculating the energy of molecular systems as a function of the atomic positions. In principle, it then provides a means of determining the heats and paths of reaction. There have been many such applications, and the first such studies of biological systems are under way. An example is provided by the reaction of water with adenosine 5'-triphosphate (ATP). ATP is the most important energy carrier in cellular metabolism, and each human being produces roughly its own weight of ATP every day. We show a model system for which we have studied two possible reactions (carbon atoms gray, oxygen red, hydrogen white, nitrogen blue, phosphorus orange). The magnesium atoms (green) act as catalysts. We are extending this work to the case of hydrolysis of ATP in the presence of protein residues.

(Jaakko Akola, Robert O. Jones, Institute of Solid State Research, Research Center Jülich)

Quantum Monte Carlo Studies of Correlated Systems

The numerical simulation of quantum many-body systems differs essentially from simulations of classical systems due to Heisenberg's uncertainty principle in quantum mechanics. A first step before performing simulations is the mathematically exact mapping of the original quantum mechanical system into an equivalent classical one.

This is achieved by so-called world-line algorithms, in which the partition function of the system in d dimensions is mapped onto a d+1 dimensional system, where the extra dimension is denoted "imaginary time". The evolution of the system in this "space-time" is described by world-lines that resemble polymers stretched in the extra dimension (in the figure: world-lines on a chain with periodic boundary conditions; world-lines that cross the boundary are marked in red). Earlier versions restricted to local moves have been superseded by new loop algorithms, with global moves that are not restricted to a given charge or spin sector.

The figure corresponds to a new quantum Monte Carlo algorithm where the spin degrees of freedom are treated with a loop algorithm that allows for global updates of spin configurations whereas for each spin configuration, the evolution of the charge degrees of freedom is calculated exactly by means of a determinantal algorithm. Hence, we designate the whole a hybrid-loop algorithm. The interplay of quantum mechanical spins with charge carriers dealt with here is at the heart of correlated electronic systems like high-temperature superconductors.

(Catia Lavalle, Alejandro Muramatsu, Institute for Theoretical Physics III, University of Stuttgart)

Microscopic Properties of Gold Surfaces

The brilliant shine of a gold surface hides unexpected details: The microscopic appearance of a surface might not remain a static equilibrium structure but may evolve in the course of time through various fascinating patterns which, of course, also play an important role in the study of epitaxial growth. The energy landscape displayed on the left-hand side refers to the energy of an additional gold atom adsorbed on the gold (001) surface, which itself is decorated by embedded stripes of hexagonal structure in contrast to the quadratic symmetry of the ideal unreconstructed surface (see the schematic drawing on the right). The rectangle refers to the support of the displayed energy. The quadratic surface structure of the cube face of the crystal is not stable and thus such strongly fluctuating domains are observed in time-dependent scanning tunneling microscopy. For example, the stripe seems to move as a whole along its longitudinal axis, which would require an anomalously high mass transport. Instead, the total energy obtained from fully quantum mechanical calculations shows a preferred valley for a path along the stripe where a single Au atom can propagate from one end to the other, thus simulating a motion of the whole stripe.

(Claudia Ramírez, Wolfgang Schattke, Institute of Theoretical Physics and Astrophysics, University of Kiel)

Properties of Nanowires

When electric wires are miniaturized down to the atomic level, interesting quantization effects appear, in particular the conductance is quantized in multiples of the conductance quantum G₀= 2e²/h. General research topics are which atomic properties determine the current, and what atoms have to be grouped in which way in order to design wires with well-defined properties. Of particular interest is the study of single atom contacts, for example in atomic gold wires.

Molecular dynamics simulations at T=4.2 K of interactive Au nanocontacts under tensile stressing resulted in single-atom contacts as well as atomic chain structures according to the "effective medium theory" (EMT). The current through a nanocontact was computed (broken down into separate channels) as well as conductance curves. Pronounced conductance plateaus appear with certain structural rearrangements, but in general the conductance curve agrees well with experimental data. The current through the contact obviously depends on the atom species and the atomic configuration at the smallest constriction. Interestingly, however, the atomic configuration in the vicinity of the constriction plays a role as well.

(Markus Dreher, Peter Nielaba, Department of Physics, University of Konstanz; Jan Heurich, Carlos Cuevas, Department of Physics, University of Karlsruhe)

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