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    Many-Particle Physics

Text "Many-Particle Physics"	Peter Grassberger, NIC Research Group for Many-Particle Physics
Flow Behaviour of Granular Matter	Tim Scheffler, Dietrich Wolf, Physics Division, University of Duisburg
Thermal Expansion of Beta-Eucryptite	Alexander I. Lichtenstein, Robert. O. Jones, Institute of Solid State Research, Research Centre Jülich
Localized Vibrational State in a Vitreous System	Uwe Müssel, Heiko Rieger, NIC Research Group for Many-Particle Physics
Computer Simulation of Glass Melts	Jürgen Horbach, Walter Kob and Kurt Binder, Institute of Physics, University of Mainz
Interfaces in Plastics	Andreas Werner, Friederike Schmid, Marcus Müller and Kurt Binder, Institute of Physics, University of Mainz
Phase Studies on Lipids	Christoph Stadler, Harald Lange and Friederike Schmid, Institute of Physics, University of Mainz

Text "Many-Particle Physics"

Many-particle physics is traditionally concerned with the question of how to explain the structure and dynamics of condensed matter from its atomic properties. In addition to these purely microscopic problems, recent years have witnessed an increasing interest in "mesoscopic" problems dealing with the interplay of many small but not atomic particles. Examples are flowing sand, the internal dynamics of stellar clusters, or the formation of traffic jams on motorways.On the microscopic scale, at the forefront of present research in material sciences are crystalline substances with very large unit cells, such as high-temperature superconductors or novel ceramics, on the one hand, and non-crystalline substances such as glasses, "soft" (organic) matter, and foams, on the other hand. The boundaries between these studies and polymer research are fluid.

An increasingly important role is played by the behaviour of surfaces and interfaces. Biological membranes are one example, the gliding of rough surfaces over each other with or without lubricants is another. Even the structure of rough surfaces arising, for instance, from fracture is still far from being understood.

Finally, a large problem area is the spontaneous formation of structures. This includes the traffic jams already mentioned above as well as the formation of sand dunes or the origin of oscillations in chemical reactions.

In general, it may be stated that many-particle physics is concerned with a large number of very different problems. This includes problems of direct technological relevance as well as those of more theoretical interest. The methods applied cover a correspondingly wide range. Apart from the fact that most calculations consist in the simulation of random samples (either by Monte Carlo or by molecular dynamics), a large number of different algorithms is used.

It is due to both improved mathematical procedures and faster computers that typical simulations today work with millions of particles, in order to describe the phenomena as realistically as possible. But for very complex problems one is still limited to much smaller sizes, and it is often hardly possible to establish thermal equilibrium even in systems with only a few hundred particles.

Moreover, it always depends on the specific problem whether the calculation has to be quantum mechanical or whether a classical approximation is sufficient. Whereas emphasis was clearly placed on quantum mechanical problems during the decades after the Second World War, a renaissance of problems to be treated classically has been observed in recent decades. Nowadays, both are about equally important. Undoubtedly, this is also due to the fact that everyday phenomena, as paradoxical as this may appear, often need enormous efforts to be modelled realistically, so that their detailed investigation has become feasible only recently.

(Peter Grassberger, NIC Research Group for Many-Particle Physics)

Flow Behaviour of Granular Matter

Granular matter such as cereals, plastic granules, tablets, sand etc. flows differently through a tube than an ordinary liquid. Whereas the flow velocity of water becomes 16 times higher if the tube diameter is enlarged 4 times, sand will only fall 8 times faster. In every collision between two grains, part of the energy is irreversibly converted into heat. This reduces their relative velocity. Scattering by the tube wall, however, changes the grain velocities significantly. Granular flow can be explained by the competition between these elementary processes. The energy loss in collisions leads to the spontaneous clustering of particles. If the tube is filled only slightly, clustering can improve the throughput, in the case of extensive filling it leads to clogging analogous to motorway traffic jams. In the diagram, fast particles are red, and slow particles blue.

(Tim Scheffler, Dietrich Wolf, Physics Division, University of Duisburg)

Thermal Expansion of Beta-Eucryptite

The main constituent of the CERAN cooking tops of the Schott company is the alumino-lithio-silica glass ceramic beta-eucryptite, which has a very small thermal expansion coefficient over a temperature range of around 1000 degrees. For the crystalline form of beta-eucryptite (see figure, oxygen atoms are green, lithium atoms brown, silicon atoms blue, and aluminium atoms red), density functional calculations - which are free of adjustable parameters - show that the thermal expansion coefficients parallel and at right angles to the lithium chains are almost constant over a large temperature range. The coefficient parallel to the chains is negative and twice as large as the positive coefficient normal to the chains, and a polycrystalline sample should have a constant and very small average thermal expansion. Since the atomic movements can also be followed in a precise way, it is possible to understand the reason for this behaviour.

(Alexander I. Lichtenstein, Robert. O. Jones, Institute of Solid State Research, Research Centre Jülich)

Localized Vibrational State in a Vitreous System

The properties of glasses differ substantially from those of ordinary solids. Their atoms are not arranged regularly on a crystal lattice, as in the case of solids, but they are distributed nearly randomly in space. This also changes the vibration properties. On lattices, only those vibrational states occur which extend over the entire solid. In glasses, on the other hand, there are also vibrations which are confined to a small region of the system, so-called localized modes. Such a mode is shown in the picture. The vibration amplitudes of the individual atoms are encoded by their colour: red atoms vibrate with a great amplitude, blue atoms with a small one. The atoms shown in pale colours do not participate in the vibration.

(Uwe Müssel, Heiko Rieger, NIC Research Group for Many-Particle Physics)

Computer Simulation of Glass Melts

The diagram shows the configuration snapshot of a supercooled quartz glass melt (SiO₂). Quartz glass is e.g. the main constituent of materials such as window glass or ceramic hobs. Essential physical properties of glass, such as density or flow behaviour, are determined by the microscopic structure of the material. Computer simulations help to better understand the microscopic structure, since they permit a detailed insight into the structure. The diagram shows a small segment of a simulation box. The green tetrahedrons represent those silicon atoms which are fourfold, i.e. ideally, bonded with the oxygen atoms (small spheres). Miscoordinated silicon atoms are light blue (fivefold bonded) and yellow (triply bonded). The ideally (doubly) bonded oxygen atoms are white, whereas the misbonded ones are blue (singly bonded) and red (triply bonded). (T = 3580 K)

(Jürgen Horbach, Walter Kob and Kurt Binder, Institute of Physics, University of Mainz)

Interfaces in Plastics

Surfaces and interfaces between immiscible liquids have a surface tension or an interface tension. One could therefore imagine that interfaces take up a particularly small area and should therefore be flat. Among all possible states of interfaces, however, the "flat" interface is so improbable (in the language of thermodynamics: its entropy is so small) that it practically does not occur. In general, interfaces are therefore always corrugated, featuring waves of any wavelength. This is a very general phenomenon. The diagram shows a snapshot of an interface between two immiscible macromolecular substances (polymers) as an example of an interface in plastics. The roughness on all length scales can be clearly seen. The waviness of the interface naturally also influences the physical properties of the plastic material.

(Andreas Werner, Friederike Schmid, Marcus Müller and Kurt Binder, Institute of Physics, University of Mainz)

Phase Studies on Lipids

Fatty acid molecules (lipids) consist of a head which likes to surround itself with water and several long tails which repel water. They therefore propagate as a monolayer on a water surface: the tails prevent molecules from dissolving in water and the head penetrates into the water and prevents the formation of droplets (as, for example, in oil). In the water itself, the monolayers combine to form bilayers so that the tails can point inwards and only the heads come into contact with the water. Such bilayers are one of the most important components of cell membranes. Depending on temperature lipid layers take on different states between which phase transitions occur. For example, there are strongly ordered and disordered phases. The pictures show an idealized model of a lipid monolayer in which the lipids are represented by simple chains of spheres. The yellow spheres represent heads and the red spheres belong to the tail. In the upper picture, the layer is present in a disordered phase, in the lower picture in an ordered phase.

(Christoph Stadler, Harald Lange and Friederike Schmid, Institute of Physics, University of Mainz)

Introduction	Super- computing	Astro- physics	Elementary Particles	Many Particles	Polymers	Chemistry	Environment	Other Fields