The escape-rate formalism and the thermostating algorithm describe relaxation towards a decaying state with absorbing boundaries and a steady state of periodic systems, respectively. It has been shown that the key features of the transport properties of both approaches, if modeled by low-dimensional dynamical systems, can conveniently be described in the framework of multibaker maps. In the present paper we discuss in detail the steps required to reach a meaningful macroscopic limit. The limit involves a sequence of coarser and coarser descriptions (projections) until one reaches the level of irreversible macroscopic advection–diffusion equations. The influence of boundary conditions is studied in detail. Only a few of the chaos characteristics possess a meaningful macroscopic limit, but none of these is sufficient to determine the entropy production in a general non-equilibrium state.

Using the semiclassical approximation we calculate the quantum fluctuations of the two-dimensional electronic scattering cross-section from three hard disks in a magnetic field. The three-disk billiard is a schematic model for a three-lead mesoscopic (ballistic) junction. As the magnetic field increases the classical trajectories in the three-disk billiard undergo a hyperbolic±non-hyperbolic transition, i.e. a transition from a completely chaotic phase space to a phase space with stable islands. We show that the traces of this transition can be seen in the quantum fluctuations of the cross-section and should therefore influence the resistance fluctuations of ballistic junctions.

We study the rate of irreversible entropy production and the entropy flux generated by low-dimensional dynamical systems modeling transport processes induced by the simultaneous presence of an external field and a density gradient. The key ingredient for understanding entropy balance is the coarse graining of the phase-space density. This mimics the fact that ever refining phase-space structures caused by chaotic dynamics can only be detected by finite resolution. Calculations are carried out for a generalized multibaker map. For the time-reversible dissipative (thermostated) version of the model, results of nonequilibrium thermodynamics are recovered in the large system Limit. Independent of the choice of boundary conditions, we obtain the rate of irreversible entropy production per particle as u(2)/D, where u is the streaming velocity (current per density) and D is the diffusion coefficient.

A multibaker map is generalized in order to mimic the thermostating algorithm of transport models. Elementary calculations yield the irreversible entropy production caused by coarse graining of the phase-space density. For different systems, either in steady states (periodic or flux boundaries) or subjected to absorbing boundaries, the specific irreversible entropy production is shown to be u(2)/D, where u denotes the local streaming velocity (current per density) and D is the diffusion coefficient.

The dynamics of orientationally disordered crystals, such as neopentane C(CH3)4, couple translational and orientational variables in a complex way. From the results of a molecular dynamics simulation of the orientationally disordered phase of neopentane, simple geometrical methods are used to define functions that can be displayed on a two-dimensional surface and yield practical information, and from these are obtained the single-molecule orientation-translation coupling, the coupling between the translation of a molecule and the orientation of one of its neighbours, and the orientation-orientation coupling of two neighbouring molecules. The single-molecule orientation-translation term, although weak, is consistent with experimental results. A distinct orientation-orientation coupling is visible when a C-C bond of one molecule points at a neighbouring molecule, while a bond of that neighbour points away from the former. Isotropy around the connecting vector tends to disqualify pseudospin-type models for neopentane. The most salient feature, however, is the strong two-molecule orientation-translation correlation, which confirms the motion of one molecule when a C-C bond of one of its neighbours points in its direction; up to now this was only inferred from partial experimental data. Predictions are made for the type of information that is likely to be obtained from neutron diffuse scattering.

In open Hamiltonian systems transport is governed by chaotic saddles which are low-dimensional if a single-particle description can be used. We show that in systems where the motion of the particle is biased towards one direction, the chaotic set is never space filling. Its escape rate splits into two parts: a) a term proportional to the square of the bias; b) a term also present in the non-driven case which vanishes in the large system limit. These general results are equivalent to previous ones on thermostatted systems if the systems have identical entropy production.

We investigate the semiclassical scattering amplitude for systems, where the classical dynamics is non-hyperbolic, i.e. where islands of KAM trajectories exist in an otherwise chaotic phase space. With the help of semiclassical calculations for the three-disk billiard in an external magnetic field, in which a hyperbolic–non-hyperbolic transition is observed as a function of the field strength, we show that the "stickiness" of the KAM tori leads to a much slower decrease of the survival probability, as compared with the hyperbolic case. This is reflected by a much narrower shape of the energy correlation function. However, we also find that the algebraic asymptotic decay of the survival probability in the non-hyperbolic case is not important for the quantum fluctuations.

We calculate the generic parameter dependence of the topological entropy at the onset of pruning: for a family of generalized Baker transformations the deviation of the topological entropy from its maximum value grows with a power law on which a self-similar fine structure is superimposed. Interpreting the onset of pruning as a boundary crisis in the regime of transient chaos, we can derive the exponent of the power law. In addition, an algorithm is presented that allows to calculate the fine structure. The results agree excellently with numerical data that are presented for maps describing conservative as well as dissipative systems. It is argued that the results hold for generic Lorenz-like maps.

An optical memory is formally equivalent to a dynamical system represented by an area-preserving 2-dimensional map. The stationary states of the memory correspond to a subset of the orbits in the invariant set of the map. Under variation of the input intensity pruning occurs in the invariant set. Accordingly, the memory is no longer able to store all possible bit strings. It acts as a data filter whose action can be determined by the input intensity.

For a ''realistic'' model of the ODIC phase of neopentane, the single, particle orientational dynamics is analyzed; the data has been obtained previously by a molecular dynamics simulation. The orientational motion of the molecules from one potential well to another is studied by analyzing their orientational trajectories directly and through the temporal self correlation of an appropriate symmetrized rotator function. Self correlation functions of other rotators give information on the librational motion of the molecules at the bottom of the orientational potential wells. The mean orientational potential is shown to better represent this librational motion than the reorientational dynamics. The method for determining which rotator functions have to be used to describe the different types of motion makes use of the symmetry group of the orientational wells.

We study the chaotic scattering of charged particles in an open three-disk billiard subject to a uniform magnetic field. We identify qualitatively distinct behaviors depending on the field strength: hyperbolic, pruned, Kol'mogorov-Arnol'd-Moser torus dominated, and regular phases. The hierarchical structure of the chaotic set and the time delay function is investigated. Our main finding is that with increasing field strength the degree of chaoticity decreases while the complexity of the small scale structures may increase. Possible consequences of our results for the ballistic transport in microjunctions are discussed.

By means of the linear response of the cat map to a constant perturbation, it is illustrated how relaxation to equilibrium occurs in chaotic hamiltonian systems.

The orientational probability distribution function (o.p.d.f.) of neopentane molecules obtained from a MD simulation of its plastic phase is compared with that deduced from a mean-field orientational potential theory. The quantitative agreement is very good at each temperature (135 K, 175 K and 230 K), while this mean-field theory has predicted in other cases even qualitatively incorrect o.p.d.f.'s. We propose that the present success is related to the symmetry of the C(CH3)4 molecule and that of the crystal lattice.

A molecular dynamics simulation of a realistic model of neopentane [C(CH3)4] in its plastic phase has been performed on a sample of 6×6×6 fcc unit cells (i.e., 864 molecules) at 135, 175, and 230 K. The molecules of the simulated sample interact through phenomenological exp-6, atom–atom potentials between all the atoms of nearest neighbor molecules. The orientational probability density function (opdf), the displacement probability density function (dpdf), and its second moment the Debye–Waller factor have been computed. We confirm the very large value and the important thermal variation of the Debye–Waller factor and the strong anisotropy of the opdf deduced from neutron diffraction experiments. The computed opdf is very well reproduced by a mean-field calculation making use only of the microscopic intermolecular potential and of the equilibrium position of the molecular centers of mass, a result in line with the isotropic character of the dpdf, but not valid for other plastic crystals made of molecules with different geometries.

A method to confront computer simulations to real nature is reported. "Experimental" results calculated from the simulation are analyzed through the same model as the actual experiments. The same terms are thus used to describe the simulated and the real sample; they can then be compared, with some reliability, to one another and also to the corresponding quantities obtained directly from the microscopic information provided by the simulation. The method is applied to neutron diffraction experiments performed on orientationally disordered neopentane (C(CD3)4) single crystals, a system for which a realistic molecular dynamics simulation has also been performed. Our method turns out to be a severe test both for the simulation and the models used to interpret the experiments.

Using the data obtained through a molecular dynamics simulation of the plastic phase of neopentane, the various coefficients of the o.p.d.f., (Ω), as expressed with the help of symmetrized rotator functions, are computed up to l = 10. This provides, inter alia, a value for the l = 9 coefficient, a coefficient of the second kind, which is here obtained for the first time. Its small (but nonzero) value, at every temperature, would have made its experimental determination impossible by the methods known so far.

We present the results of a numerical study of the effects of the induced dipole–induced dipole interaction on the line shape of the internal ν1 and ν3 modes of NF3 in the plastic phase. Comparisons are made both with the experiment and with the results of a previous theoretical analysis of the effect.