Percolation model for a selective response of the resistance of composite semiconducting np systems with respect to reducing gases.

It is shown that a two-component percolation model on a simple cubic lattice can explain an experimentally observed behavior [Savage et al., Sens. Actuators B 79, 17 (2001); Sens. Actuators B 72, 239 (2001).], namely, that a network built up by a mixture of sintered nanocrystalline semiconducting n and p grains can exhibit selective behavior, i.e., respond with a resistance increase when exposed to a reducing gas A and with a resistance decrease in response to another reducing gas B. To this end, a simple model is developed, where the n and p grains are simulated by overlapping spheres, based on realistic assumptions about the gas reactions on the grain surfaces. The resistance is calculated by random walk simulations with nn, pp, and np bonds between the grains, and the results are found in very good agreement with the experiments. Contrary to former assumptions, the np bonds are crucial to obtain this accordance.

Relaxation in ordered systems of ultrafine magnetic particles: effect of the exchange interaction.

We perform Monte Carlo simulations to study the relaxation of single-domain nanoparticles that are located on a simple cubic lattice with anisotropy axes pointing in the z-direction, under the combined influence of anisotropy energy, dipolar interaction and ferromagnetic interaction of strength J. We compare the results of classical Heisenberg systems with three-dimensional magnetic moments [Formula: see text] to those of Ising systems and find that Heisenberg systems show a much richer and more complex dynamical behavior. In contrast to Heisenberg systems, Ising systems need large activation energies to turn a spin and also possess a smaller configuration space for the orientation of the [Formula: see text]. Accordingly, Heisenberg systems possess a whole landscape of different states with very close-lying energies, while Ising systems tend to get frozen in one random state far away from the ground state. For Heisenberg systems, we identify two phase transitions: (i) at intermediate J between domain and layered states and (ii) at larger J between layered and ferromagnetic states. Between these two transitions, the layered states change their appearance and develop a sub-structure, where the orientation of the [Formula: see text] in each layer depends on J, so that for each value of J, a new ground state appears.

Exact calculation of the tortuosity in disordered linear pores in the Knudsen regime.

The squared reciprocal tortuosity kappa-2=D/D0 for linear diffusion on lattices and in pores in the Knudsen regime is calculated analytically for a large variety of disordered systems. Here, D0 and D are the self-diffusion coefficients of the smooth and the corresponding disordered system, respectively. To this end, a building-block principle is developed that composes the systems into substructures without cross correlations between them. It is shown how the solutions of the different building blocks can be combined to gain D/D0 for pores of high complexity from the geometrical properties of the systems, i.e., from the volumes of the different substructures. As a test, numerical simulations are performed that agree perfectly with the theory.

Application of the trace formula in pseudointegrable systems.

We apply periodic-orbit theory to calculate the integrated density of states N(k) of the quantum mechanical eigenvalues from the periodic orbits of pseudointegrable polygon and barrier billiards. We show that the results agree so well with the density of states obtained from numerical solutions of the Schrödinger equation that about the first 100 eigenvalues can be obtained directly from the periodic-orbit calculations with good accuracy.

Lambert diffusion in porous media in the Knudsen regime: equivalence of self-diffusion and transport diffusion.

We study molecular diffusion in nanopores with different types of roughness under the exclusion of mutual molecular collisions, i.e., in the so-called Knudsen regime. We show that the diffusion problem can be mapped onto Levy walks and discuss the roughness dependence of the diffusion coefficients D(s) and D(t) of self- and transport diffusion, respectively. While diffusion is normal in d=3, diffusion is anomalous in d=2 with D(s) approximately ln t and D(t) approximately ln L, where t and L are time and system size, respectively. Both diffusion coefficients decrease significantly when the roughness is enhanced, in remarkable disagreement with earlier findings.

Periodic orbit theory and spectral rigidity in pseudointegrable systems.

We calculate numerically the periodic orbits of pseudointegrable systems of low genus numbers g that arise from rectangular systems with one or two salient corners. From the periodic orbits, we calculate the spectral rigidity Delta3(L) using semiclassical quantum mechanics with L reaching up to quite large values. We find that the diagonal approximation is applicable when averaging over a suitable energy interval. Comparing systems of various shapes, we find that our results agree well with Delta3 calculated directly from the eigenvalues by spectral statistics. Therefore, additional terms such as, e.g., diffraction terms seem to be small in the case of the systems investigated in this work. By reducing the size of the corners, the spectral statistics of our pseudointegrable systems approaches that of an integrable system, whereas very large differences between integrable and pseudointegrable systems occur when the salient corners are large. Both types of behavior can be well understood by the properties of the periodic orbits in the system.

Level statistics and eigenfunctions of pseudointegrable systems: dependence on energy and genus number.

We study the level statistics (second half moment I0 and rigidity Delta(3)) and the eigenfunctions of pseudointegrable systems with rough boundaries of different genus numbers g. We find that the levels form energy intervals with a characteristic behavior of the level statistics and the eigenfunctions in each interval. At low enough energies, the boundary roughness is not resolved and accordingly the eigenfunctions are quite regular functions and the level statistics shows Poisson-like behavior. At higher energies, the level statistics of most systems moves from Poisson-like toward Wigner-like behavior with increasing g. On investigating the wave functions, we find many chaotic functions that can be described as a random superposition of regular wave functions. The amplitude distribution P(psi) of these chaotic functions was found to be Gaussian with the typical value of the localization volume V(loc) approximately equal 0.33. For systems with periodic boundaries we find several additional energy regimes, where I0 is relatively close to the Poisson limit. In these regimes, the eigenfunctions are either regular or localized functions, where P(psi) is close to the distribution of a sine or cosine function in the first case and strongly peaked in the second case. An interesting intermediate case between chaotic and localized eigenfunctions also appears.