Steady-state conduction in self-similar billiards

The self-similar Lorentz billiard channel is a spatially extended deterministic dynamical system which consists of an infinite one-dimensional sequence of cells whose sizes increase monotonically according to their indices. This special geometry induces a nonequilibrium stationary state with particles flowing steadily from the small to the large scales. The corresponding invariant measure has fractal properties reflected by the phase-space contraction rate of the dynamics restricted to a single cell with appropriate boundary conditions. In the near-equilibrium limit, we find numerical agreement between this quantity and the entropy production rate as specified by thermodynamics

Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom

Hundred twenty years after the fundamental work of Poincar\'e, the statistics of Poincar\'e recurrences in Hamiltonian systems with a few degrees of freedom is studied by numerical simulations. The obtained results show that in a regime, where the measure of stability islands is significant, the decay of recurrences is characterized by a power law at asymptotically large times. The exponent of this decay is found to be $\beta \approx 1.3$. This value is smaller compared to the average exponent $\beta \approx 1.5$ found previously for two-dimensional symplectic maps with divided phase space. On the basis of previous and present results a conjecture is put forward that, in a generic case with a finite measure of stability islands, the Poncar\'e exponent has a universal average value $\beta \approx 1.3$ being independent of number of degrees of freedom and chaos parameter. The detailed mechanisms of this slow algebraic decay are still to be determined.Comment: revtex 4 pages, 4 figs; Refs. and discussion adde

Modelling quasicrystals at positive temperature

We consider a two-dimensional lattice model of equilibrium statistical mechanics, using nearest neighbor interactions based on the matching conditions for an aperiodic set of 16 Wang tiles. This model has uncountably many ground state configurations, all of which are nonperiodic. The question addressed in this paper is whether nonperiodicity persists at low but positive temperature. We present arguments, mostly numerical, that this is indeed the case. In particular, we define an appropriate order parameter, prove that it is identically zero at high temperatures, and show by Monte Carlo simulation that it is nonzero at low temperatures

Linear dynamical entropy and free-independence for quantized maps on the torus

We study the relations between the averaged linear entropy production in periodically measured quantum systems and ergodic properties of their classical counterparts. Quantized linear automorphisms of the torus, both classically chaotic and regular ones, are used as examples. Numerical calculations show different entropy production regimes depending on the relation between the Kolmogorov-Sinai entropy and the measurement entropy. The hypothesis of free independence relations between the dynamics and measurement proposed to explain the initial constant and maximal entropy production is tested numerically for those models.Comment: 7 pages, 5 figure

Deterministic spin models with a glassy phase transition

We consider the infinite-range deterministic spin models with Hamiltonian $H=\sum_{i,j=1}^N J_{i,j}\sigma_i\sigma_j$, where $J$ is the quantization of a chaotic map of the torus. The mean field (TAP) equations are derived by summing the high temperature expansion. They predict a glassy phase transition at the critical temperature $T\sim 0.8$.Comment: 8 pages, no figures, RevTex forma

Quantum ergodicity for Pauli Hamiltonians with spin 1/2

Quantum ergodicity, which expresses the semiclassical convergence of almost all expectation values of observables in eigenstates of the quantum Hamiltonian to the corresponding classical microcanonical average, is proven for non-relativistic quantum particles with spin 1/2. It is shown that quantum ergodicity holds, if a suitable combination of the classical translational dynamics and the spin dynamics along the trajectories of the translational motion is ergodic.Comment: 20 pages, no figure

Recurrence and algorithmic information

In this paper we initiate a somewhat detailed investigation of the relationships between quantitative recurrence indicators and algorithmic complexity of orbits in weakly chaotic dynamical systems. We mainly focus on examples.Comment: 26 pages, no figure

From the Cover: Volatile Anesthetics Transiently Disrupt Neuronal Development in Neonatal Rats

Volatile anesthetics can cause neuronal and glial toxicity in the developing mammalian brain, as well as long-term defects in learning and memory. The goals of this study were to compare anesthetics using a clinically relevant exposure paradigm, and to assess the anesthetic effects on hippocampal development and behavior. Our hypothesis was that volatile anesthetics disrupt hippocampal development, causing neurobehavioral defects later in life. Bromodeoxyuridine (BrdU) was administered to rats on postnatal day (P)1, and the rats were exposed to volatile anesthetics (isoflurane, sevoflurane, or desflurane) for 2 h on P2. On days P7 and P14, the BrdU-labeled cells were quantified in the hippocampal dentate gyrus using immunohistochemical assays and fluorescent microscopy. Caspase-3 positive cells were quantified on P2 to evaluate apoptosis. The remaining animals underwent behavioral testing at ages 6 weeks and 6 months, using the Morris Water Maze. Significantly fewer BrdU-positive cells were detected in the hippocampal dentate gyrus in both isoflurane and desflurane-treated animals compared with controls at P7, but there were no changes in cell numbers after sevoflurane exposure. Cell counts for all three anesthetics compared with controls were equivalent at P14. Isoflurane or desflurane exposure yielded slight differences in the behavioral tests at 6 weeks, but no differences at 6 months post-exposure. We conclude that a single 2-h exposure at P2 to either isoflurane or desflurane causes a transient disruption of hippocampal neuronal development with no significant detectable long-term effects on learning and memory, whereas the same exposure to sevoflurane has no effects

Metric Features of a Dipolar Model

The lattice spin model, with nearest neighbor ferromagnetic exchange and long range dipolar interaction, is studied by the method of time series for observables based on cluster configurations and associated partitions, such as Shannon entropy, Hamming and Rohlin distances. Previous results based on the two peaks shape of the specific heat, suggested the existence of two possible transitions. By the analysis of the Shannon entropy we are able to prove that the first one is a true phase transition corresponding to a particular melting process of oriented domains, where colored noise is present almost independently of true fractality. The second one is not a real transition and it may be ascribed to a smooth balancing between two geometrical effects: a progressive fragmentation of the big clusters (possibly creating fractals), and the slow onset of a small clusters chaotic phase. Comparison with the nearest neighbor Ising ferromagnetic system points out a substantial difference in the cluster geometrical properties of the two models and in their critical behavior.Comment: 20 pages, 15 figures, submitted to JPhys

Spectral statistics for quantized skew translations on the torus

We study the spectral statistics for quantized skew translations on the torus, which are ergodic but not mixing for irrational parameters. It is shown explicitly that in this case the level--spacing distribution and other common spectral statistics, like the number variance, do not exist in the semiclassical limit.Comment: 7 pages. One figure, include