Ergodic Properties of Infinite Harmonic Crystals: an Analytic Approach

We give through pseudodifferential operator calculus a proof that the quantum dynamics of a class of infinite harmonic crystals becomes ergodic and mixing with respect to the quantum Gibbs measure if the classical infinite dynamics is respectively ergodic and mixing with respect to the classical infinite Gibbs measure. The classical ergodicity and mixing properties are recovered as $\hbar\to 0$, and the infinitely many particles limits of the quantum Gibbs averages are proved to be the averages over a classical infinite Gibbs measure of the symbols generating the quantum observables under Weyl quantization.Comment: 30 pages, plain LaTe

Observational constraints on the spin of the most massive black holes from radio observations

We use recent progress in simulating the production of magnetohydrodynamic jets around black holes to derive the cosmic spin history of the most massive black holes, with masses &gt;~10^8 Msol. Assuming the jet efficiency depends on spin a, we can approximately reproduce the observed `radio loudness' of quasars and the local radio luminosity function. Using the X-ray luminosity function and the local mass function of supermassive black holes, SMBHs we can reproduce the individual radio luminosity functions of radio sources showing high- and low-excitation narrow emission lines. The data favour spin distributions that are bimodal, with one component around spin zero and the other close to maximal spin. In the low-excitation galaxies, the two components have similar amplitudes. For the high-excitation galaxies, the amplitude of the high-spin peak is typically much smaller than that of the low-spin peak. A bimodality should be seen in the radio loudness of quasars. We predict that the low-excitation galaxies are dominated by SMBHs with masses &gt;~10^8 Msol, down to radio luminosity densities ~10^21 W Hz-1 sr-1 at 1.4~GHz. Our model is also able to predict the radio luminosity function at z=1, and predicts it to be dominated by high-excitation galaxies above luminosity densities &gt;~10^26 W Hz-1 sr-1, in full agreement with the observations. From our parametrisation and using the best fitting jet efficiencies there is marginal evidence for evolution in spin: the mean spin increases slightly from ~0.25 at z=1 to ~0.35 at z=0, and the fraction of SMBHs with a&gt;=0.5 increases from 0.16+-0.03 at z=1 to 0.24+-0.09 at z=0. Our results are in excellent agreement with the mean radiative efficiency of quasars, as well as recent cosmological simulations. We discuss the implications in terms of accretion and SMBH mergers, and galactic black holes (Abridged).</a

Adsorbate surface diffusion: The role of incoherent tunneling in light particle motion

The role of incoherent tunneling in the diffusion of light atoms on surfaces is investigated. With this purpose, a Chudley-Elliot master equation constrained to nearest neighbors is considered within the Grabert-Weiss approach to quantum diffusion in periodic lattices. This model is applied to recent measurements of atomic H and D on Pt(111), rendering friction coefficients that are in the range of those available in the literature for other species of adsorbates. A simple extension of the model has also been considered to evaluate the relationship between coverage and tunneling, and therefore the feasibility of the approach. An increase of the tunneling rate has been observed as the surface coverage decreases.Comment: 7 pages, 2 figures; important reorganization of the work (including title changes

Phonon lineshapes in atom-surface scattering

Phonon lineshapes in atom-surface scattering are obtained from a simple stochastic model based on the so-called Caldeira-Leggett Hamiltonian. In this single-bath model, the excited phonon resulting from a creation or annihilation event is coupled to a thermal bath consisting of an infinite number of harmonic oscillators, namely the bath phonons. The diagonalization of the corresponding Hamiltonian leads to a renormalization of the phonon frequencies in terms of the phonon friction or damping coefficient. Moreover, when there are adsorbates on the surface, this single-bath model can be extended to a two-bath model accounting for the effect induced by the adsorbates on the phonon lineshapes as well as their corresponding lineshapes.Comment: 14 pages, 2 figure

Risk aversion in economic transactions

Most people are risk-averse (risk-seeking) when they expect to gain (lose). Based on a generalization of ``expected utility theory'' which takes this into account, we introduce an automaton mimicking the dynamics of economic operations. Each operator is characterized by a parameter q which gauges people's attitude under risky choices; this index q is in fact the entropic one which plays a central role in nonextensive statistical mechanics. Different long term patterns of average asset redistribution are observed according to the distribution of parameter q (chosen once for ever for each operator) and the rules (e.g., the probabilities involved in the gamble and the indebtedness restrictions) governing the values that are exchanged in the transactions. Analytical and numerical results are discussed in terms of how the sensitivity to risk affects the dynamics of economic transactions.Comment: 4 PS figures, to appear in Europhys. Let