Thermodynamic formalism for the Lorentz gas with open boundaries in dd dimensions

A Lorentz gas may be defined as a system of fixed dispersing scatterers, with a single light particle moving among these and making specular collisions on encounters with the scatterers. For a dilute Lorentz gas with open boundaries in $d$ dimensions we relate the thermodynamic formalism to a random flight problem. Using this representation we analytically calculate the central quantity within this formalism, the topological pressure, as a function of system size and a temperature-like parameter \ba. The topological pressure is given as the sum of the topological pressure for the closed system and a diffusion term with a \ba-dependent diffusion coefficient. From the topological pressure we obtain the Kolmogorov-Sinai entropy on the repeller, the topological entropy, and the partial information dimension.Comment: 7 pages, 5 figure

A Near-Solar Metallicity, Nitrogen-Deficient Lyman Limit Absorber Associated with two S0 Galaxies

From UV spectra of the bright quasar PHL 1811 recorded by FUSE and the E140M configuration on STIS, we have determined the abundances of various atomic species in a Lyman limit system at z = 0.0809 with log N(H I) = 17.98. Considerably more hydrogen may be in ionized form, since the abundances of C II, Si II, S II and Fe II are very large compared to that of O I, when compared to their respective solar abundance ratios. Our determination [O/H] = -0.19 in the H I-bearing gas indicates that the chemical enrichment of the gas is unusually high for an extragalactic QSO absorption system. However, this same material has an unusually low abundance of nitrogen, [N/O] < -0.59, indicating that there may not have been enough time during this enrichment for secondary nitrogen to arise from low and intermediate mass stars. In an earlier investigation we found two galaxies at nearly the same redshift as this absorption system and displaced by 34 and 87 kpc from the line of sight. An r-band image recorded by the ACS on HST indicates these are S0 galaxies. One or both of these galaxies may be the source of the gas, which might have been expelled in a fast wind, by tidal stripping, or by ram-pressure stripping. Subtraction of the ACS point-spread function from the image of the QSO reveals the presence of a face-on spiral galaxy under the glare of the quasar; although it is possible that this galaxy may be responsible for the Lyman limit absorption, the exact alignment of the QSO with the center of the galaxy suggests that the spiral is the quasar host.Comment: 74 pages, 14 figures; to be published in the Astrophysical Journal (Part 1) May 1, 2005 issue. A version of the paper with figures of better quality may be found at http://www.astro.princeton.edu/~ebj/PHL1811_paper.ps (postscript) or http://www.astro.princeton.edu/~ebj/PHL1811_paper.pdf (pdf

Hopf's last hope: spatiotemporal chaos in terms of unstable recurrent patterns

Spatiotemporally chaotic dynamics of a Kuramoto-Sivashinsky system is described by means of an infinite hierarchy of its unstable spatiotemporally periodic solutions. An intrinsic parametrization of the corresponding invariant set serves as accurate guide to the high-dimensional dynamics, and the periodic orbit theory yields several global averages characterizing the chaotic dynamics.Comment: Latex, ioplppt.sty and iopl10.sty, 18 pages, 11 PS-figures, compressed and encoded with uufiles, 170 k

Quantum Computing of Poincare Recurrences and Periodic Orbits

Quantum algorithms are built enabling to find Poincar\'e recurrence times and periodic orbits of classical dynamical systems. It is shown that exponential gain compared to classical algorithms can be reached for a restricted class of systems. Quadratic gain can be achieved for a larger set of dynamical systems. The simplest cases can be implemented with small number of qubits.Comment: revtex, 5 pages, research at Quantware MIPS Center (see http://www.quantware.ups-tlse.fr); minor changes and references adde

Semiclassical form factor for chaotic systems with spin 1/2

We study the properties of the two-point spectral form factor for classically chaotic systems with spin 1/2 in the semiclassical limit, with a suitable semiclassical trace formula as our principal tool. To this end we introduce a regularized form factor and discuss the limit in which the so-called diagonal approximation can be recovered. The incorporation of the spin contribution to the trace formula requires an appropriate variant of the equidistribution principle of long periodic orbits as well as the notion of a skew product of the classical translational and spin dynamics. Provided this skew product is mixing, we show that generically the diagonal approximation of the form factor coincides with the respective predictions from random matrix theory.Comment: 20 pages, no figure

Interstellar and Circumstellar Optical & Ultraviolet Lines Towards SN1998S

We have observed SN1998S which exploded in NGC3877, with the UES at the WHT and with the E230M echelle of STIS aboard HST. Both data sets were obtained at two seperate epochs. From our own Galaxy we detect interstellar absorption lines of CaII, FeII, MgI, and probably MnII from the edge of the HVC Complex M. We derive gas-phase abundances which are very similar to warm disk clouds in the local ISM, which we believe argues against the HVC material having an extragalactic origin. At the velocity of NGC3877 we detect interstellar MgI, MgII, MnII, CaII, & NaI. Surprisingly, one component is seen to increase by a factor of ~1 dex in N(NaI) and N(MgI) between the two epochs over which the data were taken. Unusually, our data also show narrow Balmer, HeI, and metastable FeII P-Cygni profiles, with a narrow absorption component superimposed on the bottom of the profile's absorption trough. Both the broad and narrow components of the optical lines are seen to increase substantially in strength between the two epochs. Most of the low-ionization absorption can be understood in terms of gas co-rotating with the disk of NGC 3877, providing the SN is at the back of an HI disk with a similar thickness to that of our own Galaxy. However, the variable absorption components, and the classic P-Cygni emission profiles, most likely arise in slow-moving circumstellar outflows originating from the red supergiant progenitor of SN1998S. [Abridged.]Comment: Accepted by ApJ, 26 pages including 9 figure

Nano-displacement measurements using spatially multimode squeezed light

We demonstrate the possibility of surpassing the quantum noise limit for simultaneous multi-axis spatial displacement measurements that have zero mean values. The requisite resources for these measurements are squeezed light beams with exotic transverse mode profiles. We show that, in principle, lossless combination of these modes can be achieved using the non-degenerate Gouy phase shift of optical resonators. When the combined squeezed beams are measured with quadrant detectors, we experimentally demonstrate a simultaneous reduction in the transverse x- and y- displacement fluctuations of 2.2 dB and 3.1 dB below the quantum noise limit.Comment: 21 pages, 9 figures, submitted to "Special Issue on Fluctuations & Noise in Photonics & Quantum Optics" of J. Opt.

Coding Theorem for a Class of Quantum Channels with Long-Term Memory

In this paper we consider the transmission of classical information through a class of quantum channels with long-term memory, which are given by convex combinations of product channels. Hence, the memory of such channels is given by a Markov chain which is aperiodic but not irreducible. We prove the coding theorem and weak converse for this class of channels. The main techniques that we employ, are a quantum version of Feinstein's Fundamental Lemma and a generalization of Helstrom's Theorem.Comment: Some typos correcte

Phase transitions for suspension flows

This paper is devoted to study thermodynamic formalism for suspension flows defined over countable alphabets. We are mostly interested in the regularity properties of the pressure function. We establish conditions for the pressure function to be real analytic or to exhibit a phase transition. We also construct an example of a potential for which the pressure has countably many phase transitions.Comment: Example 5.2 expanded. Typos corrected. Section 6.1 superced the note "Thermodynamic formalism for the positive geodesic flow on the modular surface" arXiv:1009.462

Tema Con Variazioni: Quantum Channel Capacity

Channel capacity describes the size of the nearly ideal channels, which can be obtained from many uses of a given channel, using an optimal error correcting code. In this paper we collect and compare minor and major variations in the mathematically precise statements of this idea which have been put forward in the literature. We show that all the variations considered lead to equivalent capacity definitions. In particular, it makes no difference whether one requires mean or maximal errors to go to zero, and it makes no difference whether errors are required to vanish for any sequence of block sizes compatible with the rate, or only for one infinite sequence.Comment: 32 pages, uses iopart.cl