Expanding Semiflows on Branched Surfaces and One-Parameter Semigroups of Operators

We consider expanding semiflows on branched surfaces. The family of transfer operators associated to the semiflow is a one-parameter semigroup of operators. The transfer operators may also be viewed as an operator-valued function of time and so, in the appropriate norm, we may consider the vector-valued Laplace transform of this function. We obtain a spectral result on these operators and relate this to the spectrum of the generator of this semigroup. Issues of strong continuity of the semigroup are avoided. The main result is the improvement to the machinery associated with studying semiflows as one-parameter semigroups of operators and the study of the smoothness properties of semiflows defined on branched manifolds, without encoding as a suspension semiflow

Mutually Unbiased Bases for Continuous Variables

The concept of mutually unbiased bases is studied for N pairs of continuous variables. To find mutually unbiased bases reduces, for specific states related to the Heisenberg-Weyl group, to a problem of symplectic geometry. Given a single pair of continuous variables, three mutually unbiased bases are identified while five such bases are exhibited for two pairs of continuous variables. For N = 2, the golden ratio occurs in the definition of these mutually unbiased bases suggesting the relevance of number theory not only in the finite-dimensional setting.Comment: 5 pages, no figures, revised to be identical to published tex

The problem of mutually unbiased bases in dimension 6

We outline a discretization approach to determine the maximal number of mutually unbiased bases in dimension 6. We describe the basic ideas and introduce the most important definitions to tackle this famous open problem which has been open for the last 10 years. Some preliminary results are also listed

A J-band detection of the sub-stellar mass donor in SDSS J1433+1011

We present time-resolved J-band spectroscopy of the short period cataclysmic variable SDSS J143317.78+101123.3. We detect absorption lines from the sub-stellar donor star in this system, which contributes 38 +/- 5% to the J-band light. From the relative strengths of the absorption lines in the J-band, we estimate the spectral type of the donor star to be L2 +/- 1. These data are the first spectroscopic detection of a confirmed sub-stellar donor in a cataclysmic variable, and the spectral type is consistent with that expected from semi-empirical evolutionary models. Using skew mapping, we have been able to derive an estimate for the radial velocity of the donor of Kd = 520 +/- 60 km/s. This value is consistent with, though much less precise than, predictions from mass determinations found via photometric fitting of the eclipse light curves.Comment: 6 pages, 4 figures. Accepted for publication in Monthly Notices of the Royal Astronomical Societ

Hunting For Eclipses: High Speed Observations of Cataclysmic Variables

We present new time-resolved photometry of 74 cataclysmic variables (CVs), 47 of which are eclipsing. 13 of these eclipsing systems are newly discovered. For all 47 eclipsing systems we show high cadence (1-20 seconds) light curves obtained with the high-speed cameras ultracam and ultraspec. We provide new or refined ephemerides, and supply mid-eclipse times for all observed eclipses. We assess the potential for light curve modelling of all 47 eclipsing systems to determine their system parameters, finding 20 systems which appear to be suitable for future study

Upper bound on the density of Ruelle resonances for Anosov flows

Using a semiclassical approach we show that the spectrum of a smooth Anosov vector field V on a compact manifold is discrete (in suitable anisotropic Sobolev spaces) and then we provide an upper bound for the density of eigenvalues of the operator (-i)V, called Ruelle resonances, close to the real axis and for large real parts.Comment: 57 page

A Bell Inequality Analog in Quantum Measure Theory

One obtains Bell's inequalities if one posits a hypothetical joint probability distribution, or {\it measure}, whose marginals yield the probabilities produced by the spin measurements in question. The existence of a joint measure is in turn equivalent to a certain causality condition known as ``screening off''. We show that if one assumes, more generally, a joint {\it quantal measure}, or ``decoherence functional'', one obtains instead an analogous inequality weaker by a factor of $\sqrt{2}$. The proof of this ``Tsirel'son inequality'' is geometrical and rests on the possibility of associating a Hilbert space to any strongly positive quantal measure. These results lead both to a {\it question}: ``Does a joint measure follow from some quantal analog of `screening off'?'', and to the {\it observation} that non-contextual hidden variables are viable in histories-based quantum mechanics, even if they are excluded classically.Comment: 38 pages, TeX. Several changes and added comments to bring out the meaning more clearly. Minor rewording and extra acknowledgements, now closer to published versio

Entropic Fluctuations in Statistical Mechanics I. Classical Dynamical Systems

Within the abstract framework of dynamical system theory we describe a general approach to the Transient (or Evans-Searles) and Steady State (or Gallavotti-Cohen) Fluctuation Theorems of non-equilibrium statistical mechanics. Our main objective is to display the minimal, model independent mathematical structure at work behind fluctuation theorems. Besides its conceptual simplicity, another advantage of our approach is its natural extension to quantum statistical mechanics which will be presented in a companion paper. We shall discuss several examples including thermostated systems, open Hamiltonian systems, chaotic homeomorphisms of compact metric spaces and Anosov diffeomorphisms.Comment: 72 pages, revised version 12/10/2010, to be published in Nonlinearit

Long-term eclipse timing of white dwarf binaries: an observational hint of a magnetic mechanism at work

We present a long-term programme for timing the eclipses of white dwarfs in close binaries to measure apparent and/or real variations in their orbital periods. Our programme includes 67 close binaries, both detached and semi-detached and with M-dwarfs, K-dwarfs, brown dwarfs or white dwarfs secondaries. In total, we have observed more than 650 white dwarf eclipses. We use this sample to search for orbital period variations and aim to identify the underlying cause of these variations. We find that the probability of observing orbital period variations increases significantly with the observational baseline. In particular, all binaries with baselines exceeding 10 yr, with secondaries of spectral type K2 – M5.5, show variations in the eclipse arrival times that in most cases amount to several minutes. In addition, among those with baselines shorter than 10 yr, binaries with late spectral type (>M6), brown dwarf or white dwarf secondaries appear to show no orbital period variations. This is in agreement with the so-called Applegate mechanism, which proposes that magnetic cycles in the secondary stars can drive variability in the binary orbits. We also present new eclipse times of NN Ser, which are still compatible with the previously published circumbinary planetary system model, although only with the addition of a quadratic term to the ephemeris. Finally, we conclude that we are limited by the relatively short observational baseline for many of the binaries in the eclipse timing programme, and therefore cannot yet draw robust conclusions about the cause of orbital period variations in evolved, white dwarf binaries