Multiplicative combinatorial properties of return time sets in minimal dynamical systems

We investigate the relationship between the dynamical properties of minimal topological dynamical systems and the multiplicative combinatorial properties of return time sets arising from those systems. In particular, we prove that for a residual sets of points in any minimal system, the set of return times to any non-empty, open set contains arbitrarily long geometric progressions. Under the separate assumptions of total minimality and distality, we prove that return time sets have positive multiplicative upper Banach density along $\mathbb{N}$ and along multiplicative subsemigroups of $\mathbb{N}$, respectively. The primary motivation for this work is the long-standing open question of whether or not syndetic subsets of the positive integers contain arbitrarily long geometric progressions; our main result is some evidence for an affirmative answer to this question.Comment: 32 page

Ehrenfest-time dependence of counting statistics for chaotic ballistic systems

Transport properties of open chaotic ballistic systems and their statistics can be expressed in terms of the scattering matrix connecting incoming and outgoing wavefunctions. Here we calculate the dependence of correlation functions of arbitrarily many pairs of scattering matrices at different energies on the Ehrenfest time using trajectory based semiclassical methods. This enables us to verify the prediction from effective random matrix theory that one part of the correlation function obtains an exponential damping depending on the Ehrenfest time, while also allowing us to obtain the additional contribution which arises from bands of always correlated trajectories. The resulting Ehrenfest-time dependence, responsible e.g. for secondary gaps in the density of states of Andreev billiards, can also be seen to have strong effects on other transport quantities like the distribution of delay times.Comment: Refereed version. 15 pages, 14 figure

Ne II Observations of Gas Motions in Compact and Ultracompact H II Regions

We present high spatial and spectral resolution observations of 16 Galactic compact and ultracompact H II regions in the [Ne II] 12.8 mu m fine-structure line. The small thermal width of the neon line and the high dynamic range of the maps provide an unprecedented view of the kinematics of compact and ultracompact H II regions. These observations solidify an emerging picture of the structure of ultracompact H II regions suggested in our earlier studies of G29.96-0.02 and Mon R2 IRS 1; systematic surface flows, rather than turbulence or bulk expansion, dominate the gas motions in the H II regions. The observations show that almost all of the sources have significant (5-20 km s(-1)) velocity gradients and that most of the sources are limb-brightened. In many cases, the velocity pattern implies tangential flow along a dense shell of ionized gas. None of the observed sources clearly fits into the categories of filled expanding spheres, expanding shells, filled blister flows, or cometary H II regions formed by rapidly moving stars. Instead, the kinematics and morphologies of most of the sources lead to a picture of H II regions confined to the edges of cavities created by stellar wind ram pressure and flowing along the cavity surfaces. In sources where the radio continuum and [Ne II] morphologies agree, the majority of the ionic emission is blueshifted relative to nearby molecular gas. This is consistent with sources lying on the near side of their natal clouds being less affected by extinction and with gas motions being predominantly outward, as is expected for pressure-driven flows.NSF AST-0607312, NSF-0708074SOFIA USRA8500-98-008NYSTAR Faculty Development ProgramNASA NNG 04-GG92G, CAN-NCC5-679Lunar and Planetary InstituteAstronom

On Katznelson's Question for skew product systems

Katznelson's Question is a long-standing open question concerning recurrence in topological dynamics with strong historical and mathematical ties to open problems in combinatorics and harmonic analysis. In this article, we give a positive answer to Katznelson's Question for certain towers of skew product extensions of equicontinuous systems, including systems of the form $(x,t) \mapsto (x + \alpha, t + h(x))$. We describe which frequencies must be controlled for in order to ensure recurrence in such systems, and we derive combinatorial corollaries concerning the difference sets of syndetic subsets of the natural numbers.Comment: 31 page

The density of states of chaotic Andreev billiards

Quantum cavities or dots have markedly different properties depending on whether their classical counterparts are chaotic or not. Connecting a superconductor to such a cavity leads to notable proximity effects, particularly the appearance, predicted by random matrix theory, of a hard gap in the excitation spectrum of quantum chaotic systems. Andreev billiards are interesting examples of such structures built with superconductors connected to a ballistic normal metal billiard since each time an electron hits the superconducting part it is retroreflected as a hole (and vice-versa). Using a semiclassical framework for systems with chaotic dynamics, we show how this reflection, along with the interference due to subtle correlations between the classical paths of electrons and holes inside the system, are ultimately responsible for the gap formation. The treatment can be extended to include the effects of a symmetry breaking magnetic field in the normal part of the billiard or an Andreev billiard connected to two phase shifted superconductors. Therefore we are able to see how these effects can remold and eventually suppress the gap. Furthermore the semiclassical framework is able to cover the effect of a finite Ehrenfest time which also causes the gap to shrink. However for intermediate values this leads to the appearance of a second hard gap - a clear signature of the Ehrenfest time.Comment: Refereed version. 23 pages, 19 figure

TEXES Observations of Pure Rotational H_2 Emission from AB Aurigae

We present observations of pure rotational molecular hydrogen emission from the Herbig Ae star, AB Aur. Our observations were made using the Texas Echelon Cross Echelle Spectrograph (TEXES) at the NASA Infrared Telescope Facility and the Gemini North Observatory. We searched for H_2 emission in the S(1), S(2), and S(4) lines at high spectral resolution and detected all three. By fitting a simple model for the emission in the three transitions, we derive T = 670 ± 40 K and M = 0.52 ± 0.15 M_⊙ for the emitting gas. On the basis of the 8.5 km s^(-1) FWHM of the S(2) line, assuming the emission comes from the circumstellar disk, and with an inclination estimate of the AB Aur system taken from the literature, we place the location for the emission near 18 AU. Comparison of our derived temperature to a disk structure model suggests that UV and X-ray heating are important in heating the disk atmosphere

Semiclassical approach to the ac-conductance of chaotic cavities

We address frequency-dependent quantum transport through mesoscopic conductors in the semiclassical limit. By generalizing the trajectory-based semiclassical theory of dc quantum transport to the ac case, we derive the average screened conductance as well as ac weak-localization corrections for chaotic conductors. Thereby we confirm respective random matrix results and generalize them by accounting for Ehrenfest time effects. We consider the case of a cavity connected through many leads to a macroscopic circuit which contains ac-sources. In addition to the reservoir the cavity itself is capacitively coupled to a gate. By incorporating tunnel barriers between cavity and leads we obtain results for arbitrary tunnel rates. Finally, based on our findings we investigate the effect of dephasing on the charge relaxation resistance of a mesoscopic capacitor in the linear low-frequency regime

Bax/Bak-independent mitochondrial depolarization and reactive oxygen species induction by sorafenib overcome resistance to apoptosis in renal cell carcinoma

Renal cell carcinoma (RCC) is polyresistant to chemo- and radiotherapy or biologicals including TNF-related apoptosis inducing ligand (TRAIL). Sorafenib, a multikinase inhibitor approved for the treatment of RCC, has been shown to sensitize cancer cells toward TRAIL-induced apoptosis, in particular by downregulation of the Bak-inhibitory Bcl 2 family protein Mcl 1. Here, we demonstrate that sorafenib overcomes TRAIL resistance in RCC by a mechanism that does not rely on Mcl 1 downregulation. Instead, sorafenib induces a rapid dissipation of the mitochondrial membrane potential (ΔΨ(m)) that is accompanied by the accumulation of reactive oxygen species (ROS). Loss of ΔΨ(m) and ROS production induced by sorafenib are independent of caspase activities and do not depend on the presence of the pro-apoptotic Bcl 2 family proteins Bax or Bak indicating that both events are functionally up-stream of the mitochondrial apoptosis signaling cascade. More intriguingly, we find that it is sorafenib-induced ROS accumulation that enables TRAIL to activate caspase 8 in RCC. This leads to apoptosis that involves activation of an amplification loop via the mitochondrial apoptosis pathway. Thus, our mechanistic data indicate that sorafenib bypasses central resistance mechanisms through a direct induction of ΔΨ(m) breakdown and ROS production. Activation of this pathway might represent a useful strategy to overcome the cell-inherent resistance to cancer therapeutics including TRAIL in multiresistant cancers such as RCC

Conductance fluctuations in chaotic systems with tunnel barriers

Quantum effects are expected to disappear in the short-wavelength, semiclassical limit. As a matter of fact, recent investigations of transport through quantum chaotic systems have demonstrated the exponential suppression of the weak localization corrections to the conductance and of the Fano factor for shot-noise when the Ehrenfest time exceeds the electronic dwell time. On the other hand, conductance fluctuations, an effect of quantum coherence, retain their universal value in the limit of the ratio of Ehrenfest time over dwell time to infinity, when the system is ideally coupled to external leads. Motivated by this intriguing result we investigate conductance fluctuations through quantum chaotic cavities coupled to external leads via (tunnel) barriers of arbitrary transparency. Using the trajectory-based semiclassical theory of transport, we find a linear Ehrenfest time-dependence of the conductance variance showing a nonmonotonous, sinusoidal behavior as a function of the transperancy. Most notably, we find an increase of the conductance fluctuations with the Ehrenfest time, above their universal value, for the transparency less than 0.5. These results, confirmed by numerical simulations, show that, contrarily to the common wisdom, effects of quantum coherence may increase in the semiclassical limit, under special circumstances