Markov evolutions and hierarchical equations in the continuum I. One-component systems

General birth-and-death as well as hopping stochastic dynamics of infinite particle systems in the continuum are considered. We derive corresponding evolution equations for correlation functions and generating functionals. General considerations are illustrated in a number of concrete examples of Markov evolutions appearing in applications.Comment: 47 page

Vlasov scaling for stochastic dynamics of continuous systems

We describe a general scheme of derivation of the Vlasov-type equations for Markov evolutions of particle systems in continuum. This scheme is based on a proper scaling of corresponding Markov generators and has an algorithmic realization in terms of related hierarchical chains of correlation functions equations. Several examples of the realization of the proposed approach in particular models are presented.Comment: 23 page

Lowering and raising operators for the free Meixner class of orthogonal polynomials

We compare some properties of the lowering and raising operators for the classical and free classes of Meixner polynomials on the real line

Pulsar Science with the Green Bank 43m Telescope

The 43m telescope at the NRAO site in Green Bank, WV has recently been outfitted with a clone of the Green Bank Ultimate Pulsar Processing Instrument (GUPPI \cite{Ransom:2009}) backend, making it very useful for a number of pulsar related studies in frequency ranges 800-1600 MHz and 220-440 MHz. Some of the recent science being done with it include: monitoring of the Crab pulsar, a blind search for transient sources, pulsar searches of targets of opportunity, and an all-sky mapping project. For the Crab monitoring project, regular observations are searched for giant pulses (GPs), which are then correlated with $\gamma$-ray photons from the \emph{Fermi} spacecraft. Data from the all-sky mapping project are first run through a pipeline that does a blind transient search, looking for single pulses over a DM range of 0-500 pc~cm$^{-3}$. These projects are made possible by MIT Lincoln Labs.Comment: 2 pages, 1 figure, to appear in AIP Conference Proceedings of Pulsar Conference 2010 "Radio Pulsars: a key to unlock the secrets of the Universe", Sardinia, October 201

A Search for Pulsed and Bursty Radio Emission from X-ray Dim Isolated Neutron Stars

We have carried out a search for radio emission from six X-ray dim isolated neutron stars (XDINSs) observed with the Robert C. Byrd Green Bank Radio Telescope (GBT) at 820 MHz. No bursty or pulsed radio emission was found down to a 4sigma significance level. The corresponding flux limit is 0.01-0.04 mJy depending on the integration time for the particular source and pulse duty cycle of 2%. These are the most sensitive limits yet on radio emission from these objects.Comment: 3 pages, 3 figures, to be appeared in the Proceedings of the conference "40 Years of Pulsars: Millisecond Pulsars, Magnetars, and More" held on August 12-17, 2007, McGill University, Montreal, Canad

The Inklings in America

Transcription of a panel discussion at the 19th Mythopoeic Conference

A Giant Sample of Giant Pulses from the Crab Pulsar

We observed the Crab pulsar with the 43-m telescope in Green Bank, WV over a timespan of 15 months. In total we obtained 100 hours of data at 1.2 GHz and seven hours at 330 MHz, resulting in a sample of about 95000 giant pulses (GPs). This is the largest sample, to date, of GPs from the Crab pulsar taken with the same telescope and backend and analyzed as one data set. We calculated power-law fits to amplitude distributions for main pulse (MP) and interpulse (IP) GPs, resulting in indices in the range of 2.1-3.1 for MP GPs at 1.2 GHz and in the range of 2.5-3.0 and 2.4-3.1 for MP and IP GPs at 330 MHz. We also correlated the GPs at 1.2 GHz with GPs from the Robert C. Byrd Green Bank Telescope (GBT), which were obtained simultaneously at a higher frequency (8.9 GHz) over a span of 26 hours. In total, 7933 GPs from the 43-m telescope at 1.2 GHz and 39900 GPs from the GBT were recorded during these contemporaneous observations. At 1.2 GHz, 236 (3%) MP GPs and 23 (5%) IP GPs were detected at 8.9 GHz, both with zero chance probability. Another 15 (4%) low-frequency IP GPs were detected within one spin period of high-frequency IP GPs, with a chance probability of 9%. This indicates that the emission processes at high and low radio frequencies are related, despite significant pulse profile shape differences. The 43-m GPs were also correlated with Fermi gamma-ray photons to see if increased pair production in the magnetosphere is the mechanism responsible for GP emission. A total of 92022 GPs and 393 gamma-ray photons were used in this correlation analysis. No significant correlations were found between GPs and gamma-ray photons. This indicates that increased pair production in the magnetosphere is likely not the dominant cause of GPs. Possible methods of GP production may be increased coherence of synchrotron emission or changes in beaming direction.Comment: 33 pages, 10 figures, 6 tables, accepted for publication in Ap

Phase transitions and quantum effects in anharmonic crystals

The most important recent results in the theory of phase transitions and quantum effects in quantum anharmonic crystals are presented and discussed. In particular, necessary and sufficient conditions for a phase transition to occur at some temperature are given in the form of simple inequalities involving the interaction strength and the parameters describing a single oscillator. The main characteristic feature of the theory is that both mentioned phenomena are described in one and the same setting, in which thermodynamic phases of the model appear as probability measures on path spaces. Then the possibility of a phase transition to occur is related to the existence of multiple phases at the same values of the relevant parameters. Other definitions of phase transitions, based on the non-differentiability of the free energy density and on the appearance of ordering, are also discussed