A DMRG Study of Low-Energy Excitations and Low-Temperature Properties of Alternating Spin Systems

We use the density matrix renormalization group (DMRG) method to study the ground and low-lying excited states of three kinds of uniform and dimerized alternating spin chains. The DMRG procedure is also employed to obtain low-temperature thermodynamic properties of these systems. We consider a 2N site system with spins $s_1$ and $s_2$ alternating from site to site and interacting via a Heisenberg antiferromagnetic exchange. The three systems studied correspond to $(s_1 ,s_2 )$ being equal to $(1,1/2),(3/2,1/2)$ and $(3/2,1)$; all of them have very similar properties. The ground state is found to be ferrimagnetic with total spin $s_G =N(s_1 - s_2)$. We find that there is a gapless excitation to a state with spin $s_G -1$, and a gapped excitation to a state with spin $s_G +1$. Surprisingly, the correlation length in the ground state is found to be very small for this gapless system. The DMRG analysis shows that the chain is susceptible to a conditional spin-Peierls instability. Furthermore, our studies of the magnetization, magnetic susceptibility $\chi$ and specific heat show strong magnetic-field dependences. The product $\chi T$ shows a minimum as a function of temperature T at low magnetic fields; the minimum vanishes at high magnetic fields. This low-field behavior is in agreement with earlier experimental observations. The specific heat shows a maximum as a function of temperature, and the height of the maximum increases sharply at high magnetic fields. Although all the three systems show qualitatively similar behavior, there are some notable quantitative differences between the systems in which the site spin difference, $|s_1 - s_2|$, is large and small respectively.Comment: 16 LaTeX pages, 13 postscript figure

Formal vs self-organised knowledge systems: a network approach

In this work we consider the topological analysis of symbolic formal systems in the framework of network theory. In particular we analyse the network extracted by Principia Mathematica of B. Russell and A.N. Whitehead, where the vertices are the statements and two statements are connected with a directed link if one statement is used to demonstrate the other one. We compare the obtained network with other directed acyclic graphs, such as a scientific citation network and a stochastic model. We also introduce a novel topological ordering for directed acyclic graphs and we discuss its properties in respect to the classical one. The main result is the observation that formal systems of knowledge topologically behave similarly to self-organised systems.Comment: research pape

On the Putative Detection of z>0 X-ray Absorption Features in the Spectrum of Markarian 421

In a series of papers, Nicastro et al. have reported the detection of z>0 OVII absorption features in the spectrum of Mrk421 obtained with the Chandra Low Energy Transmission Grating Spectrometer (LETGS). We evaluate this result in the context of a high quality spectrum of the same source obtained with the Reflection Grating Spectrometer (RGS) on XMM-Newton. The data comprise over 955ks of usable exposure time and more than 26000 counts per 50 milliAngstrom at 21.6 Angstroms. We concentrate on the spectrally clean region (21.3 < lambda < 22.5 Angstroms) where sharp features due to the astrophysically abundant OVII may reveal an intervening, warm--hot intergalactic medium (WHIM). We do not confirm detection of any of the intervening systems claimed to date. Rather, we detect only three unsurprising, astrophysically expected features down to the Log(N_i)~14.6 (3 sigma) sensitivity level. Each of the two purported WHIM features is rejected with a statistical confidence that exceeds that reported for its initial detection. While we can not rule out the existence of fainter, WHIM related features in these spectra, we suggest that previous discovery claims were premature. A more recent paper by Williams et al. claims to have demonstrated that the RGS data we analyze here do not have the resolution or statistical quality required to confirm or deny the LETGS detections. We show that our careful analysis resolves the issues encountered by Williams et al. and recovers the full resolution and statistical quality of the RGS data. We highlight the differences between our analysis and those published by Williams et al. as this may explain our disparate conclusions.Comment: 19 pages/7 figures/4 tables. 060424 submitted to ApJ 060522 re-submitted following ApJ reques

You Ain\u27t Heard Nothing Yet

https://digitalcommons.library.umaine.edu/mmb-vp/5021/thumbnail.jp

Macroscopic Geo-Magnetic Radiation Model; Polarization effects and finite volume calculations

An ultra-high-energy cosmic ray (UHECR) colliding with the Earth's atmosphere gives rise to an Extensive Air Shower (EAS). Due to different charge separation mechanisms within the thin shower front coherent electromagnetic radiation will be emitted within the radio frequency range. A small deviation of the index of refraction from unity will give rise to Cherenkov radiation up to distances of 100 meters from the shower core and therefore has to be included in a complete description of the radio emission from an EAS. Interference between the different radiation mechanisms, in combination with different polarization behavior will reflect in a lateral distribution function (LDF) depending on the orientation of the observer and a non-trivial fall-off of the radio signal as function of distance to the shower core.Comment: Proceedings of the ARENA2010 conference, Nantes, Franc