Evolution of entanglement after a local quench

We study free electrons on an infinite half-filled chain, starting in the ground state with a bond defect. We find a logarithmic increase of the entanglement entropy after the defect is removed, followed by a slow relaxation towards the value of the homogeneous chain. The coefficients depend continuously on the defect strength.Comment: 14 pages, 9 figures, final versio

Entanglement Entropy in the Calogero-Sutherland Model

We investigate the entanglement entropy between two subsets of particles in the ground state of the Calogero-Sutherland model. By using the duality relations of the Jack symmetric polynomials, we obtain exact expressions for both the reduced density matrix and the entanglement entropy in the limit of an infinite number of particles traced out. From these results, we obtain an upper bound value of the entanglement entropy. This upper bound has a clear interpretation in terms of fractional exclusion statistics.Comment: 14 pages, 3figures, references adde

Detection of blood aspiration in deadly head gunshots comparing postmortem computed tomography (PMCT) and autopsy

BACKGROUND: The aim of our study was to analyze the reliability of postmortem computed tomography (PMCT) versus autopsy in detecting signs of blood aspiration in a distinct group of patients following deadly head, mouth or floor of mouth gunshot injuries. METHODS: In this study, in 41 cases PMCT was compared to autopsy reports, the gold standard of postmortem exams, regarding detection of blood aspiration. PMCT was evaluated for the presence and level of typical signs of blood aspiration in the major airways and lung using a semi-quantitative scale ranging from level 0 (no aspiration) to 3 (significant aspiration) also taking density values of the described potential aspiratory changes into account. RESULTS: Overall, in 29 (70.7%) of 41 enrolled cases PMCT and autopsy revealed the same level of aspiration. A difference of one level between PMCT and autopsy resulted for 5 (12.2%) of the remaining 12 cases. More than one level difference between both methods resulted for 7 cases (17.2%). Autopsy described no signs of aspiration in 10 cases, compared to 31 cases with reported blood aspiration. In contrast, PMCT revealed no signs of blood aspiration in 15 cases whereas 26 cases were rated as positive for signs of aspiration in the major airways. In 18 of these 26 cases considered positive for blood aspiration by autopsy and PMCT, clear signs of aspiration signs were also described bilaterally by both methods. CONCLUSIONS: The presented study provides evidence for the assumption that PMCT seems to be helpful in the detection of blood aspiration in cases of deadly head gunshots. In conclusion, it seems reasonable to suggest performing PMCT additionally to traditional postmortem exams in cases of suspected aspiration to rule out false-negative cases and to possibly allow for a more detailed and rather evidence based examination reconnoitering the cause of death. However, the adequate use of PMCT in this context needs further evaluation and the definition of an objective scale for aspiration detection on PMCT needs to be established in future studies

Entanglement in solvable many-particle models

Lecture notes for the Brazilian School on Statistical Mechanics, Natal, Brazil, July 2011. The five lectures introduce to the description of entanglement in many-particle systems and review the ground-state entanglement features of standard solvable lattice models. This is done using a thermodynamic formulation in which the eigenvalue spectrum of a certain Hamiltonian determines the entanglement properties. The methods to obtain it are discussed and results, both analytical and numerical, for various cases including time evolution are presented.Comment: 44 pages, 30 figures. Lecture notes for the Brazilian School on Statistical Mechanics, Natal, July 2011. For the Brazilian Journal of Physic

Spin-orbit coupling and electron spin resonance for interacting electrons in carbon nanotubes

We review the theoretical description of spin-orbit scattering and electron spin resonance in carbon nanotubes. Particular emphasis is laid on the effects of electron-electron interactions. The spin-orbit coupling is derived, and the resulting ESR spectrum is analyzed both using the effective low-energy field theory and numerical studies of finite-size Hubbard chains and two-leg Hubbard ladders. For single-wall tubes, the field theoretical description predicts a double peak spectrum linked to the existence of spin-charge separation. The numerical analysis basically confirms this picture, but also predicts additional features in finite-size samples.Comment: 19 pages, 4 figures, invited review article for special issue in J. Phys. Cond. Mat., published versio

Universal corrections to scaling for block entanglement in spin-1/2 XX chains

We consider the R\'enyi entropies $S_n(\ell)$ in the one dimensional spin-1/2 Heisenberg XX chain in a magnetic field. The case n=1 corresponds to the von Neumann ``entanglement'' entropy. Using a combination of methods based on the generalized Fisher-Hartwig conjecture and a recurrence relation connected to the Painlev\'e VI differential equation we obtain the asymptotic behaviour, accurate to order ${\cal O}(\ell^{-3})$, of the R\'enyi entropies $S_n(\ell)$ for large block lengths $\ell$. For n=1,2,3,10 this constitutes the 3,6,10,48 leading terms respectively. The o(1) contributions are found to exhibit a rich structure of oscillatory behaviour, which we analyze in some detail both for finite $n$ and in the limit $n\to\infty$.Comment: 25 pages, 5 figure