Tensor product representation of topological ordered phase: necessary symmetry conditions

The tensor product representation of quantum states leads to a promising variational approach to study quantum phase and quantum phase transitions, especially topological ordered phases which are impossible to handle with conventional methods due to their long range entanglement. However, an important issue arises when we use tensor product states (TPS) as variational states to find the ground state of a Hamiltonian: can arbitrary variations in the tensors that represent ground state of a Hamiltonian be induced by local perturbations to the Hamiltonian? Starting from a tensor product state which is the exact ground state of a Hamiltonian with $\mathbb{Z}_2$ topological order, we show that, surprisingly, not all variations of the tensors correspond to the variation of the ground state caused by local perturbations of the Hamiltonian. Even in the absence of any symmetry requirement of the perturbed Hamiltonian, one necessary condition for the variations of the tensors to be physical is that they respect certain $\mathbb{Z}_2$ symmetry. We support this claim by calculating explicitly the change in topological entanglement entropy with different variations in the tensors. This finding will provide important guidance to numerical variational study of topological phase and phase transitions. It is also a crucial step in using TPS to study universal properties of a quantum phase and its topological order.Comment: 10 pages, 6 figure

Nuclear symmetry energy and the r-mode instability of neutron stars

We analyze the role of the symmetry energy slope parameter $L$ on the {\it r}-mode instability of neutron stars. Our study is performed using both microscopic and phenomenological approaches of the nuclear equation of state. The microscopic ones include the Brueckner--Hartree--Fock approximation, the well known variational equation of state of Akmal, Pandharipande and Ravenhall, and a parametrization of recent Auxiliary Field Diffusion Monte Carlo calculations. For the phenomenological approaches, we use several Skyrme forces and relativisic mean field models. Our results show that the {\it r}-mode instability region is smaller for those models which give larger values of $L$. The reason is that both bulk ($\xi$) and shear ($\eta$) viscosities increase with $L$ and, therefore, the damping of the mode is more efficient for the models with larger $L$. We show also that the dependence of both viscosities on $L$ can be described at each density by simple power-laws of the type $\xi=A_{\xi}L^{B_\xi}$ and $\eta=A_{\eta}L^{B_\eta}$. Using the measured spin frequency and the estimated core temperature of the pulsar in the low-mass X-ray binary 4U 1608-52, we conclude that observational data seem to favor values of $L$ larger than $\sim 50$ MeV if this object is assumed to be outside the instability region, its radius is in the range $11.5-12$($11.5-13$) km, and its mass $1.4M_\odot$($2M_\odot$). Outside this range it is not possible to draw any conclusion on $L$ from this pulsar.Comment: 10 pages, 6 figures. Version published in Physical Review

Comparison of embedded and added motor imagery training in patients after stroke: Study protocol of a randomised controlled pilot trial using a mixed methods approach

Copyright @ 2009 Schuster et al; licensee BioMed Central Ltd. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.Background: Two different approaches have been adopted when applying motor imagery (MI) to stroke patients. MI can be conducted either added to conventional physiotherapy or integrated within therapy sessions. The proposed study aims to compare the efficacy of embedded MI to an added MI intervention. Evidence from pilot studies reported in the literature suggests that both approaches can improve performance of a complex motor skill involving whole body movements, however, it remains to be demonstrated, which is the more effective one.Methods/Design: A single blinded, randomised controlled trial (RCT) with a pre-post intervention design will be carried out. The study design includes two experimental groups and a control group (CG). Both experimental groups (EG1, EG2) will receive physical practice of a clinical relevant motor task ('Going down, laying on the floor, and getting up again') over a two week intervention period: EG1 with embedded MI training, EG2 with MI training added after physiotherapy. The CG will receive standard physiotherapy intervention and an additional control intervention not related to MI.The primary study outcome is the time difference to perform the task from pre to post-intervention. Secondary outcomes include level of help needed, stages of motor task completion, degree of motor impairment, balance ability, fear of falling measure, motivation score, and motor imagery ability score. Four data collection points are proposed: twice during baseline phase, once following the intervention period, and once after a two week follow up. A nested qualitative part should add an important insight into patients' experience and attitudes towards MI. Semi-structured interviews of six to ten patients, who participate in the RCT, will be conducted to investigate patients' previous experience with MI and their expectations towards the MI intervention in the study. Patients will be interviewed prior and after the intervention period.Discussion: Results will determine whether embedded MI is superior to added MI. Findings of the semi-structured interviews will help to integrate patient's expectations of MI interventions in the design of research studies to improve practical applicability using MI as an adjunct therapy technique

Land/Homeland, Story/History: the social landscapes of the Southern Levant from Alexander to Augustus

This material has been published in revised form in The Social Archaeology of the Levant from Prehistory to the Present edited by Assaf Yasur-Landau, Eric H. Cline, and Yorke Rowan https://doi.org/10.1017/9781316661468.024. This version is free to view and download for private research and study only. Not for re-distribution or re-use. © Cambridge University PressThe Hellenistic era opens with Alexander the Great’s triumph over Achaemenid Persia, an event that inaugurates a millennium of western political hegemony over the Levant and paves the way for an infusion of western cultural ideas. I examine the social repercussions of this juncture of politics and culture for five self-identifying ethnoi within the region: Phoenicians (meaning Tyrians and Sidonians), Samaritans, Judeans, Idumeans, and Nabateans. I consider physical and written evidence as reflections of agency, opportunity, status, and authority, in order to reconstruct how people defined and presented themselves, and how they jockeyed for position and security in a crowded region and a volatile world. Fortunes fluctuated along with changes in imperial rule. The Ptolemies instituted a rapacious system of resource extraction, under which only the most nimble or removed kept their footing (i.e., Phoenicians, Nabateans). The Seleucids followed in the more magnanimous footsteps of the Achaemenids, offering a measure of economic and legal autonomy, an approach that placated some (e.g., Samaritans) and empowered others (e.g., Judeans). As Seleucid control weakened, groups used various means to claim status and authority. Samaritans, Judeans, and Idumeans deployed history and geography; Phoenicians and Nabateans depended on economic connections and cultural currency. Waning imperial powers in the later second century BCE left the region’s ethnoi effectively autonomous. Phoenicians and Nabateans became wealthy cosmopolitans connected to Mediterranean markets. Judeans unleashed an aggressive program of territorial acquisition, first successfully against Idumeans and Samaritans, then less so against Tyrians and Nabateans. Contemporary writers turned these events into historical narratives – divinely countenanced (1 Maccabees, Dead Sea Scrolls) vs. opportunistic circumstance (2 Maccabees, Tacitus, Josephus). These accounts offered people differing templates by which to situate themselves in place and history – templates ill-suited for co-existence. By the time Roman authorities established their imperial presence here in the mid-first century BCE, the social landscape was mined and ready to erupt.Accepted manuscrip

Das Levitenhaus : häusliche Ceremonial- u. Ritual-Gesetze, das Schema-Lesen, Schaufäden, Denkriemen, Hebe am Teige, Lichtanzünden, u. das Fleischsalzen enthaltend ; a. d. Hebr. bearb. u. mit Erklärungen versehen

Isaac Landa

Das Levitenhaus : häusliche Ceremonial- u. Ritual-Gesetze, das Schema-Lesen, Schaufäden u. Denkriemen enthaltend ; Abhandlung in deutscher Sprache, a. d. Hebr. bearb. u. mit Erklärungen versehen

Isaac Landa

Masekhet Sofrim : ʻim beʾur Miḳra sofrim ṿe-ʻIṭur sofrim /

וו/2ז־ ס 55 1862 XXVCPLSHThis book is from the private library of Mattityahu Strashun.BSLW YIVOL Clean-up ProjectDigital imag