Ground states of a frustrated quantum spin chain with long-range interactions

The ground state of a spin-1/2 Heisenberg chain with both frustration and long-range interactions is studied using Lanczos exact diagonalization. The evolution of the well known dimerization transition of the system with short-range frustrated interactions (the J1-J2 chain) is investigated in the presence of additional unfrustrated interactions decaying with distance as 1/r^a. It is shown that the continuous (infinite-order) dimerization transition develops into a first-order transition between a long-range ordered antiferromagnetic state and a state with coexisting dimerization and critical spin correlations at wave-number k=\pi/2. The relevance of the model to real systems is discussed.Comment: 4 pages, 5 figures, final published versio

Energy and multipartite entanglement in multidimensional and frustrated spin models

We investigate the relation between the entanglement properties of a quantum state and its energy for macroscopic spin models. To this aim, we develop a general method to compute energy bounds for states without certain forms of multipartite entanglement. Violation of these bounds implies the presence of these types of multipartite entanglement. As examples, we investigate the Heisenberg model in different dimensions, the Ising model and the XX model in the presence of a magnetic field. Finally, by studying the Heisenberg model on a triangular lattice, we demonstrate that our techniques can be applied also to frustrated systems.Comment: 9 pages, 6 figures, v2: small change

Electro-disintegration following beta-decay

I show that the disintegration of weakly-bound nuclei and the ionization of weakly-bound atomic electrons due to their interaction with leptons from beta decay is a negligible effect.Comment: 3 pages, 1 figure, to be published in the Physical Review

Hardcore dimer aspects of the SU(2) Singlet wavefunction

We demonstrate that any SU(2) singlet wavefunction can be characterized by a set of Valence Bond occupation numbers, testing dimer presence/vacancy on pairs of sites. This genuine quantum property of singlet states (i) shows that SU(2) singlets share some of the intuitive features of hardcore quantum dimers, (ii) gives rigorous basis for interesting albeit apparently ill-defined quantities introduced recently in the context of Quantum Magnetism or Quantum Information to measure respectively spin correlations and bipartite entanglement and, (iii) suggests a scheme to define consistently a wide family of quantities analogous to high order spin correlation. This result is demonstrated in the framework of a general functional mapping between the Hilbert space generated by an arbitrary number of spins and a set of algebraic functions found to be an efficient analytical tool for the description of quantum spins or qubits systems.Comment: 5 pages, 2 figure

Ground state projection of quantum spin systems in the valence bond basis

A Monte Carlo method for quantum spin systems is formulated in the basis of valence bond (singlet pair) states. The non-orthogonality of this basis allows for an efficient importance-sampled projection of the ground state out of an arbitrary state. The method provides access to resonating valence-bond physics, enables a direct improved estimator for the singlet-triplet gap, and extends the class of models that can be studied without negative-sign problems. As a demonstration, the valence bond distribution in the ground state of the 2D Heisenberg antiferromagnet is calculated. Generalizations of the method to fermion systems are also discussed.Comment: 4+ pages, accepted for publication in Phys. Rev. Let

Southern Route or Northern Sea Route--Whether seaworthiness impacts a ship-owners decision on what route to travel

En stor del av världens sjötransporter går mellan Asien och Europa. Idag är den södra rutten genom Suez-kanalen populärast, men efter att isen i Arktis börjat smälta har den norra rutten öppnats upp som en möjlig utmanare till den södra rutten och skeppsägare ställs nu inför ett val. Sjötransport är en riskfylld verksamhet och både den södra och den norra rutten innehåller områden med ökad risk. På den södra rutten består den ökade risken av risk för piratattacker. På den norra rutten består den ökade risken av is och hårda väderförhållanden. Syftet med denna uppsats är att undersöka om rättsliga förhållanden kan inverka på vilken rutt en skeppsägare väljer. De valda aspekterna är förutsebarhet i domstolars bedömning om ett skepp är sjövärdigt under ett kontrakt att frakta gods styrt av Hague och Hague-Visby reglerna samt under ett sjöförsäkringskontrakt styrt av den engelska sjöförsäkringslagen. I tvister under båda kontrakten är frågan om sjövärdighet av stor ekonomisk betydelse eftersom den är avgörande för ansvar för lasten och för att försäkringsersättning betalas ut. Skeppsägaren är under Hague och Hague-Visby reglerna skyldig att ha utövat due diligence för att tillse att skeppet är sjövärdigt samt under den engelska sjörösäkringslagen att han inte har kunskap om att skeppet inte är sjövärdigt. Standarden för vad som är sjövärdigt skepp, och för vad som krävs för att anses ha utövat due diligence för att tillse att skeppet är sjövärdigt sätts utifrån vad en erfaren och aktsam skeppsägare i den aktuella situationen skulle bedöma som ett sjövärdigt skepp och vad han hade gjort för att tillse att det var sjövärdigt. Det är en objektiv standard som sätts utifrån kunskap i sjötransportbranschen utifrån information i bland annat IMO-instrument. Jurister hävdar att IMO-instrument har inverkan på bedömningen av ett skepps sjövärdighet i en kontraktsrättslig tvist, i vart fall om den aktuella regeln har till syfte att försäkra att skeppet når sin destination. Domare verkar dock inte använda IMO-instrument i särskilt stor utsträckning. Det beror främst på att informationen de innehåller inte har någon direkt relevans för olyckan. Informationen i IMO-instrument är ofta för generell och innehåller inte vad som behövs för att avgöra vad som orsakade olyckan. Ett certifikat behöver inte innebära att besättningen har den kompetens och erfarenhet certifikatet anger eller att fartyget är i det skick certifikatet anger. IMO har publicerat riskspecifika rekommendationer både i förhållande till risken för piratattack och att färdas i områden med hårt väder och is. De två rekommendationerna har jämförts utifrån dess lämplighet att användas som objektiva standarder i domstolars avgörande av ett skepps sjövärdighet och följaktligen om en skeppsägare kan vara säkrare på att tillhandahålla ett sjövärdigt skepp på en av rutterna. Om en skeppsägare kan förutse att fartyget bedöms sjövärdigt vid val av en rutt, så att han inte blir ansvarig för skadat eller förlorat gods och erhåller försäkringsersättning vid skada på eller förlust av fartyget, är det ett incitament att välja den rutten. IMO;s rekommendationer i förhållande till den norra rutten är mer omfattande och mer detaljerade men saknar ett helhetsperspektiv. Certifikat utges för att bevisa att rekommendationer är uppfyllda. Den norra rutten är lämpligast i ett försäkringsmål eftersom skeppsägaren med hjälp av certifikaten kan bevisa att han trodde att fartyget var sjövärdigt. Rekommendationerna för den södra rutten är mer generella men är baserade på vad som har fungerat tidigare och har ett helhetsperspektiv. Om rekommendationerna för den södra rutten är följda torde skeppsägaren anses ha uppfyllt due diligence för sjövärdighet. Eftersom skeppsägaren bär bevisbördan i ett mål under Hague och Hague-Visby reglerna och due-diligence är en objektiv standard i motsats till under ett försäkringsmål där försäkringsgivaren bär bevisbördan och måste visa att skeppsägaren har kännedom om att skeppet inte är sjövärdigt är det viktigast att välja den rutt där due diligence lättast kan bevisas. Om förutsebarhet i den rättsliga bedömningen av sjövärdighet är avgörande bör den södra rutten väljas. Alltför stor tillit bör dock inte denna aspekten tillmätas eftersom sjövärdighet är ett vagt begrepp som aldrig är riktigt förutsebart.There are two main shipping routes between Europe and Asia, among those the Southern Route through the Suez Canal is by far the most popular route. Due to a decrease in Arctic sea ice, the Northern Sea Route have opened up and is expected to become a viable alternative and a possible competitor to the Southern Route. The purpose of this essay is to contribute by advising ship-owners on what route they should use from a legal perspective. Both routes have their specific risk, the Southern Route by piracy and the Northern Route by harsh weather conditions, ice and floating icebergs. Both hazards are such that no matter how much precaution is taken, casualties will occur and legal issues on who will be liable for damage and loss will arise and referred to dispute resolution. This thesis is limited to whether certainty in providing a vessel that the court will deem seaworthy differs between the two routes and whether it is a relevant aspect to take into account. Seaworthiness derives from the law merchant, it is an implied obligation in contracts of affreightment by common law, an implied warranty in insurance policies and explicitly inserted in most contracts. This thesis will be limited to Hull Insurance regulated in s 39(5) Marine Insurance Act 1906 United Kingdome (‘MIA’) and Bills of Lading (‘BOL’) mandatory regulated by the Hague and the Hague-Visby Rules. Under a Hull Insurance the insurer will be exempted from liability to indemnify the assured for loss if the loss is attributable to unseaworthiness to which the assured is privy. Under the Hague and the Hague-Visby Rules the ship-owner is obliged to exercise due diligence to make the ship seaworthy before and at the beginning of the voyage. If cargo is damaged or lost the ship-owner will be liable to the cargo-owner unless he can show that he had exercised due diligence to make the ship seaworthy and the damage or loss was caused by an act for which the ship-owner is exempted from liability. The applicable test to determine if a vessel is seaworthy and if due diligence has been exercised to make the ship seaworthy is whether a prudent ship-owner knowing in the particular ship-owners place would deem the vessel seaworthy and have done what a prudent ship-owner would have done to ensure it´s seaworthiness. The tests are objective measured against standards and knowledge in the shipping industry as a whole. Privy to seaworthiness is a subjective test, based on the ship-owners actual, or blind-eye-knowledge. Courts don´t consider objective standards that are not causative to the casualty or are not adequate because the ship-owner should have known that the ship needed better standards for the intended adventure or certain factors contained risks for defect and needed better surveillance. If there are objective standards that fit the intended voyage and adventure they are taken into account and if the ship-owner can show he complies with all standards due diligence is exercised to seaworthiness. Objective standards can show the ship-owner is not privy to seaworthiness. The International Maritime Organization (‘IMO’) guidelines are accepted as objective standards, and IMO has issued hazard-specific guidelines both in respect of piracy, harsh weather conditions and ice, the Best Management Practices for Protection against Somali based Piracy (‘BMP’) and the Guidelines for Ships Operating in Polar Waters (‘Polar guidelines’). These guidelines are different in respect of form, scope and content. By comparing the guidelines in the light of factors courts take into account in assessing seaworthiness, it has been concluded that they serve differently in seaworthiness assessments under the two contracts. The Polar guidelines are more detailed and comprehensive and certificates are issued to prove compliance in respect of the crew and the vessel and are better for the ship-owner in an insurance claim. The BMP are based on real accidents, the information is practical and more suitable as objective factors for a seaworthiness claim. If a ship-owner complies with these, he will most likely have been deemed to have exercised due diligence to seaworthiness. The insurer bears the burden of proving privy to unseaworthiness whereas the ship-owner bears the burden of proving he has exercised due diligence to seaworthiness. The claim under the BOL is therefore more difficult to succeed and the advice is for the ship-owner to travel the Southern Route. However, seaworthiness is a very broad term and relates to every aspect of the adventure; although seaworthy in relation to the specific hazard it may be unseaworthy for a general aspect. Because it is so uncertain and impossible to pre-empt what the court will decide, ship-owners should not place too great reliance on this aspect in deciding whether to travel the Southern Route or the Northern Sea Route

Placental pathology regarding inflammation and a new classification of stillbirth

Background: The incidence of stillbirth has remained almost constant during the last 2-3 decades despite obvious improvements in obstetric care. To achieve a reduction of stillbirth, better understanding of the etiology is imperative. Relevant test protocols and audit work is reported to reduce the number of unexplained cases. Classification of death can help the audit group identifying relevant etiology and causes of fetal death. Since 1954 more than 35 classification systems for perinatal death have been published but there is still no international consensus. Few studies have investigated how causes of stillbirth differ over gestational ages, with varying and conflicting results. Infection is known as an important cause of stillbirth, particularly before gestational week (gw) 28. Various infections are thought to cause different forms of inflammation/infection in placenta. Bacterial infection is supposed to give a maternal inflammatory response in the placenta; histological chorioamnionitis (CAM) followed by a histological fetal response (FIR) including vasculitis (inflammation in vessels in the placenta and/or umbilical cord) and funisitis (inflammation in the Wharton's jelly), whereas a viral infection is supposed to cause chronic villitis. Histological CAM has shown to be clearly associated to stillbirth. Method: In paper I “the Stockholm classification of stillbirth” is presented and validated regarding inter observer variability. In paper II, a cohort of all 1089 singleton pregnancies in Stockholm during a 12 year period was compared regarding primary and primary + associated cause of death, according to the classification. The cases were divided in early preterm (gw 22+0 to 28+6) and moderately preterm (gw 29+0 to 36+6) plus, term (gw 37+0 to 40+6) and post-term (gw ≥ 41+0). Two case-control studies including singleton placentas from 126 term stillborn cases and 273 live born controls (paper III) as well as 112 early preterm (gw 22+0 to 32+6) stillborn cases and 166 gestational week matched references (paper IV) were compared with focus on CAM, FIR and chronic villitis. Results: We have developed a classification, exclusive for stillbirth, consisting of 17 groups of causes of death and allowing for one primary and several associated causes if needed. Most causes are graded in probability levels (definite, probable, or possible). The validated overall agreement regarding primary cause of death was substantial. When using the classification in the 12 year cohort of stillbirth, almost 90% of cases were ascribed a cause of death. Placental abruption and preeclampsia/hypertension were both more common as cause of death among preterm stillbirths compared to the term/post-term stillbirths, who showed a higher proportion of umbilical cord complications and infection. Infection was more common in post-terms compared to term stillbirths, and in extremely preterm compared to moderately premature stillbirths. In paper III we found CAM (especially severe), chronic villitis, villous immaturity, fetus who was small for gestational age (SGA) and maternal overweight, but not vasculitis or funisitis, to be independently associated with an elevated risk for stillbirth at term. In paper IV we found SGA and “CAM without FIR”, but not “CAM with FIR,” to be independently associated with a higher risk for stillbirth at early preterm gestation. Conclusion: The Stockholm classification of stillbirth, primarily meant to be used by audit groups, has showed a low percentage of unclassifiable cases and a low inter observer variability. Knowledge about how causes of stillbirth are distributed over gestational ages could be clinically important and useful in developing strategies for prevention. Results in the case-control studies indicate that the presence of CAM, especially severe, is a risk factor for fetal death in term pregnancies whereas FIR is not. In early preterm pregnancies the presence of CAM is not a risk factor for fetal death if FIR exists, but it is a threat to the fetus if FIR does not occur. Further research is needed to clarify if the development of FIR is actually protecting the fetus from death, a finding that of course could be of great importance for the understanding of the mechanisms of stillbirth

Orbital-controlled magnetic transition between gapful and gapless phases in the Haldane system with t2g-orbital degeneracy

In order to clarify a key role of orbital degree of freedom in the spin S=1 Haldane system, we investigate ground-state properties of the t2g-orbital degenerate Hubbard model on the linear chain by using numerical techniques. Increasing the Hund's rule coupling in multi-orbital systems, in general, there occurs a transition from an antiferromagnetic to a ferromagnetic phase. We find that the antiferromagnetic phase is described as the Haldane system with spin gap, while in the ferromagnetic phase, there exists the gapless excitation with respect to orbital degree of freedom. Possible relevance of the present results to actual systems is also discussed.Comment: 4 pages, 3 figures, to appear in Phys. Rev.

Neel order in the two-dimensional S=1/2 Heisenberg Model

The existence of Neel order in the S=1/2 Heisenberg model on the square lattice at T=0 is shown using inequalities set up by Kennedy, Lieb and Shastry in combination with high precision Quantum Monte Carlo data.Comment: 4 pages, 1 figur