Complete Characterization of the Ground Space Structure of Two-Body Frustration-Free Hamiltonians for Qubits

The problem of finding the ground state of a frustration-free Hamiltonian carrying only two-body interactions between qubits is known to be solvable in polynomial time. It is also shown recently that, for any such Hamiltonian, there is always a ground state that is a product of single- or two-qubit states. However, it remains unclear whether the whole ground space is of any succinct structure. Here, we give a complete characterization of the ground space of any two-body frustration-free Hamiltonian of qubits. Namely, it is a span of tree tensor network states of the same tree structure. This characterization allows us to show that the problem of determining the ground state degeneracy is as hard as, but no harder than, its classical analog.Comment: 5pages, 3 figure

Dynamical delocalization of Majorana edge states by sweeping across a quantum critical point

We study the adiabatic dynamics of Majorana fermions across a quantum phase transition. We show that the Kibble-Zurek scaling, which describes the density of bulk defects produced during the critical point crossing, is not valid for edge Majorana fermions. Therefore, the dynamics governing an edge state quench is nonuniversal and depends on the topological features of the system. Besides, we show that the localization of Majorana fermions is a necessary ingredient to guaranty robustness against defect production.Comment: Submitted to the Special Issue on "Dynamics and Thermalization in Isolated Quantum Many-Body Systems" in New Journal of Physics. Editors:M. Cazalilla, M. Rigol. New references and some typos correcte

Simvastatin improves the sexual health-related quality of life in men aged 40 years and over with erectile dysfunction : Additional data from the Erectile Dysfunction and Statin trial

© 2014 Trivedi et al. 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 credited.Background: Erectile dysfunction is prevalent in men over 40 years, affecting their quality of life and that of their partners. The aims of this study were:a)To evaluate the internal reliability of the male erectile dysfunction specific quality of life (MED-QoL) scale and explore its factor structure.b)To evaluate the effect of simvastatin on subscales of the MED-QoL in men over forty years with erectile dysfunction. Methods: This is a double blind randomised controlled trial of 40 mg simvastatin or placebo given once daily for six months to men over forty years with untreated erectile dysfunction, who were not at high cardiovascular risk and were not on anti-hypertensive or lipid-lowering medication. 173 eligible men were recruited from 10 general practices in East of England. Data were collected at two points over 30 weeks. We report on the factor structure of MED-QoL, the internal reliability of the scale and the derived subscales, and the effect of simvastatin on MED-QoL subscales. Results: An initial analysis of the MED-QoL items suggested that a number of items should be removed (MED-QoL-R). Exploratory factor analysis identified three subscales within the MED-QoL-R which accounted for 96% of the variance, related to feelings of Control, initiating Intimacy, and Emotional response to erectile dysfunction. The alpha value for the revised scale (MED-Qol-R) was >0.95 and exceeded .82 for each subscale. Regression analysis showed that patients in the placebo group experienced a significantly reduced feeling of Control over erectile dysfunction than those in the statin group. Those in the placebo group had significantly lower Emotional response than those in the statin group at the close of trial, but there was no significant treatment effect on Intimacy. Conclusions: Our revised MED-QoL-R identified three subscales. Secondary analysis showed a significant improvement in sexual health related quality of life, specifically in relation to perception of control and emotional health in men with untreated erectile dysfunction given 40 mg simvastatin for six months. Trial registration: Current Controlled Trials ISRCTN66772971.Peer reviewe

Whole blood long-chain n-3 fatty acids as a measure of fish oil compliance in children with acute lymphoblastic leukemia: a pilot study

Long-chain n-3 fatty acids (n-3 LCPUFA) may prevent chemotherapy-induced hyperlipidemia in children with acute lymphoblastic leukemia (ALL). However, compliance could be a problem and intake-biomarker correlations may be affected by bodyweight and blood transfusions. We assessed whole blood n-3 LCPUFA three times during the first 83 days of treatment in six 1-17-year-old children with ALL, who received 2.4-4.9 g/d n-3 LCPUFA depending on bodyweight. Mean compliance was 73%, which resulted in a 2.5-fold increase in blood n-3 LCPUFA irrespective of blood transfusions. The correlation between relative blood content of n-3 LCPUFA and intake in g/d across the study period was strong (r=0.76, p=0.001). When n-3 LCPUFA was expressed in absolute concentrations and intake per kg bodyweight the correlation decreased (r=0.39, p=0.164) and was driven by baseline values. Thus, relative content of n-3 LCPUFA in blood reflects fish oil compliance in children with ALL despite blood transfusions and differences in bodyweight

On quantum mean-field models and their quantum annealing

This paper deals with fully-connected mean-field models of quantum spins with p-body ferromagnetic interactions and a transverse field. For p=2 this corresponds to the quantum Curie-Weiss model (a special case of the Lipkin-Meshkov-Glick model) which exhibits a second-order phase transition, while for p>2 the transition is first order. We provide a refined analytical description both of the static and of the dynamic properties of these models. In particular we obtain analytically the exponential rate of decay of the gap at the first-order transition. We also study the slow annealing from the pure transverse field to the pure ferromagnet (and vice versa) and discuss the effect of the first-order transition and of the spinodal limit of metastability on the residual excitation energy, both for finite and exponentially divergent annealing times. In the quantum computation perspective this quantity would assess the efficiency of the quantum adiabatic procedure as an approximation algorithm.Comment: 44 pages, 23 figure

Close encounters: Analyzing how social similarity and propinquity contribute to strong network connections.

Models of network formation emphasize the importance of social similarity and propinquity in producing strong interpersonal connections. The positive effect each factor can have on tie strength has been documented across a number of studies, and yet we know surprisingly very little about how the two factors combine to produce strong ties. Being in close proximity could either amplify or dampen the positive effect that social similarity can have on tie strength. Data on tie strength among teachers working in five public schools were analyzed to shed light on this theoretical question. The empirical results indicate that teachers who were similar in age were more likely to be connected by a strong tie, especially teachers for whom age similarity was more likely to be salient. Moreover, teachers who took breaks at the same time or who had classrooms on the same floor communicated more frequently and felt more emotionally attached. Among the public school teachers, propinquity amplified the positive effect that age similarity had on tie strength. The strongest network connections occurred among age-similar teachers who had classrooms on the same floor. The empirical results illustrate the value of considering how social similarity and propinquity contribute to strong ties independently and when combined with each other