Reduced density matrix and entanglement in interacting quantum field theory with Hamiltonian truncation.

Entanglement is the fundamental difference between classical and quantum systems and has become one of the guiding principles in the exploration of high- and low-energy physics. The calculation of entanglement entropies in interacting quantum field theories, however, remains challenging. Here, we present the first method for the explicit computation of reduced density matrices of interacting quantum field theories using truncated Hamiltonian methods. The method is based on constructing an isomorphism between the Hilbert space of the full system and the tensor product of Hilbert spaces of sub-intervals. This naturally enables the computation of the von Neumann and arbitrary R\'enyi entanglement entropies as well as mutual information, logarithmic negativity and other measures of entanglement. Our method is applicable to equilibrium states and non-equilibrium evolution in real time. It is model independent and can be applied to any Hamiltonian truncation method that uses a free basis expansion. We benchmark the method on the free Klein-Gordon theory finding excellent agreement with the analytic results. We further demonstrate its potential on the interacting sine-Gordon model, studying the scaling of von Neumann entropy in ground states and real time dynamics following quenches of the model

Preprint arXiv: 2206.10563 Submitted on 21 Jun 2022

Theoretical understanding of the scaling of entropies and the mutual information in quantum many-body systems has led to significant advances in the research of correlated states of matter, quantum field theory, and gravity. Although there have been several experimental measurements of R\'{e}nyi and von Neumann entropies in systems with discrete degrees of freedom, the measurement of entropies between extensive intervals of continuous systems has remained elusive. In this work, we measure the von Neumann entropy of spatially extended subsystems in an ultra-cold atom simulator of one-dimensional quantum field theories. We experimentally verify one of the fundamental properties of equilibrium states of gapped quantum many-body systems, the area law of quantum mutual information. We also study the dependence of mutual information on temperature and the separation between the subsystems. Our work demonstrates the capability of ultra-cold atom simulators to measure entanglement in quantum field theories

Energy deficiency, menstrual disturbances, and low bone mass : what do exercising Australian women know about the female athlete triad?

Purpose: Prevention of the female athlete triad is essential to protect female athletes&rsquo; health. The aim of this study was to investigate the knowledge, attitudes, and behaviors of regularly exercising adult women in Australia toward eating patterns, menstrual cycles, and bone health. Methods: A total of 191 female exercisers, age 18&ndash;40 yr, engaging in &ge;2 hr/wk of strenuous activity, completed a survey. After 11 surveys were excluded (due to incomplete answers), the 180 participants were categorized into lean-build sports (n = 82; running/ athletics, triathlon, swimming, cycling, dancing, rowing), non-lean-build sports (n = 94; basketball, netball, soccer, hockey, volleyball, tennis, trampoline, squash, Australian football), or gym/fitness activities (n = 4). Results: Mean (&plusmn; SD) training volume was 9.0 &plusmn; 5.5 hr/wk, with participants competing from local up to international level. Only 10% of respondents could name the 3 components of the female athlete triad. Regardless of reported history of stress fracture, 45% of the respondents did not think that amenorrhea (absence of menses for &ge;3 months) could affect bone health, and 22% of those involved in lean-build sports would do nothing if experiencing amenorrhea (vs. 3.2% in non-lean-build sports, p = .005). Lean-build sports, history of amenorrhea, and history of stress fracture were all significantly associated with not taking action in the presence of amenorrhea (all p &lt; .005). Conclusions: Few active Australian women are aware of the detrimental effects of menstrual dysfunction on bone health. Education programs are needed to prevent the female athlete triad and ensure that appropriate actions are taken by athletes when experiencing amenorrhea.<br /

Obstacles in the optimization of bone health outcomes in the female athlete triad

Maintaining low body weight for the sake of performance and aesthetic purposes is a common feature among young girls and women who exercise on a regular basis, including elite, college and high-school athletes, members of fitness centres, and recreational exercisers. High energy expenditure without adequate compensation in energy intake leads to an energy deficiency, which may ultimately affect reproductive function and bone health. The combination of low energy availability, menstrual disturbances and low bone mineral density is referred to as the &lsquo;female athlete triad&rsquo;. Not all athletes seek medical assistance in response to the absence of menstruation for 3 or more months as some believe that long-term amenorrhoea is not harmful. Indeed, many women may not seek medical attention until they sustain a stress fracture. This review investigates current issues, controversies and strategies in the clinical management of bone health concerns related to the female athlete triad. Current recommendations focus on either increasing energy intake or decreasing energy expenditure, as this approach remains the most efficient strategy to prevent further bone health complications. However, convincing the athlete to increase energy availability can be extremely challenging. Oral contraceptive therapy seems to be a common strategy chosen by many physicians to address bone health issues in young women with amenorrhoea, although there is little evidence that this strategy improves bone mineral density in this population. Assessment of bone health itself is difficult due to the limitations of dual-energy X-ray absorptiometry (DXA) to estimate bone strength. Understanding how bone strength is affected by low energy availability, weight gain and resumption of menses requires further investigations using 3-dimensional bone imaging techniques in order to improve the clinical management of the female athlete triad. <br /

The chromatin modifying complex CoREST/LSD1 negatively regulates notch pathway during cerebral cortex development

© 2016 Wiley Periodicals, Inc. The development of the cerebral cortex is a dynamic and coordinated process in which cell division, cell death, migration, and differentiation must be highly regulated to acquire the final architecture and functional competence of the mature organ. Notch pathway is an important regulator of differentiation and it is essential to maintain neural stem cell (NSC) pool. Here, we studied the role of epigenetic modulators such as lysine-specific demethylase 1 (LSD1) and its interactor CoREST in the regulation of the Notch pathway activity during the development of the cerebral cortex. We found that CoREST and LSD1 interact in vitro with RBPJ-κ in the repressor complex and these proteins are released upon overexpression of Notch intracellular domain (NICD). We corroborated LSD1 and RBPJ-κ interaction in developing cerebral cortex and also found that LSD1 binds to the hes1 promoter. Knock-down of CoREST and LSD1 by in utero electroporation increases Hes1 express