GOLDSTONE THEOREM AND JAHN-TELLER EFFECT

The Goldstone theorem requires that a many-body system with broken symmetry has an excitation branch, whose frequency tends to zero in the limit of infinite wavelength. We treat a system where the broken symmetry comes from the terms which give rise to the Jahn-Teller effect. Both the excitation branches we discuss in detail have finite frequencies at infinite wavelength when there is no Jahn-Teller term; the introduction of this term forces one branch to have zero frequency at infinite wavelength, in agreement with the Goldstone theorem The main point of this paper is this striking illustration of Goldstone's conjecture. Some of the simpler features of the excitation branches are discussed, they do not appear to have been treated in detail in the literature. Systems of ions in twofold degenerate E ground states may exhibit such excitations, which will have a characteristic velocity considerably less than that of sound

Quantum Phase and Quantum Phase Operators: Some Physics and Some History

After reviewing the role of phase in quantum mechanics, I discuss, with the aid of a number of unpublished documents, the development of quantum phase operators in the 1960's. Interwoven in the discussion are the critical physics questions of the field: Are there (unique) quantum phase operators and are there quantum systems which can determine their nature? I conclude with a critique of recent proposals which have shed new light on the problem.Comment: 19 pages, 2 Figs. taken from published articles, LaTeX, to be published in Physica Scripta, Los Alamos preprint LA-UR-92-352

Acute Cardiovascular Manifestations in 286 Children With Multisystem Inflammatory Syndrome Associated With COVID-19 Infection in Europe

Background: The aim of the study was to document cardiovascular clinical findings, cardiac imaging, and laboratory markers in children presenting with the novel multisystem inflammatory syndrome associated with coronavirus disease 2019 (COVID-19) infection. Methods: This real-time internet-based survey has been endorsed by the Association for European Paediatric and Congenital Cardiologists Working Groups for Cardiac Imaging and Cardiovascular Intensive Care. Children 0 to 18 years of age admitted to a hospital between February 1 and June 6, 2020, with a diagnosis of an inflammatory syndrome and acute cardiovascular complications were included. Results: A total of 286 children from 55 centers in 17 European countries were included. The median age was 8.4 years (interquartile range, 3.8-12.4 years) and 67% were boys. The most common cardiovascular complications were shock, cardiac arrhythmias, pericardial effusion, and coronary artery dilatation. Reduced left ventricular ejection fraction was present in over half of the patients, and a vast majority of children had raised cardiac troponin when checked. The biochemical markers of inflammation were raised in most patients on admission: elevated C-reactive protein, serum ferritin, procalcitonin, N-terminal pro B-type natriuretic peptide, interleukin-6 level, and D-dimers. There was a statistically significant correlation between degree of elevation in cardiac and biochemical parameters and the need for intensive care support (P<0.05). Polymerase chain reaction for severe acute respiratory syndrome coronavirus 2 was positive in 33.6%, whereas immunoglobulin M and immunoglobulin G antibodies were positive in 15.7% cases and immunoglobulin G in 43.6% cases, respectively, when checked. One child in the study cohort died. Conclusions: Cardiac involvement is common in children with multisystem inflammatory syndrome associated with the Covid-19 pandemic. The majority of children have significantly raised levels of N-terminal pro B-type natriuretic peptide, ferritin, D-dimers, and cardiac troponin in addition to high C-reactive protein and procalcitonin levels. In comparison with adults with COVID-19, mortality in children with multisystem inflammatory syndrome associated with COVID-19 is uncommon despite multisystem involvement, very elevated inflammatory markers, and the need for intensive care support.info:eu-repo/semantics/publishedVersio