Mathematical Structure of Magnons in Quantum Ferromagnets

We provide the mathematical structure and a simple, transparent and rigorous derivation of the magnons as elementary quasi-particle excitations at low temperatures and in the infinite spin limit for a large class of Heisenberg ferromagnets. The magnon canonical variables are obtained as fluctuation operators in the infinite spin limit. Their quantum character is governed by the size of the magnetization

Non-Extensive Bose-Einstein Condensation Model

The imperfect Boson gas supplemented with a gentle repulsive interaction is completely solved. In particular it is proved that it has non-extensive Bose-Einstein condensation, i.e., there is condensation without macroscopic occupation of the ground state (k=0) level

BEC for a Coupled Two-type Hard Core Bosons Model

We study a solvable model of two types hard core Bose particles. A complete analysis is given of its equilibrium states including the proof of existence of Bose-Einstein condensation. The plasmon frequencies and the quantum normal modes corresponding to these frequencies are rigorously constructed. In particular we show a two-fold degeneracy of these frequencies. We show that all this results from spontaneous gauge symmetry breakdown

Transport of interface states in the Heisenberg chain

We demonstrate the transport of interface states in the one-dimensional ferromagnetic Heisenberg model by a time dependent magnetic field. Our analysis is based on the standard Adiabatic Theorem. This is supplemented by a numerical analysis via the recently developed time dependent DMRG method, where we calculate the adiabatic constant as a function of the strength of the magnetic field and the anisotropy of the interaction.Comment: minor revision, final version; 13 pages, 4 figure

Neuropsychological deficits in disordered screen use behaviours : A systematic review and meta-analysis

Over the last few decades, excessive and disordered screen use has become more prevalent, prompting investigations into its associated consequences. The extent to which disordered screen use behaviours impact neuropsychological functioning has been reportedly mixed and at times inconsistent. This review sought to synthesise the literature and estimate the magnitude of overall cognitive impairment across a wide range of disordered screen use behaviours. We also sought to determine the cognitive domains most impacted, and whether the observed impairments were moderated by the classification of screen-related behaviours (i.e., Internet or gaming) or the format of cognitive test administration (i.e., paper-and-pencil or computerised). A systematic search of databases (Embase, PsycINFO, MEDLINE) identified 43 cross-sectional articles that assessed neuropsychological performance in disordered screen use populations, 34 of which were included in the meta-analysis. A random-effects meta-analysis revealed significant small/medium (g = .38) cognitive deficits for individuals with disordered screen use behaviours relative to controls. The most affected cognitive domain with a significant medium effect size (g = .50) was attention and focus followed by a significant reduction in executive functioning (g = .31). The classification of disordered screen use behaviours into Internet or gaming categories or the format of cognitive testing did not moderate these deficits. Additionally, excluding disordered social media use in an exploratory analysis had little effect on the observed outcomes. This study highlights a number of methodological considerations that may have contributed to disparate findings and shows that disordered screen use can significantly impact cognitive performance. Recommendations for future research are also discussed. Data for this study can be found at https://osf.io/upeha/

Module networks revisited: computational assessment and prioritization of model predictions

The solution of high-dimensional inference and prediction problems in computational biology is almost always a compromise between mathematical theory and practical constraints such as limited computational resources. As time progresses, computational power increases but well-established inference methods often remain locked in their initial suboptimal solution. We revisit the approach of Segal et al. (2003) to infer regulatory modules and their condition-specific regulators from gene expression data. In contrast to their direct optimization-based solution we use a more representative centroid-like solution extracted from an ensemble of possible statistical models to explain the data. The ensemble method automatically selects a subset of most informative genes and builds a quantitatively better model for them. Genes which cluster together in the majority of models produce functionally more coherent modules. Regulators which are consistently assigned to a module are more often supported by literature, but a single model always contains many regulator assignments not supported by the ensemble. Reliably detecting condition-specific or combinatorial regulation is particularly hard in a single optimum but can be achieved using ensemble averaging.Comment: 8 pages REVTeX, 6 figure

The Canonical Perfect Bose Gas in Casimir Boxes

We study the problem of Bose-Einstein condensation in the perfect Bose gas in the canonical ensemble, in anisotropically dilated rectangular parallelpipeds (Casimir boxes). We prove that in the canonical ensemble for these anisotropic boxes there is the same type of generalized Bose-Einstein condensation as in the grand-canonical ensemble for the equivalent geometry. However the amount of condensate in the individual states is different in some cases and so are the fluctuations.Comment: 23 page

Quantum spin systems at positive temperature

We develop a novel approach to phase transitions in quantum spin models based on a relation to their classical counterparts. Explicitly, we show that whenever chessboard estimates can be used to prove a phase transition in the classical model, the corresponding quantum model will have a similar phase transition, provided the inverse temperature $\beta$ and the magnitude of the quantum spins \CalS satisfy \beta\ll\sqrt\CalS. From the quantum system we require that it is reflection positive and that it has a meaningful classical limit; the core technical estimate may be described as an extension of the Berezin-Lieb inequalities down to the level of matrix elements. The general theory is applied to prove phase transitions in various quantum spin systems with \CalS\gg1. The most notable examples are the quantum orbital-compass model on $\Z^2$ and the quantum 120-degree model on $\Z^3$ which are shown to exhibit symmetry breaking at low-temperatures despite the infinite degeneracy of their (classical) ground state.Comment: 47 pages, version to appear in CMP (style files included