Energy correlations for a random matrix model of disordered bosons

Linearizing the Heisenberg equations of motion around the ground state of an interacting quantum many-body system, one gets a time-evolution generator in the positive cone of a real symplectic Lie algebra. The presence of disorder in the physical system determines a probability measure with support on this cone. The present paper analyzes a discrete family of such measures of exponential type, and does so in an attempt to capture, by a simple random matrix model, some generic statistical features of the characteristic frequencies of disordered bosonic quasi-particle systems. The level correlation functions of the said measures are shown to be those of a determinantal process, and the kernel of the process is expressed as a sum of bi-orthogonal polynomials. While the correlations in the bulk scaling limit are in accord with sine-kernel or GUE universality, at the low-frequency end of the spectrum an unusual type of scaling behavior is found.Comment: 20 pages, 3 figures, references adde

Quantum chaos in QCD at finite temperature

We study complete eigenvalue spectra of the staggered Dirac matrix in quenched QCD on a $6^3\times 4$ lattice. In particular, we investigate the nearest-neighbor spacing distribution $P(s)$ for various values of $\beta$ both in the confinement and deconfinement phase. In both phases except far into the deconfinement region, the data agree with the Wigner surmise of random matrix theory which is indicative of quantum chaos. No signs of a transition to Poisson regularity are found, and the reasons for this result are discussed.Comment: 3 pages, 6 figures (included), poster presented by R. Pullirsch at "Lattice 97", to appear in the proceeding

Topics, trends, and sentiments of Tweets about the COVID-19 pandemic: temporal infoveillance study

With restricted movements and stay-at-home orders due to COVID-19 pandemic, social media platforms like Twitter have become an outlet for users to express their concerns, opinions and feelings about the pandemic. Individuals, health agencies and governments are using Twitter to communicate about COVID-19. This research builds on the emergent stream of studies to examine COVID-19 related English tweets covering a time period from Jan 1, 2020 to May 9, 2020. We perform a temporal assessment and examine variations in the topics and sentiment-scores to uncover key trends. To examine key themes and topics from COVID-19 related English tweets posted by individuals, and to explore the trends and variations in how the COVID-19 related tweets, key topics and associated sentiments changed over a period of time before and after the disease was declared as pandemic. Combining data from two publicly available COVID-19 tweet datasets with our own search, we compiled a dataset of 13.9 million COVID-19 related English tweets made by individuals. We use Guided latent Dirichlet allocation (LDA) to infer themes and topics underlying the tweets, and use VADER sentiment analysis to compute sentiment scores and examine weekly trends for 17 weeks. Topic modelling yielded 26 topics, grouped into 10 broader themes underlying the COVID-19 tweets. 20.51% of tweets were about COVID-19's impact of economy and markets, followed by spread and growth in cases (15.45%), treatment and recovery (13.14%), impact on healthcare sector (11.40%), and governments' response (11.19%). Average compound sentiment scores were found to be negative throughout the time period of our examination for spread and growth of cases, symptoms, racism, source of the outbreak and political impacts of COVID-19. In contrast, we saw a reversal of sentiments from negative to positive for prevention, impact on economy and market, governments' response, impact on healthcare industry, treatment and recovery. Identification of dominant themes, topics, sentiments and changing trends about COVID-19 pandemic can help governments, healthcare agencies and policy makers to frame appropriate responses to prevent and control the spread of pandemic

Smoothing of sandpile surfaces after intermittent and continuous avalanches: three models in search of an experiment

We present and analyse in this paper three models of coupled continuum equations all united by a common theme: the intuitive notion that sandpile surfaces are left smoother by the propagation of avalanches across them. Two of these concern smoothing at the `bare' interface, appropriate to intermittent avalanche flow, while one of them models smoothing at the effective surface defined by a cloud of flowing grains across the `bare' interface, which is appropriate to the regime where avalanches flow continuously across the sandpile.Comment: 17 pages and 26 figures. Submitted to Physical Review

Leading Large N Modification of QCD_2 on a Cylinder by Dynamical Fermions

We consider 2-dimensional QCD on a cylinder, where space is a circle. We find the ground state of the system in case of massless quarks in a $1/N$ expansion. We find that coupling to fermions nontrivially modifies the large $N$ saddle point of the gauge theory due to the phenomenon of `decompactification' of eigenvalues of the gauge field. We calculate the vacuum energy and the vacuum expectation value of the Wilson loop operator both of which show a nontrivial dependence on the number of quarks flavours at the leading order in $1/N$.Comment: 24 pages, TIFR-TH-94/3

A trivial observation on time reversal in random matrix theory

It is commonly thought that a state-dependent quantity, after being averaged over a classical ensemble of random Hamiltonians, will always become independent of the state. We point out that this is in general incorrect: if the ensemble of Hamiltonians is time reversal invariant, and the quantity involves the state in higher than bilinear order, then we show that the quantity is only a constant over the orbits of the invariance group on the Hilbert space. Examples include fidelity and decoherence in appropriate models.Comment: 7 pages 3 figure

Connes-Lott model building on the two-sphere

In this work we examine generalized Connes-Lott models on the two-sphere. The Hilbert space of the continuum spectral triple is taken as the space of sections of a twisted spinor bundle, allowing for nontrivial topological structure (magnetic monopoles). The finitely generated projective module over the full algebra is also taken as topologically non-trivial, which is possible over $S^2$. We also construct a real spectral triple enlarging this Hilbert space to include "particle" and "anti-particle" fields.Comment: 57 pages, LATE

Searching and fixating: scale-invariance vs. characteristic timescales in attentional processes

In an experiment involving semantic search, the visual movements of sample populations subjected to visual and aural input were tracked in a taskless paradigm. The probability distributions of saccades and fixations were obtained and analyzed. Scale-invariance was observed in the saccadic distributions, while the fixation distributions revealed the presence of a characteristic (attentional) time scale for literate subjects. A detailed analysis of our results suggests that saccadic eye motions are an example of Levy, rather than Brownian, dynamics.Comment: Accepted to Europhysics Letters (2011

Assessment of the feasibility of an ultra-low power, wireless digital patch for the continuous ambulatory monitoring of vital signs.

BACKGROUND AND OBJECTIVES: Vital signs are usually recorded at 4–8 h intervals in hospital patients, and deterioration between measurements can have serious consequences. The primary study objective was to assess agreement between a new ultra-low power, wireless and wearable surveillance system for continuous ambulatory monitoring of vital signs and a widely used clinical vital signs monitor. The secondary objective was to examine the system's ability to automatically identify and reject invalid physiological data. SETTING: Single hospital centre. PARTICIPANTS: Heart and respiratory rate were recorded over 2 h in 20 patients undergoing elective surgery and a second group of 41 patients with comorbid conditions, in the general ward. OUTCOME MEASURES: Primary outcome measures were limits of agreement and bias. The secondary outcome measure was proportion of data rejected. RESULTS: The digital patch provided reliable heart rate values in the majority of patients (about 80%) with normal sinus rhythm, and in the presence of abnormal ECG recordings (excluding aperiodic arrhythmias such as atrial fibrillation). The mean difference between systems was less than ±1 bpm in all patient groups studied. Although respiratory data were more frequently rejected as invalid because of the high sensitivity of impedance pneumography to motion artefacts, valid rates were reported for 50% of recordings with a mean difference of less than ±1 brpm compared with the bedside monitor. Correlation between systems was statistically significant (p<0.0001) for heart and respiratory rate, apart from respiratory rate in patients with atrial fibrillation (p=0.02). CONCLUSIONS: Overall agreement between digital patch and clinical monitor was satisfactory, as was the efficacy of the system for automatic rejection of invalid data. Wireless monitoring technologies, such as the one tested, may offer clinical value when implemented as part of wider hospital systems that integrate and support existing clinical protocols and workflows

Spatial correlations in chaotic nanoscale systems with spin-orbit coupling

We investigate the statistical properties of wave functions in chaotic nanostructures with spin-orbit coupling (SOC), focussing in particular on spatial correlations of eigenfunctions. Numerical results from a microscopic model are compared with results from random matrix theory in the crossover from the gaussian orthogonal to the gaussian symplectic ensembles (with increasing SOC); one- and two-point distribution functions were computed to understand the properties of eigenfunctions in this crossover. It is found that correlations of wave function amplitudes are suppressed with SOC; nevertheless, eigenfunction correlations play a more important role in the two-point distribution function(s), compared to the case with vanishing SOC. Experimental consequences of our results are discussed.Comment: Submitted to PR