Order in de Broglie - Bohm quantum mechanics

A usual assumption in the so-called {\it de Broglie - Bohm} approach to quantum dynamics is that the quantum trajectories subject to typical `guiding' wavefunctions turn to be quite irregular, i.e. {\it chaotic} (in the dynamical systems' sense). In the present paper, we consider mainly cases in which the quantum trajectories are {\it ordered}, i.e. they have zero Lyapunov characteristic numbers. We use perturbative methods to establish the existence of such trajectories from a theoretical point of view, while we analyze their properties via numerical experiments. Using a 2D harmonic oscillator system, we first establish conditions under which a trajectory can be shown to avoid close encounters with a moving nodal point, thus avoiding the source of chaos in this system. We then consider series expansions for trajectories both in the interior and the exterior of the domain covered by nodal lines, probing the domain of convergence as well as how successful the series are in comparison with numerical computations or regular trajectories. We then examine a H\'{e}non - Heiles system possessing regular trajectories, thus generalizing previous results. Finally, we explore a key issue of physical interest in the context of the de Broglie - Bohm formalism, namely the influence of order in the so-called {\it quantum relaxation} effect. We show that the existence of regular trajectories poses restrictions to the quantum relaxation process, and we give examples in which the relaxation is suppressed even when we consider initial ensembles of only chaotic trajectories, provided, however, that the system as a whole is characterized by a certain degree of order.Comment: 25 pages, 12 figure

Hypersensitivity to perturbations of quantum-chaotic wave-packet dynamics

We re-examine the problem of the "Loschmidt echo", which measures the sensitivity to perturbation of quantum chaotic dynamics. The overlap squared $M(t)$ of two wave packets evolving under slightly different Hamiltonians is shown to have the double-exponential initial decay $\propto \exp(-{\rm constant}\times e^{2\lambda_0 t})$ in the main part of phase space. The coefficient $\lambda_0$ is the self-averaging Lyapunov exponent. The average decay $\bar{M}\propto e^{-\lambda_1 t}$ is single exponential with a different coefficient $\lambda_1$. The volume of phase space that contributes to $\bar{M}$ vanishes in the classical limit $\hbar\to 0$ for times less than the Ehrenfest time $\tau_E=\frac{1}{2}\lambda_0^{-1}|\ln \hbar|$. It is only after the Ehrenfest time that the average decay is representative for a typical initial condition.Comment: 4 pages, 4 figures, [2017: fixed broken postscript figures

Integrated analysis of dermal blister fluid proteomics and genome-wide skin gene expression in systemic sclerosis: an observational study

Background: Skin fibrosis is a hallmark feature of systemic sclerosis. Skin biopsy transcriptomics and blister fluid proteomics give insight into the local environment of the skin. We have integrated these modalities with the aim of developing a surrogate for the modified Rodnan skin score (mRSS), using candidate genes and proteins from the skin and blister fluid as anchors to identify key analytes in the plasma. Methods: In this single-centre, prospective observational study at the Royal Free Campus, University College London, London, UK, transcriptional and proteomic analyses of blood and skin were performed in a cohort of patients with systemic sclerosis (n=52) and healthy controls (n=16). Weighted gene co-expression network analysis was used to explore the association of skin transcriptomics data, clinical traits, and blister fluid proteomic results. Candidate hub analytes were identified as those present in both blister and skin gene sets (modules), and which correlated with plasma (module membership >0·7 and gene significance >0·6). Hub analytes were confirmed using RNA transcript data obtained from skin biopsy samples from patients with early diffuse cutaneous systemic sclerosis at 12 months. Findings: We identified three modules in the skin, and two in blister fluid, which correlated with a diagnosis of early diffuse cutaneous systemic sclerosis. From these modules, 11 key hub analytes were identified, present in both skin and blister fluid modules, whose transcript and protein levels correlated with plasma protein concentrations, mRSS, and showed statistically significant correlation on repeat transcriptomic samples taken at 12 months. Multivariate analysis identified four plasma analytes as correlates of mRSS (COL4A1, COMP, SPON1, and TNC), which can be used to differentiate disease subtype. Interpretation: This unbiased approach has identified potential biological candidates that might be drivers of local skin pathogenesis in systemic sclerosis. By focusing on measurable analytes in the plasma, we generated a promising composite plasma protein biomarker that could be used for assessment of skin severity, case stratification, and as a potential outcome measure for clinical trials and practice. Once fully validated, the biomarker score could replace a clinical score such as the mRSS, which carries substantial variability. Funding: GlaxoSmithKline and UK Medical Research Council

Evolution of entanglement under echo dynamics

Echo dynamics and fidelity are often used to discuss stability in quantum information processing and quantum chaos. Yet fidelity yields no information about entanglement, the characteristic property of quantum mechanics. We study the evolution of entanglement in echo dynamics. We find qualitatively different behavior between integrable and chaotic systems on one hand and between random and coherent initial states for integrable systems on the other. For the latter the evolution of entanglement is given by a classical time scale. Analytic results are illustrated numerically in a Jaynes Cummings model.Comment: 5 RevTeX pages, 3 EPS figures (one color) ; v2: considerable revision ;inequality proof omitte

Molecular basis for clinical diversity between autoantibody subsets in diffuse cutaneous systemic sclerosis.

OBJECTIVES: Clinical heterogeneity is a cardinal feature of systemic sclerosis (SSc). Hallmark SSc autoantibodies are central to diagnosis and associate with distinct patterns of skin-based and organ-based complications. Understanding molecular differences between patients will benefit clinical practice and research and give insight into pathogenesis of the disease. We aimed to improve understanding of the molecular differences between key diffuse cutaneous SSc subgroups as defined by their SSc-specific autoantibodies METHODS: We have used high-dimensional transcriptional and proteomic analysis of blood and the skin in a well-characterised cohort of SSc (n=52) and healthy controls (n=16) to understand the molecular basis of clinical diversity in SSc and explore differences between the hallmark antinuclear autoantibody (ANA) reactivities. RESULTS: Our data define a molecular spectrum of SSc based on skin gene expression and serum protein analysis, reflecting recognised clinical subgroups. Moreover, we show that antitopoisomerase-1 antibodies and anti-RNA polymerase III antibodies specificities associate with remarkably different longitudinal change in serum protein markers of fibrosis and divergent gene expression profiles. Overlapping and distinct disease processes are defined using individual patient pathway analysis. CONCLUSIONS: Our findings provide insight into clinical diversity and imply pathogenetic differences between ANA-based subgroups. This supports stratification of SSc cases by ANA antibody subtype in clinical trials and may explain different outcomes across ANA subgroups in trials targeting specific pathogenic mechanisms

A randomized, phase II study of sequential belimumab and rituximab in primary Sjögren's syndrome

BACKGROUND. Primary Sjögren's syndrome (pSS) is characterized by B cell hyperactivity and elevated B-lymphocyte stimulator (BLyS). Anti-BLyS treatment (e.g., belimumab) increases peripheral memory B cells; decreases naive, activated, and plasma B cell subsets; and increases stringency on B cell selection during reconstitution. Anti-CD20 therapeutics (e.g., rituximab) bind and deplete CD20-expressing B cells in circulation but are less effective in depleting tissue-resident CD20+ B cells. Combined, these 2 mechanisms may achieve synergistic effects. METHODS. This 68-week, phase II, double-blind study (GSK study 201842) randomized 86 adult patients with active pSS to 1 of 4 arms: placebo, s.c. belimumab, i.v. rituximab, or sequential belimumab + rituximab. RESULTS. Overall, 60 patients completed treatment and follow-up until week 68. The incidence of adverse events (AEs) and drug-related AEs was similar across groups. Infections/infestations were the most common AEs, and no serious infections of special interest occurred. Near-complete depletion of minor salivary gland CD20+ B cells and a greater and more sustained depletion of peripheral CD19+ B cells were observed with belimumab + rituximab versus monotherapies. With belimumab + rituximab, reconstitution of peripheral B cells occurred, but it was delayed compared with rituximab. At week 68, mean (± standard error) total EULAR Sjögren's syndrome disease activity index scores decreased from 11.0 (1.17) at baseline to 5.0 (1.27) for belimumab + rituximab and 10.4 (1.36) to 8.6 (1.57) for placebo. CONCLUSION. The safety profile of belimumab + rituximab in pSS was consistent with the monotherapies. Belimumab + rituximab induced enhanced salivary gland B cell depletion relative to the monotherapies, potentially leading to improved clinical outcomes

The survival probability and the local density of states for one-dimensional Hamiltonian systems

For chaotic systems there is a theory for the decay of the survival probability, and for the parametric dependence of the local density of states. This theory leads to the distinction between "perturbative" and "non-perturbative" regimes, and to the observation that semiclassical tools are useful in the latter case. We discuss what is "left" from this theory in the case of one-dimensional systems. We demonstrate that the remarkably accurate {\em uniform} semiclassical approximation captures the physics of {\em all} the different regimes, though it cannot take into account the effect of strong localization.Comment: 17 pages, 2 figures, textual improvement

Insulin resistance and inflammatory activation in older patients with systolic and diastolic heart failure

Objective: To evaluate insulin resistance and systemic inflammation in older patients with systolic (SHF) or diastolic heart failure (DHF). Patients: 52 non-diabetic patients (> 70 and < 90 years old) with chronic heart failure (CHF) and hospitalised within the previous six months for heart failure were studied, together with a control group of older healthy volunteers (n  =  26). On the basis of Doppler echocardiographic criteria patients were classed as having SHF (n  =  27) or DHF (n  =  25). Main outcome measures: Fasting glucose, insulin, C reactive protein, interleukin 6, and tumour necrosis factor α soluble receptor II (TNF-αSRII) concentrations were determined. Insulin resistance was estimated by the homeostasis model assessment (HOMA). Results: HOMA index (median, interquartile range) was higher in patients with DHF (1.77, 1.06–2.26) than in patients with SHF (0.97, 0.81–1.85) or healthy volunteers (1.04, 0.76–1.44; p  =  0.01). After adjustment for body mass index, age, and use of angiotensin converting enzyme inhibitors, both groups of patients with CHF were more insulin resistant than were healthy volunteers (p  =  0.02). C reactive protein, interleukin 6, and TNF-αSRII were all significantly (p < 0.001) higher in patients with DHF and SHF than in healthy volunteers. All markers of systemic inflammation were independently associated with the presence of clinical CHF. Conclusion: Insulin resistance and inflammatory activation are present in older patients with SHF and DHF