Quasi Markovian behavior in mixing maps

We consider the time dependent probability distribution of a coarse grained observable Y whose evolution is governed by a discrete time map. If the map is mixing, the time dependent one-step transition probabilities converge in the long time limit to yield an ergodic stochastic matrix. The stationary distribution of this matrix is identical to the asymptotic distribution of Y under the exact dynamics. The nth time iterate of the baker map is explicitly computed and used to compare the time evolution of the occupation probabilities with those of the approximating Markov chain. The convergence is found to be at least exponentially fast for all rectangular partitions with Lebesgue measure. In particular, uniform rectangles form a Markov partition for which we find exact agreement.Comment: 16 pages, 1 figure, uses elsart.sty, to be published in Physica D Special Issue on Predictability: Quantifying Uncertainty in Models of Complex Phenomen

Variational Approach to Real-Time Evolution of Yang-Mills Gauge Fields on a Lattice

Applying a variational method to a Gaussian wave ansatz, we have derived a set of semi-classical evolution equations for SU(2) lattice gauge fields, which take the classical form in the limit of a vanishing width of the Gaussian wave packet. These equations are used to study the quantum effects on the classical evolutions of the lattice gauge fields.Comment: LaTeX, 12 pages, 5 figures contained in a separate uuencoded file, DUKE-TH-93-4

When does activism benefit well-being? Evidence from a longitudinal study of Clinton voters in the 2016 U.S. presidential election

Contrary to the expectations of many, Hillary Clinton lost the 2016 U.S. presidential election. The initial shock to her supporters turned into despair for most, but not everyone was affected equally. We draw from the literature on political activism, identity, and self-other overlap in predicting that not all Clinton voters would be equivalently crushed by her loss. Specifically, we hypothesize that pre-election measures of political activism, and level of self-other identification between participants and Clinton-that is, how much a person was "with her"-will interact to predict the level of distress of Clinton voters two months later. Longitudinal data support our hypothesis. Notably, among Clinton voters, greater activism negatively predicted depressive symptoms, and positively predicted sleep quality, but only when participants were highly identified with Clinton. We discuss the implications of the results for theory and research on social action and well-being

Two-point correlations of the Gaussian symplectic ensemble from periodic orbits

We determine the asymptotics of the two-point correlation function for quantum systems with half-integer spin which show chaotic behaviour in the classical limit using a method introduced by Bogomolny and Keating [Phys. Rev. Lett. 77 (1996) 1472-1475]. For time-reversal invariant systems we obtain the leading terms of the two-point correlation function of the Gaussian symplectic ensemble. Special attention has to be paid to the role of Kramers' degeneracy.Comment: 7 pages, no figure

Negative moments of characteristic polynomials of random GOE matrices and singularity-dominated strong fluctuations

We calculate the negative integer moments of the (regularized) characteristic polynomials of N x N random matrices taken from the Gaussian Orthogonal Ensemble (GOE) in the limit as $N \to \infty$. The results agree nontrivially with a recent conjecture of Berry & Keating motivated by techniques developed in the theory of singularity-dominated strong fluctuations. This is the first example where nontrivial predictions obtained using these techniques have been proved.Comment: 13 page

Correspondence in Quasiperiodic and Chaotic Maps: Quantization via the von Neumann Equation

A generalized approach to the quantization of a large class of maps on a torus, i.e. quantization via the von Neumann Equation, is described and a number of issues related to the quantization of model systems are discussed. The approach yields well behaved mixed quantum states for tori for which the corresponding Schrodinger equation has no solutions, as well as an extended spectrum for tori where the Schrodinger equation can be solved. Quantum-classical correspondence is demonstrated for the class of mappings considered, with the Wigner-Weyl density $\rho(p,q,t)$ going to the correct classical limit. An application to the cat map yields, in a direct manner, nonchaotic quantum dynamics, plus the exact chaotic classical propagator in the correspondence limit.Comment: 36 pages, RevTex preprint forma

On the semiclassical theory for universal transmission fluctuations in chaotic systems: the importance of unitarity

The standard semiclassical calculation of transmission correlation functions for chaotic systems is severely influenced by unitarity problems. We show that unitarity alone imposes a set of relationships between cross sections correlation functions which go beyond the diagonal approximation. When these relationships are properly used to supplement the semiclassical scheme we obtain transmission correlation functions in full agreement with the exact statistical theory and the experiment. Our approach also provides a novel prediction for the transmission correlations in the case where time reversal symmetry is present

The governance of personal data for COVID-19 response: perspective from the access to COVID-19 tools accelerator

COVID-19 is the world’s first digital pandemic. Digital tools and technologies have been developed to track and trace the spread of the virus, screen for infection, and the pandemic has accelerated the use of digital technology in the delivery of healthcare. The continued development of these tools and technologies, the monitoring of the virus and the development of new tests, treatments and vaccines are dependent on the collection of and access to vast amounts of personal data. This includes clinical data, epidemiological data and public health data that may be collected from laboratories, medical records, wearables and smartphone apps. Previous public health emergencies (PHEs) have demonstrated the importance in making this data available, and early in the COVID-19 pandemic, there were calls for making all kinds of data, including clinical trial data, routine surveillance data, genetic sequencing, and data on the ongoing monitoring of disease control programmes, openly and rapidly available. As part of this, personal data on age, race, sex, health, ethnic group, and socioeconomic factors have been shared. This has helped led to the rapid development of COVID-19 interventions. It has also enabled the better understanding of factors contributing to difference in infection rates and effectiveness of tests, treatments, and vaccines. However, the use of this particularly sensitive data can infringe upon individual and group privacy, increase the risks of individual and group stigma and discrimination, and it may negatively impact already vulnerable, marginalised or minority populations. [...

Mutual Coherence of Polarized Light in Disordered Media: Two-Frequency Method Extended

The paper addresses the two-point correlations of electromagnetic waves in general random, bi-anisotropic media whose constitutive tensors are complex Hermitian, positive- or negative-definite matrices. A simplified version of the two-frequency Wigner distribution (2f-WD) for polarized waves is introduced and the closed form Wigner-Moyal equation is derived from the Maxwell equations. In the weak-disorder regime with an arbitrarily varying background the two-frequency radiative transfer (2f-RT) equations for the associated $2\times 2$ coherence matrices are derived from the Wigner-Moyal equation by using the multiple scale expansion. In birefringent media, the coherence matrix becomes a scalar and the 2f-RT equations take the scalar form due to the absence of depolarization. A paraxial approximation is developed for spatialy anisotropic media. Examples of isotropic, chiral, uniaxial and gyrotropic media are discussed

Geometric phases and anholonomy for a class of chaotic classical systems

Berry's phase may be viewed as arising from the parallel transport of a quantal state around a loop in parameter space. In this Letter, the classical limit of this transport is obtained for a particular class of chaotic systems. It is shown that this ``classical parallel transport'' is anholonomic --- transport around a closed curve in parameter space does not bring a point in phase space back to itself --- and is intimately related to the Robbins-Berry classical two-form.Comment: Revtex, 11 pages, no figures