Plasma Physics

Contains reports on six research projects.United States Atomic Energy Commission (Contract AT(30-1)-1842

Remarks on Shannon's Statistical Inference and the Second Law in Quantum Statistical Mechanics

We comment on a formulation of quantum statistical mechanics, which incorporates the statistical inference of Shannon. Our basic idea is to distinguish the dynamical entropy of von Neumann, $H = -k Tr \hat{\rho}\ln\hat{\rho}$, in terms of the density matrix $\hat{\rho}(t)$, and the statistical amount of uncertainty of Shannon, $S= -k \sum_{n}p_{n}\ln p_{n}$, with $p_{n}=$ in the representation where the total energy and particle numbers are diagonal. These quantities satisfy the inequality $S\geq H$. We propose to interprete Shannon's statistical inference as specifying the {\em initial conditions} of the system in terms of $p_{n}$. A definition of macroscopic observables which are characterized by intrinsic time scales is given, and a quantum mechanical condition on the system, which ensures equilibrium, is discussed on the basis of time averaging. An interesting analogy of the change of entroy with the running coupling in renormalization group is noted. A salient feature of our approach is that the distinction between statistical aspects and dynamical aspects of quantum statistical mechanics is very transparent.Comment: 16 pages. Minor refinement in the statements in the previous version. This version has been published in Journal of Phys. Soc. Jpn. 71 (2002) 6

Periodic Chaotic Billiards: Quantum-Classical Correspondence in Energy Space

We investigate the properties of eigenstates and local density of states (LDOS) for a periodic 2D rippled billiard, focusing on their quantum-classical correspondence in energy representation. To construct the classical counterparts of LDOS and the structure of eigenstates (SES), the effects of the boundary are first incorporated (via a canonical transformation) into an effective potential, rendering the one-particle motion in the 2D rippled billiard equivalent to that of two-interacting particles in 1D geometry. We show that classical counterparts of SES and LDOS in the case of strong chaotic motion reveal quite a good correspondence with the quantum quantities. We also show that the main features of the SES and LDOS can be explained in terms of the underlying classical dynamics, in particular of certain periodic orbits. On the other hand, statistical properties of eigenstates and LDOS turn out to be different from those prescribed by random matrix theory. We discuss the quantum effects responsible for the non-ergodic character of the eigenstates and individual LDOS that seem to be generic for this type of billiards with a large number of transverse channels.Comment: 13 pages, 18 figure

Chaos in Time Dependent Variational Approximations to Quantum Dynamics

Dynamical chaos has recently been shown to exist in the Gaussian approximation in quantum mechanics and in the self-consistent mean field approach to studying the dynamics of quantum fields. In this study, we first show that any variational approximation to the dynamics of a quantum system based on the Dirac action principle leads to a classical Hamiltonian dynamics for the variational parameters. Since this Hamiltonian is generically nonlinear and nonintegrable, the dynamics thus generated can be chaotic, in distinction to the exact quantum evolution. We then restrict attention to a system of two biquadratically coupled quantum oscillators and study two variational schemes, the leading order large N (four canonical variables) and Hartree (six canonical variables) approximations. The chaos seen in the approximate dynamics is an artifact of the approximations: this is demonstrated by the fact that its onset occurs on the same characteristic time scale as the breakdown of the approximations when compared to numerical solutions of the time-dependent Schrodinger equation.Comment: 10 pages (12 figures), RevTeX (plus macro), uses epsf, minor typos correcte

License prices for financially constrained firms

It is often alleged that high auction prices inhibit service deployment. We investigate this claim under the extreme case of financially constrained bidders. If demand is just slightly elastic, auctions maximize consumer surplus if consumer surplus is a convex function of quantity (a common assumption), or if consumer surplus is concave and the proportion of expenditure spent on deployment is greater than one over the elasticity of demand. The latter condition appears to be true for most of the large telecom auctions in the US and Europe. Thus, even if high auction prices inhibit service deployment, auctions appear to be optimal from the consumers’ point of view

Hormonal Signal Amplification Mediates Environmental Conditions during Development and Controls an Irreversible Commitment to Adulthood

Many animals can choose between different developmental fates to maximize fitness. Despite the complexity of environmental cues and life history, different developmental fates are executed in a robust fashion. The nematode Caenorhabditis elegans serves as a powerful model to examine this phenomenon because it can adopt one of two developmental fates (adulthood or diapause) depending on environmental conditions. The steroid hormone dafachronic acid (DA) directs development to adulthood by regulating the transcriptional activity of the nuclear hormone receptor DAF-12. The known role of DA suggests that it may be the molecular mediator of environmental condition effects on the developmental fate decision, although the mechanism is yet unknown. We used a combination of physiological and molecular biology techniques to demonstrate that commitment to reproductive adult development occurs when DA levels, produced in the neuroendocrine XXX cells, exceed a threshold. Furthermore, imaging and cell ablation experiments demonstrate that the XXX cells act as a source of DA, which, upon commitment to adult development, is amplified and propagated in the epidermis in a DAF-12 dependent manner. This positive feedback loop increases DA levels and drives adult programs in the gonad and epidermis, thus conferring the irreversibility of the decision. We show that the positive feedback loop canalizes development by ensuring that sufficient amounts of DA are dispersed throughout the body and serves as a robust fate-locking mechanism to enforce an organism-wide binary decision, despite noisy and complex environmental cues. These mechanisms are not only relevant to C. elegans but may be extended to other hormonal-based decision-making mechanisms in insects and mammals

'Sexercise': Working out heterosexuality in Jane Fonda’s fitness books

This is an Author's Accepted Manuscript of an article published in Leisure Studies, 30(2), 237 - 255, 2011, copyright Taylor & Francis, available online at: http://www.tandfonline.com/10.1080/02614367.2010.523837.This paper explores the connection between the promotion of heterosexual norms in women’s fitness books written by or in the name of Jane Fonda during the 1980s and the commodification of women’s fitness space in both the public and private spheres. The paper is set in the absence of overt discussions of normative heterosexuality in leisure studies and draws on critical heterosexual scholarship as well as the growing body of work theorising geographies of corporeality and heterosexuality. Using the principles of media discourse analysis, the paper identifies three overlapping characteristics of heterosexuality represented in Jane Fonda’s fitness books, and embodied through the exercise regimes: respectable heterosexual desire, monogamous procreation and domesticity. The paper concludes that the promotion and prescription of exercise for women in the Jane Fonda workout books centred on the reproduction and embodiment of heterosexual corporeality. Set within an emerging commercial landscape of women’s fitness in the 1980s, such exercise practices were significant in the legitimation and institutionalisation of heteronormativity

Multitemporal generalization of the Tangherlini solution

The n-time generalization of the Tangherlini solution [1] is considered. The equations of geodesics for the metric are integrated. For $n = 2$ it is shown that the naked singularity is absent only for two sets of parameters, corresponding to the trivial extensions of the Tangherlini solution. The motion of a relativistic particle in the multitemporal background is considered. This motion is governed by the gravitational mass tensor. Some generalizations of the solution, including the multitemporal analogue of the Myers-Perry charged black hole solution, are obtained.Comment: 14 pages. RGA-CSVR-005/9

Characterizing COVID-19 clinical phenotypes and associated comorbidities and complication profiles

Purpose Heterogeneity has been observed in outcomes of hospitalized patients with coronavirus disease 2019 (COVID-19). Identification of clinical phenotypes may facilitate tailored therapy and improve outcomes. The purpose of this study is to identify specific clinical phenotypes across COVID-19 patients and compare admission characteristics and outcomes. Methods This is a retrospective analysis of COVID-19 patients from March 7, 2020 to August 25, 2020 at 14 U.S. hospitals. Ensemble clustering was performed on 33 variables collected within 72 hours of admission. Principal component analysis was performed to visualize variable contributions to clustering. Multinomial regression models were fit to compare patient comorbidities across phenotypes. Multivariable models were fit to estimate associations between phenotype and in-hospital complications and clinical outcomes. Results The database included 1,022 hospitalized patients with COVID-19. Three clinical phenotypes were identified (I, II, III), with 236 [23.1%] patients in phenotype I, 613 [60%] patients in phenotype II, and 173 [16.9%] patients in phenotype III. Patients with respiratory comorbidities were most commonly phenotype III (p = 0.002), while patients with hematologic, renal, and cardiac (all p<0.001) comorbidities were most commonly phenotype I. Adjusted odds of respiratory, renal, hepatic, metabolic (all p<0.001), and hematological (p = 0.02) complications were highest for phenotype I. Phenotypes I and II were associated with 7.30- fold (HR:7.30, 95% CI:(3.11-17.17), p<0.001) and 2.57-fold (HR:2.57, 95% CI:(1.10-6.00), p = 0.03) increases in hazard of death relative to phenotype III. Conclusion We identified three clinical COVID-19 phenotypes, reflecting patient populations with different comorbidities, complications, and clinical outcomes. Future research is needed to determine the utility of these phenotypes in clinical practice and trial design