Lower bound of minimal time evolution in quantum mechanics

We show that the total time of evolution from the initial quantum state to final quantum state and then back to the initial state, i.e., making a round trip along the great circle over S^2, must have a lower bound in quantum mechanics, if the difference between two eigenstates of the 2\times 2 Hamiltonian is kept fixed. Even the non-hermitian quantum mechanics can not reduce it to arbitrarily small value. In fact, we show that whether one uses a hermitian Hamiltonian or a non-hermitian, the required minimal total time of evolution is same. It is argued that in hermitian quantum mechanics the condition for minimal time evolution can be understood as a constraint coming from the orthogonality of the polarization vector \bf P of the evolving quantum state \rho={1/2}(\bf 1+ \bf{P}\cdot\boldsymbol{\sigma}) with the vector \boldsymbol{\mathcal O}(\Theta) of the 2\times 2 hermitian Hamiltonians H ={1/2}({\mathcal O}_0\boldsymbol{1}+ \boldsymbol{\mathcal O}(\Theta)\cdot\boldsymbol{\sigma}) and it is shown that the Hamiltonian H can be parameterized by two independent parameters {\mathcal O}_0 and \Theta.Comment: 4 pages, no figure, revtex

Dynamical aspects of mean field plane rotators and the Kuramoto model

The Kuramoto model has been introduced in order to describe synchronization phenomena observed in groups of cells, individuals, circuits, etc... We look at the Kuramoto model with white noise forces: in mathematical terms it is a set of N oscillators, each driven by an independent Brownian motion with a constant drift, that is each oscillator has its own frequency, which, in general, changes from one oscillator to another (these frequencies are usually taken to be random and they may be viewed as a quenched disorder). The interactions between oscillators are of long range type (mean field). We review some results on the Kuramoto model from a statistical mechanics standpoint: we give in particular necessary and sufficient conditions for reversibility and we point out a formal analogy, in the N to infinity limit, with local mean field models with conservative dynamics (an analogy that is exploited to identify in particular a Lyapunov functional in the reversible set-up). We then focus on the reversible Kuramoto model with sinusoidal interactions in the N to infinity limit and analyze the stability of the non-trivial stationary profiles arising when the interaction parameter K is larger than its critical value K_c. We provide an analysis of the linear operator describing the time evolution in a neighborhood of the synchronized profile: we exhibit a Hilbert space in which this operator has a self-adjoint extension and we establish, as our main result, a spectral gap inequality for every K>K_c.Comment: 18 pages, 1 figur

Coupled-mode equations and gap solitons in a two-dimensional nonlinear elliptic problem with a separable periodic potential

We address a two-dimensional nonlinear elliptic problem with a finite-amplitude periodic potential. For a class of separable symmetric potentials, we study the bifurcation of the first band gap in the spectrum of the linear Schr\"{o}dinger operator and the relevant coupled-mode equations to describe this bifurcation. The coupled-mode equations are derived by the rigorous analysis based on the Fourier--Bloch decomposition and the Implicit Function Theorem in the space of bounded continuous functions vanishing at infinity. Persistence of reversible localized solutions, called gap solitons, beyond the coupled-mode equations is proved under a non-degeneracy assumption on the kernel of the linearization operator. Various branches of reversible localized solutions are classified numerically in the framework of the coupled-mode equations and convergence of the approximation error is verified. Error estimates on the time-dependent solutions of the Gross--Pitaevskii equation and the coupled-mode equations are obtained for a finite-time interval.Comment: 32 pages, 16 figure

Resummation of Nonalternating Divergent Perturbative Expansions

A method for the resummation of nonalternating divergent perturbation series is described. The procedure constitutes a generalization of the Borel-Pad\'{e} method. Of crucial importance is a special integration contour in the complex plane. Nonperturbative imaginary contributions can be inferred from the purely real perturbative coefficients. A connection is drawn from the quantum field theoretic problem of resummation to divergent perturbative expansions in other areas of physics.Comment: 5 pages, LaTeX, 2 tables, 1 figure; discussion of the Carleman criterion added; version to appear in Phys. Rev.

Changing energy profiles and consumption patterns following electrification in five rural villages, South Africa

Following the democratic transition in South Africa in the early 1990s the government has implemented a widespread electrification programme, as well as introduced a free basic electricity allowance as a means of poverty alleviation. Yet there are limited longitudinal studies on the impacts of the introduction of electricity on the patterns of household energy use, and even more so in the neglected rural sector. This study reports on the patterns of household energy use in five rural settlements in 1991 and again in 2002. Results indicate a changing pattern of energy use for lighting and powering entertainment appliances, more specifically from dry-cell batteries and paraffin to electricity. Yet for thermal needs, most notably cooking, fuelwood has remained the most widespread fuel, and the amount used per month has not changed, despite increasing scarcity of wood in the local environment. There has been an increase in the proportion of households purchasing fuelwood as opposed to collecting their own. Overall, the mean total number of fuel types used per household has increased, indicating that electricity is simply viewed as an additional energy, rather than an alternative. Yet, electricity accounted for approximately 60% of expenditure on energy sources in 2002, despite the government's policy of a free basic allowance of 5–6 kWh per month. This has implications for energy supply costing, as well as the poverty alleviation dimensions of the whole programme

Krein-Space Formulation of PT-Symmetry, CPT-Inner Products, and Pseudo-Hermiticity

Emphasizing the physical constraints on the formulation of a quantum theory based on the standard measurement axiom and the Schroedinger equation, we comment on some conceptual issues arising in the formulation of PT-symmetric quantum mechanics. In particular, we elaborate on the requirements of the boundedness of the metric operator and the diagonalizability of the Hamiltonian. We also provide an accessible account of a Krein-space derivation of the CPT-inner product that was widely known to mathematicians since 1950's. We show how this derivation is linked with the pseudo-Hermitian formulation of PT-symmetric quantum mechanics.Comment: published version, 17 page

Evidence of Final-State Suppression of High-p_T Hadrons in Au + Au Collisions Using d + Au Measurements at RHIC

Transverse momentum spectra of charged hadrons with ${p_{T} <}$ 6 GeV/c have been measured near mid-rapidity (0.2 $< \eta <$ 1.4) by the PHOBOS experiment at RHIC in Au + Au and d + Au collisions at ${\sqrt{s_{_{NN}}} = \rm {200 GeV}}$. The spectra for different collision centralities are compared to ${p + \bar{p}}$ collisions at the same energy. The resulting nuclear modification factor for central Au + Au collisions shows evidence of strong suppression of charged hadrons in the high-$p_{T}$ region (${>2}$ GeV/c). In contrast, the d + Au nuclear modification factor exhibits no suppression of the high-$p_{T}$ yields. These measurements suggest a large energy loss of the high-$p_{T}$ particles in the highly interacting medium created in the central Au + Au collisions. The lack of suppression in d + Au collisions suggests that it is unlikely that initial state effects can explain the suppression in the central Au + Au collisions.Comment: 3 pages, 4 figures, International Europhysics Conference on High Energy Physics EPS (July 17th-23rd 2003) in Aachen, German

Identified particles in Au+Au collisions at sqrt{s_NN} = 200 GeV

The yields of identified particles have been measured at RHIC for Au+Au collisions at sqrt{s_NN} = 200 GeV using the PHOBOS spectrometer. The ratios of antiparticle to particle yields near mid-rapidity are presented. The first measurements of the invariant yields of charged pions, kaons and protons at very low transverse momenta are also shown.Comment: 4 pages, 4 figures, Contribution to Quark Matter 2002, Nantes, France, July 200

Recent Results from PHOBOS at RHIC

The PHOBOS experiment at RHIC has recorded measurements for Au-Au collisions spanning nucleon-nucleon center-of-mass energies from 19.6 GeV to 200 GeV. Global observables such as elliptic flow and charged particle multiplicity provide important constraints on model predictions that characterize the state of matter produced in these collisions. The nearly 4 pi acceptance of the PHOBOS experiment provides excellent coverage for complete flow and multiplicity measurements. Results including beam energy and centrality dependencies are presented and compared to elementary systems.Comment: 4 pages, 4 figures, proceedings from PANIC02 in Osaka, Japa

Fertility, Living Arrangements, Care and Mobility

There are four main interconnecting themes around which the contributions in this book are based. This introductory chapter aims to establish the broad context for the chapters that follow by discussing each of the themes. It does so by setting these themes within the overarching demographic challenge of the twenty-first century – demographic ageing. Each chapter is introduced in the context of the specific theme to which it primarily relates and there is a summary of the data sets used by the contributors to illustrate the wide range of cross-sectional and longitudinal data analysed