Multiplicity of periodic solutions for systems of weakly coupled parametrized second order differential equations

We prove a multiplicity result of periodic solutions for a system of second order differential equations having asymmetric nonlinearities. The proof is based on a recent generalization of the Poincar\ue9\u2013Birkhoff fixed point theorem provided by Fonda and Ure\uf1a

Exponential behavior of a quantum system in a macroscopic medium

An exponential behavior at all times is derived for a solvable dynamical model in the weak-coupling, macroscopic limit. Some implications for the quantum measurement problem are discussed, in particular in connection with dissipation.Comment: 8 pages, report BA-TH/94-17

Suppression of Zeno effect for distant detectors

We describe the influence of continuous measurement in a decaying system and the role of the distance from the detector to the initial location of the system. The detector is modeled first by a step absorbing potential. For a close and strong detector, the decay rate of the system is reduced; weaker detectors do not modify the exponential decay rate but suppress the long-time deviations above a coupling threshold. Nevertheless, these perturbing effects of measurement disappear by increasing the distance between the initial state and the detector, as well as by improving the efficiency of the detector.Comment: 4 pages, 4 figure

Quantum Zeno effect in a probed downconversion process

The distorsion of a spontaneous downconvertion process caused by an auxiliary mode coupled to the idler wave is analyzed. In general, a strong coupling with the auxiliary mode tends to hinder the downconversion in the nonlinear medium. On the other hand, provided that the evolution is disturbed by the presence of a phase mismatch, the coupling may increase the speed of downconversion. These effects are interpreted as being manifestations of quantum Zeno or anti-Zeno effects, respectively, and they are understood by using the dressed modes picture of the device. The possibility of using the coupling as a nontrivial phase--matching technique is pointed out.Comment: 11 pages, 4 figure

'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

Complex Scaled Spectrum Completeness for Coupled Channels

The Complex Scaling Method (CSM) provides scattering wave functions which regularize resonances and suggest a resolution of the identity in terms of such resonances, completed by the bound states and a smoothed continuum. But, in the case of inelastic scattering with many channels, the existence of such a resolution under complex scaling is still debated. Taking advantage of results obtained earlier for the two channel case, this paper proposes a representation in which the convergence of a resolution of the identity can be more easily tested. The representation is valid for any finite number of coupled channels for inelastic scattering without rearrangement.Comment: Latex file, 13 pages, 4 eps-figure

The role of initial state reconstruction in short and long time deviations from exponential decay

We consider the role of the reconstruction of the initial state in the deviation from exponential decay at short and long times. The long time decay can be attributed to a wave that was, in a classical-like, probabilistic sense, fully outside the initial state or the inner region at intermediate times, i.e., to a completely reconstructed state, whereas the decay during the exponential regime is due instead to a non-reconstructed wave. At short times quantum interference between regenerated and non-regenerated paths is responsible for the deviation from the exponential decay. We may thus conclude that state reconstruction is a ``consistent history'' for long time deviations but not for short ones.Comment: 4 pages, 6 figure

The various power decays of the survival probability at long times for free quantum particle

The long time behaviour of the survival probability of initial state and its dependence on the initial states are considered, for the one dimensional free quantum particle. We derive the asymptotic expansion of the time evolution operator at long times, in terms of the integral operators. This enables us to obtain the asymptotic formula for the survival probability of the initial state $\psi (x)$, which is assumed to decrease sufficiently rapidly at large $|x|$. We then show that the behaviour of the survival probability at long times is determined by that of the initial state $\psi$ at zero momentum $k=0$. Indeed, it is proved that the survival probability can exhibit the various power-decays like $t^{-2m-1}$ for an arbitrary non-negative integers $m$ as $t \to \infty$, corresponding to the initial states with the condition $\hat{\psi} (k) = O(k^m)$ as $k\to 0$.Comment: 15 pages, to appear in J. Phys.

The decay law can have an irregular character

Within a well-known decay model describing a particle confined initially within a spherical $\delta$ potential shell, we consider the situation when the undecayed state has an unusual energy distribution decaying slowly as $k\to\infty$; the simplest example corresponds to a wave function constant within the shell. We show that the non-decay probability as a function of time behaves then in a highly irregular, most likely fractal way.Comment: 4 pages, 3 eps figure