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

Representations of the discrete inhomogeneous Lorentz group and Dirac wave equation on the lattice

We propose the fundamental and two dimensional representation of the Lorentz groups on a (3+1)-dimensional hypercubic lattice, from which representations of higher dimensions can be constructed. For the unitary representation of the discrete translation group we use the kernel of the Fourier transform. From the Dirac representation of the Lorentz group (including reflections) we derive in a natural way the wave equation on the lattice for spin 1/2 particles. Finally the induced representation of the discrete inhomogeneous Lorentz group is constructed by standard methods and its connection with the continuous case is discussed.Comment: LaTeX, 20 pages, 1 eps figure, uses iopconf.sty (late submission

Fermi's golden rule and exponential decay as a RG fixed point

We discuss the decay of unstable states into a quasicontinuum using models of the effective Hamiltonian type. The goal is to show that exponential decay and the golden rule are exact in a suitable scaling limit, and that there is an associated renormalization group (RG) with these properties as a fixed point. The method is inspired by a limit theorem for infinitely divisible distributions in probability theory, where there is a RG with a Cauchy distribution, i.e. a Lorentz line shape, as a fixed point. Our method of solving for the spectrum is well known; it does not involve a perturbation expansion in the interaction, and needs no assumption of a weak interaction. We use random matrices for the interaction, and show that the ensemble fluctuations vanish in the scaling limit. Thus the limit is the same for every model in the ensemble with probability one.Comment: 20 pages, 1 figur

Relating the Lorentzian and exponential: Fermi's approximation,the Fourier transform and causality

The Fourier transform is often used to connect the Lorentzian energy distribution for resonance scattering to the exponential time dependence for decaying states. However, to apply the Fourier transform, one has to bend the rules of standard quantum mechanics; the Lorentzian energy distribution must be extended to the full real axis $-\infty<E<\infty$ instead of being bounded from below $0\leq E <\infty$ (``Fermi's approximation''). Then the Fourier transform of the extended Lorentzian becomes the exponential, but only for times $t\geq 0$, a time asymmetry which is in conflict with the unitary group time evolution of standard quantum mechanics. Extending the Fourier transform from distributions to generalized vectors, we are led to Gamow kets, which possess a Lorentzian energy distribution with $-\infty<E<\infty$ and have exponential time evolution for $t\geq t_0 =0$ only. This leads to probability predictions that do not violate causality.Comment: 23 pages, no figures, accepted by Phys. Rev.

Photoproduction of the Eta-Prime Mesons as a New Tool to Probe Baryon Resonances

We examine eta prime photoproduction, as a novel tool to study baryon resonances around 2 GeV, of particular interest to the quark shell model, which predicts a number of them. We find important roles of the form factors at the strong vertices, and show that the N^*(2080) can be probed efficiently by this reaction.Comment: Will be published in Phys. Rev.

Spontaneous emission and lifetime modification caused by an intense electromagnetic field

We study the temporal evolution of a three-level system (such as an atom or a molecule), initially prepared in an excited state, bathed in a laser field tuned at the transition frequency of the other level. The features of the spontaneous emission are investigated and the lifetime of the initial state is evaluated: a Fermi "golden rule" still applies, but the on-shell matrix elements depend on the intensity of the laser field. In general, the lifetime is a decreasing function of the laser intensity. The phenomenon we discuss can be viewed as an "inverse" quantum Zeno effect and can be analyzed in terms of dressed states.Comment: 25 pages, 6 figure

Can Doubly Strange Dibaryon Resonances be Discovered at RHIC?

The baryon-baryon continuum invariant mass spectrum generated from relativistic nucleus + nucleus collision data may reveal the existence of doubly-strange dibaryons not stable against strong decay if they lie within a few MeV of threshold. Furthermore, since the dominant component of these states is a superposition of two color-octet clusters which can be produced intermediately in a color-deconfined quark-gluon plasma (QGP), an enhanced production of dibaryon resonances could be a signal of QGP formation. A total of eight, doubly-strange dibaryon states are considered for experimental search using the STAR detector (Solenoidal Tracker at RHIC) at the new Relativistic Heavy Ion Collider (RHIC). These states may decay to Lambda-Lambda and/or proton-Cascade-minus, depending on the resonance energy. STAR's large acceptance, precision tracking and vertex reconstruction capabilities, and large data volume capacity, make it an ideal instrument to use for such a search. Detector performance and analysis sensitivity are studied as a function of resonance production rate and width for one particular dibaryon which can directly strong decay to proton-Cascade-minus but not Lambda-Lambda. Results indicate that such resonances may be discovered using STAR if the resonance production rates are comparable to coalescence model predictions for dibaryon bound states.Comment: 28 pages, 5 figures, revised versio

The Mediterranean Sea Regime Shift at the End of the 1980s, and Intriguing Parallelisms with Other European Basins

Background: Regime shifts are abrupt changes encompassing a multitude of physical properties and ecosystem variables, which lead to new regime conditions. Recent investigations focus on the changes in ecosystem diversity and functioning associated to such shifts. Of particular interest, because of the implication on climate drivers, are shifts that occur synchronously in separated basins. Principal Findings: In this work we analyze and review long-term records of Mediterranean ecological and hydro-climate variables and find that all point to a synchronous change in the late 1980s. A quantitative synthesis of the literature (including observed oceanic data, models and satellite analyses) shows that these years mark a major change in Mediterranean hydrographic properties, surface circulation, and deep water convection (the Eastern Mediterranean Transient). We provide novel analyses that link local, regional and basin scale hydrological properties with two major indicators of large scale climate, the North Atlantic Oscillation index and the Northern Hemisphere Temperature index, suggesting that the Mediterranean shift is part of a large scale change in the Northern Hemisphere. We provide a simplified scheme of the different effects of climate vs. temperature on pelagic ecosystems. Conclusions: Our results show that the Mediterranean Sea underwent a major change at the end of the 1980s that encompassed atmospheric, hydrological, and ecological systems, for which it can be considered a regime shift. We further provide evidence that the local hydrography is linked to the larger scale, northern hemisphere climate. These results suggest that the shifts that affected the North, Baltic, Black and Mediterranean (this work) Seas at the end of the 1980s, that have been so far only partly associated, are likely linked as part a northern hemisphere change. These findings bear wide implications for the development of climate change scenarios, as synchronous shifts may provide the key for distinguishing local (i.e., basin) anthropogenic drivers, such as eutrophication or fishing, from larger scale (hemispheric) climate drivers

Geographical Perspectives on Transport and Ageing

In terms of ageing, we are living in unprecedented times. People across the globe are living longer than ever before and societies are ageing at increasing rates. In low to middle income countries reductions in mortality at young ages have fuelled this growth. A person born today in Brazil, for example, can expect to live 20 years longer than someone born 50 years ago (WHO, 2015). For the first time life expectancy across the globe is over 60 years of age. In high Income countries, someone born now can expect to live up to around 80 years of age on average (ONS, 2015). There are not simply a growing number of older people, but also a growing number of older people as a total percentage of the population due to people living longer and declining birth rates in many countries. Across Europe, for example, people aged over 65 years will account for 29.5% of the population in 2060 compared to around 19% now (EUROSTAT, 2017). The share of those aged 80 years or above across Europe will almost triple by 2060 (EUROSTAT, 2017)The macro level demographics and associated trends mask big differences within the ageing populations. There can be as much as 10 years difference in life expectancy within high income countries, for example in the UK someone born a baby boy born in Kensington and Chelsea has a life expectancy of 83.3 years, compared with a boy born in Glasgow who has a life expectancy of 10 years lower (73.0 years) (ONS, 2015). For newborn baby girls, life expectancy is highest in Chiltern at 86.7 years and 8 years lower Glasgow at 78.5 years (ONS, 2015; NRS, 2016). There is also considerable variation within cities, spatially and socially.This volume brings together contributions from a broad range of human geographers, with different disciplinary perspectives of transport and ageing. This chapter outlines some of the key contemporary issues for an ageing society in terms of transport and mobility, highlights the importance of considering transport and mobility for ageing populations and outlines the contribution that a geographical approach can offer to studies of transport and ageing

Seasonal Dynamics of Mobile Carbon Supply in Quercus aquifolioides at the Upper Elevational Limit

Many studies have tried to explain the physiological mechanisms of the alpine treeline phenomenon, but the debate on the alpine treeline formation remains controversial due to opposite results from different studies. The present study explored the carbon-physiology of an alpine shrub species (Quercus aquifolioides) grown at its upper elevational limit compared to lower elevations, to test whether the elevational limit of alpine shrubs (<3 m in height) are determined by carbon limitation or growth limitation. We studied the seasonal variations in non-structural carbohydrate (NSC) and its pool size in Q. aquifolioides grown at 3000 m, 3500 m, and at its elevational limit of 3950 m above sea level (a.s.l.) on Zheduo Mt., SW China. The tissue NSC concentrations along the elevational gradient varied significantly with season, reflecting the season-dependent carbon balance. The NSC levels in tissues were lowest at the beginning of the growing season, indicating that plants used the winter reserve storage for re-growth in the early spring. During the growing season, plants grown at the elevational limit did not show lower NSC concentrations compared to plants at lower elevations, but during the winter season, storage tissues, especially roots, had significantly lower NSC concentrations in plants at the elevational limit compared to lower elevations. The present results suggest the significance of winter reserve in storage tissues, which may determine the winter survival and early-spring re-growth of Q. aquifolioides shrubs at high elevation, leading to the formation of the uppermost distribution limit. This result is consistent with a recent hypothesis for the alpine treeline formation