Determination of a Wave Function Functional

In this paper we propose the idea of expanding the space of variations in standard variational calculations for the energy by considering the wave function $\psi$ to be a functional of a set of functions $\chi: \psi = \psi[\chi]$, rather than a function. In this manner a greater flexibility to the structure of the wave function is achieved. A constrained search in a subspace over all functions $\chi$ such that the wave function functional $\psi[\chi]$ satisfies a constraint such as normalization or the Fermi-Coulomb hole charge sum rule, or the requirement that it lead to a physical observable such as the density, diamagnetic susceptibility, etc. is then performed. A rigorous upper bound to the energy is subsequently obtained by variational minimization with respect to the parameters in the approximate wave function functional. Hence, the terminology, the constrained-search variational method. The \emph{rigorous} construction of such a constrained-search--variational wave function functional is demonstrated by example of the ground state of the Helium atom.Comment: 10 pages, 2 figures, changes made, references adde

Glassforming Liquids, Amorphous and Semicrystalline Polymers: Exploring their Energy Landscape and Dynamical Heterogeneity by Multi-frequency High-Field EPR

We review past and recent work carried out on viscous liquids, amorphous and semicrystalline polymers by multifrequency high-field electron paramagnetic resonance (HF-EPR) facility in Pisa. The emphasis is on the enhanced ability to provide fine details of the reorientation process of the paramagnetic guest, the spin probe, revealing features driving the dynamics of the host system, including the energy-barrier distribution of glassy polymers, the dynamical heterogeneity of semicrystalline polymers, and the dynamical changes occurring at the critical temperature predicted by the ideal mode-coupling theory

Glassforming Liquids, Amorphous and Semicrystalline Polymers: Exploring their Energy Landscape and Dynamical Heterogeneity by Multi-frequency High-Field EPR

AbstractWe review past and recent work carried out on viscous liquids, amorphous and semicrystalline polymers by multifrequency high-field electron paramagnetic resonance (HF-EPR) facility in Pisa. The emphasis is on the enhanced ability to provide fine details of the reorientation process of the paramagnetic guest, the spin probe, revealing features driving the dynamics of the host system, including the energy-barrier distribution of glassy polymers, the dynamical heterogeneity of semicrystalline polymers, and the dynamical changes occurring at the critical temperature predicted by the ideal mode-coupling theory

A study of the deep structure of the energy landscape of glassy polystyrene: the exponential distribution of the energy-barriers revealed by high-field Electron Spin Resonance spectroscopy

The reorientation of one small paramagnetic molecule (spin probe) in glassy polystyrene (PS) is studied by high-field Electron Spin Resonance spectroscopy at two different Larmor frequencies (190 and 285 GHz). The exponential distribution of the energy-barriers for the rotational motion of the spin probe is unambigously evidenced at both 240K and 270K. The same shape for the distribution of the energy-barriers of PS was evidenced by the master curves provided by previous mechanical and light scattering studies. The breadth of the energy-barriers distribution of the spin probe is in the range of the estimates of the breadth of the PS energy-barriers distribution. The evidence that the deep structure of the energy landscape of PS exhibits the exponential shape of the energy-barriers distribution agrees with results from extreme-value statistics and the trap model by Bouchaud and coworkers.Comment: Final version in press as Letter to the Editor on J.Phys.:Condensed Matter. Changes in bol

Ecological change, sliding baselines and the importance of historical data: Lessons from combing observational and quantitative data on a temperate reef over 70 years

Understanding the effects of environmental change on ecosystems requires the identification of baselines that may act as reference conditions. However, the continuous change of these references challenges our ability to define the true natural status of ecosystems. The so-called sliding baseline syndrome can be overcome through the analysis of quantitative time series, which are, however, extremely rare. Here we show how combining historical quantitative data with descriptive 'naturalistic' information arranged in a chronological chain allows highlighting long-term trends and can be used to inform present conservation schemes.We analysed the long-term change of a coralligenous reef, a marine habitat endemic to the Mediterranean Sea. The coralligenous assemblages of Mesco Reef (Ligurian Sea, NW Mediterranean) have been studied, although discontinuously, since 1937 thus making available both detailed descriptive information and scanty quantitative data: while the former was useful to understand the natural history of the ecosystem, the analysis of the latter was of paramount importance to provide a formal measure of change over time. Epibenthic assemblages remained comparatively stable until the 1990s, when species replacement, invasion by alien algae, and biotic homogenisation occurred within few years, leading to a new and completely different ecosystem state. The shift experienced by the coralligenous assemblages of Mesco Reef was probably induced by a combination of seawater warming and local human pressures, the latter mainly resulting in increased water turbidity; in turn, cumulative stress may have favoured the establishment of alien species. This study showed that the combined analysis of quantitative and descriptive historical data represent a precious knowledge to understand ecosystem trends over time and provide help to identify baselines for ecological management

Effects of inhibition of the renin-angiotensin system on hypertension-induced target organ damage: Clinical and experimental evidence

The dysregulation of renin-angiotensin-system (RAS) plays a pivotal role in hypertension and in the development of the related target organ damage (TOD). The main goal of treating hypertension is represented by the long-term reduction of cardiovascular (CV) risk. RAS inhibition either by angiotensin converting enzyme (ACE)-inhibitors or by type 1 Angiotensin II receptors blockers (ARBs), reduce the incidence of CV events in hypertensive patients. Actually, ACE-inhibitors and ARBs have been demonstrated to be effective to prevent, or delay TOD like left ventricular hypertrophy, chronic kidney disease, and atherosclerosis. The beneficial effects of RAS blockers on clinical outcome of hypertensive patients are due to the key role of angiotensin II in the pathogenesis of TOD. In particular, Angiotensin II through an inflammatory-mediated mechanism plays a role in the initiation, progression and vulnerability of atherosclerotic plaque. In addition, Angiotensin II can be considered the hormonal transductor of the pressure overload in cardiac myocytes, and through an autocrine-paracrine mechanism plays a role in the development of left ventricular hypertrophy. Angiotensin II by modulating the redox status and the immune system participates to the development of chronic kidney disease. The RAS blocker should be considered the first therapeutic option in patients with hypertension, even if ACE-inhibitors and ARBs have different impact on CV prevention. ARBs seem to have greater neuro-protective effects, while ACE-inhibitors have greater cardio-protective action

Conservation of energy and momenta in nonholonomic systems with affine constraints

We characterize the conditions for the conservation of the energy and of the components of the momentum maps of lifted actions, and of their `gauge-like' generalizations, in time-independent nonholonomic mechanical systems with affine constraints. These conditions involve geometrical and mechanical properties of the system, and are codified in the so-called reaction-annihilator distribution