Is the Book Really Better?: Comparing the Facets of Fantasy Apparent in C.S. Lewis\u27s \u3ci\u3eThe Lion, the Witch and the Wardrobe\u3c/i\u3e and its 2005 Cinematic Adaptation

“Once there were four children whose names were Peter, Susan, Edmund and Lucy. This story is about something that happened to them when they were sent away from London during the war because of the air-raids” (Lewis 2). Sixty-eight years ago, these two simple lines introduced the world to the Pevensie children, who were destined to travel through a wardrobe into one of literature’s most creative, compelling, and enveloping fantasy worlds. Seven books later, the Pevensie children were kings and queens, yes, but considering the hugely expanded scope, they were merely inhabitants of the sprawling lore of The Chronicles of Narnia. Narnia, then, became much more than a world beyond a wardrobe. Narnia, the place and the lore, became a staple of any sturdy fantasy diet

Separability Criteria and Entanglement Measures for Pure States of N Identical Fermions

The study of the entanglement properties of systems of N fermions has attracted considerable interest during the last few years. Various separability criteria for pure states of N identical fermions have been recently discussed but, excepting the case of two-fermions systems, these criteria are difficult to implement and of limited value from the practical point of view. Here we advance simple necessary and sufficient separability criteria for pure states of N identical fermions. We found that to be identified as separable a state has to comply with one single identity involving either the purity or the von Neumann entropy of the single-particle reduced density matrix. These criteria, based on the verification of only one identity, are drastically simpler than the criteria discussed in the recent literature. We also derive two inequalities verified respectively by the purity and the entropy of the single particle, reduced density matrix, that lead to natural entanglement measures for N-fermion pure states. Our present considerations are related to some classical results from the Hartree-Fock theory, which are here discussed from a different point of view in order to clarify some important points concerning the separability of fermionic pure states.Comment: 6 pages, 0 figure

Simple relationship between the virial-route hypernetted-chain and the compressibility-route Percus--Yevick values of the fourth virial coefficient

As is well known, approximate integral equations for liquids, such as the hypernetted chain (HNC) and Percus--Yevick (PY) theories, are in general thermodynamically inconsistent in the sense that the macroscopic properties obtained from the spatial correlation functions depend on the route followed. In particular, the values of the fourth virial coefficient $B_4$ predicted by the HNC and PY approximations via the virial route differ from those obtained via the compressibility route. Despite this, it is shown in this paper that the value of $B_4$ obtained from the virial route in the HNC theory is exactly three halves the value obtained from the compressibility route in the PY theory, irrespective of the interaction potential (whether isotropic or not), the number of components, and the dimensionality of the system. This simple relationship is confirmed in one-component systems by analytical results for the one-dimensional penetrable-square-well model and the three-dimensional penetrable-sphere model, as well as by numerical results for the one-dimensional Lennard--Jones model, the one-dimensional Gaussian core model, and the three-dimensional square-well model.Comment: 8 pages; 4 figures; v2: slight change of title; proof extended to multicomponent fluid

Information theory of quantum systems with some hydrogenic applications

The information-theoretic representation of quantum systems, which complements the familiar energy description of the density-functional and wave-function-based theories, is here discussed. According to it, the internal disorder of the quantum-mechanical non-relativistic systems can be quantified by various single (Fisher information, Shannon entropy) and composite (e.g. Cramer-Rao, LMC shape and Fisher-Shannon complexity) functionals of the Schr\"odinger probability density. First, we examine these concepts and its application to quantum systems with central potentials. Then, we calculate these measures for hydrogenic systems, emphasizing their predictive power for various physical phenomena. Finally, some recent open problems are pointed out.Comment: 9 pages, 3 figure

Complexity analysis of Klein-Gordon single-particle systems

The Fisher-Shannon complexity is used to quantitatively estimate the contribution of relativistic effects to on the internal disorder of Klein-Gordon single-particle Coulomb systems which is manifest in the rich variety of three-dimensional geometries of its corresponding quantum-mechanical probability density. It is observed that, contrary to the non-relativistic case, the Fisher-Shannon complexity of these relativistic systems does depend on the potential strength (nuclear charge). This is numerically illustrated for pionic atoms. Moreover, its variation with the quantum numbers (n, l, m) is analysed in various ground and excited states. It is found that the relativistic effects enhance when n and/or l are decreasing.Comment: 4 pages, 3 figures, Accepted in EPL (Europhysics Letters