Integrability in the mesoscopic dynamics

The Mesoscopic Mechanics (MeM), which has been introduced in a previous paper, is relevant to the electron gas confined to two spatial dimensions. It predicts a special way of collective response of correlated electrons to the external magnetic field. The dynamic variable of this theory is a finite-dimensional operator, which is required to satisfy the mesoscopic Schr\"{o}dinger equation (cf. text). In this article, we describe general solutions of the mesoscopic Schr\"{o}dinger equation. Our approach is specific to the problem at hand. It relies on the unique structure of the equation and makes no reference to any other techniques, with the exception of the geometry of unitary groups. In conclusion, a surprising fact comes to light. Namely, the mesoscopic dynamics "filters" through the (microscopic) Schr\"odinger dynamics as the latter turns out to be a clearly separable part, in fact an autonomous factor, of the evolution. This is a desirable result also from the physical standpoint

Mesoscopic Mechanics

This article is concerned with the existence, status and description of the so-called emergent phenomena believed to occur in certain principally planar electronic systems. In fact, two distinctly different if inseparable tasks are accomplished. First, a rigorous mathematical model is proposed of emergent character, which is conceptually bonded with Quantum Mechanics while apparently non-derivable from the many-body Schr\"{o}dinger equation. I call the resulting conceptual framework the Mesoscopic Mechanics (MeM). Its formulation is space-independent and comprises a nonlinear and holistic extension of the free electron model. Secondly, the question of relevancy of the proposed ``emergent mechanics" to the actually observed phenomena is discussed. In particular, I postulate a probabilistic interpretation, and indicate how the theory could be applied and verified by experiment. The Mesoscopic Mechanics proposed here has been deduced from the Nonlinear Maxwell Theory (NMT)--a classical in character nonlinear field theory. This latter theory has already been shown to provide a consistent phenomenological model of such phenomena as superconductivity, charge stripes, magnetic vortex lattice, and magnetic oscillations. The NMT, which arose from geometric considerations, has long been awaiting an explanation as to its ties with the fundamental principles. I believe the MeM provides at least a partial explanation to this effect.Comment: 20 pages, 2 figure

Magnetic Oscillations and Maxwell Theory

We explore the possibility of using the Kaluza-Klein geometry of Riemannian Submersions to modify the classical Maxwell Theory. We further argue that the resulting modification of Electromagnetism may be interesting in the context of, among other topics, magnetic oscillations in metals.Comment: 10 pages, Latex, 6 Postscript figures, submitted to Physics Letters

Modeling a quantum Hall system via elliptic equations

Quantum Hall systems are a suitable theme for a case study in the general area of nanotechnology. In particular, it is a good framework in which to search for universal principles relevant to nanosystem modeling, and nanosystem-specific signal processing. Recently, we have been able to construct a PDE model of a quantum Hall system, which consists of the Schr\"odinger equation supplemented with a special type nonlinear feedback loop. This result stems from a novel theoretical approach, which in particular brings to the fore the notion of quantum information. In this article we undertake to modify the original model by substituting the dynamics based on the Dirac operator. This leads to a model that consists of a system of three nonlinearly coupled first order elliptic equations in the plane.Comment: 1 figure, revised version (minor changes

Kiedy człowiek rodzi potwora? (Arystoteles o rodzeniu się zwierząt)

In this paper I discuss the problem of the borderline between the lack of resemblance to any family member and monstrosity in Aristotle’s Generation of Animals. In book IV both phenomena have been explained as a result of ‘resolution’ or ‘loosening’ of the ‘movements’ in the sperm, whose function is to recreate in the offspring’s body the features of its parents or ancestors. Consequently, sometimes the offspring bears no resemblance to any ancestor, and sometimes ‘it no longer has the appearance of a human being at all’. According to T. V. Upton, both groups are ‘monsters’ of some kind; he names them ‘generic individuals’, assuming that after ‘loosening’ of the movements which carry particular traits, the task of completing the embryo’s development is taken by the movements of universals (genus or species) present in the sperm. In contrast to Upton’s opinion, I try to prove that the movements of particular – although ‘merged’ and changed – still remain active, leading to the final development of any given individual; in the case of a ‘monster’, however, a deformation of the offspring’s whole body or its parts results not only in the lack of resemblance to any representatives of its own species, but also in disability.Przedmiotem artykułu jest zagadnienie granicy pomiędzy narodzinami dziecka niepodobnego do członków swojej rodziny a przyjściem na świat „potwora” . Oba te zjawiska zostały opisane przez Arystotelesa w IV księdze traktatu O rodzeniu się zwierząt (De generatione animalium) jako rezultat słabnięcia „ruchów” kształtujących płód na podobieństwo rodziców i przodków. W artykule polemizuję ze stanowiskiem T. V. Uptona, który do „potworów” zalicza obie wymienione grupy istot i uznaje, że – wobec osłabnięcia „ruchów” przekazujących cechy jednostkowe – za ich kształtowanie odpowiadają „ruchy” powszechników (odpowiednio gatunku i rodzaju). Staram się wykazać, że „ruchy” przekazujące cechy ogólnie nie są w stanie doprowadzić do końca procesu rozwoju embrionu, a za podstawowe kryterium odróżniające człowieka od „potwora” należy uznać deformację powodującą nie tylko zanik podobieństwa do przedstawicieli własnego gatunku, lecz także kalectwo uniemożliwiające spełnianie właściwych dla danego gatunku funkcji

Health Status, Functional Limitations and Disability: Changes in Poland

The social changes in Poland over the last two decades have had an impact on many dimensions of life, including on important elements of human capital, such as health and functional and instrumental daily activities. This article contains an overview of the available data and indicators on health status, morbidity and disability. It presents the changes in the level of functional and legal disability and aims to show the reasons for these trends. Functional disability is highlighted as one of the major challenges for social and health policy in the next few decades in the context of dynamic aging

The Development of Long-Term Care in Post-Socialist Member States of the EU

Long-term care (LTC) in the new EU member states, which used to belong to the former socialist countries, is not yet a legally separated sector of social security. However, the ageing dynamics are more intensive in these states than in the old EU member states. This paper analyses the process of creating an LTC sector in the context of institutional reforms of social protection systems during the transition period. The authors explain LTC’s position straddling the health and social sectors, the underdevelopment of formal LTC, and the current policies regarding the risk of LTC dependency. The paper is based mainly on the analysis of information provided by country experts in the ANCIEN project