8,087 research outputs found
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
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