214 research outputs found
The charge-dyon bound system in the spherical quantum well
The spherical wave functions of charge-dyon bounded system in a rectangular
spherical quantum dot of infinitely and finite height are calculated. The
transcendent equations, defining the energy spectra of the systems are
obtained. The dependence of the energy levels from the wall sizes is found.Comment: 8 pages, 5 figure
Symmetries of N=4 supersymmetric CP(n) mechanics
We explicitly constructed the generators of group which commute
with the supercharges of N=4 supersymmetric mechanics in the
background U(n) gauge fields. The corresponding Hamiltonian can be represented
as a direct sum of two Casimir operators: one Casimir operator on
group contains our bosonic and fermionic coordinates and momenta, while the
second one, on the SU(1,n) group, is constructed from isospin degrees of
freedom only.Comment: 10 pages, PACS numbers: 11.30.Pb, 03.65.-w; minor changes in
Introduction, references adde
Frenet-Serret dynamics
We consider the motion of a particle described by an action that is a
functional of the Frenet-Serret [FS] curvatures associated with the embedding
of its worldline in Minkowski space. We develop a theory of deformations
tailored to the FS frame. Both the Euler-Lagrange equations and the physical
invariants of the motion associated with the Poincar\'e symmetry of Minkowski
space, the mass and the spin of the particle, are expressed in a simple way in
terms of these curvatures. The simplest non-trivial model of this form, with
the lagrangian depending on the first FS (or geodesic) curvature, is
integrable. We show how this integrability can be deduced from the Poincar\'e
invariants of the motion. We go on to explore the structure of these invariants
in higher-order models. In particular, the integrability of the model described
by a lagrangian that is a function of the second FS curvature (or torsion) is
established in a three dimensional ambient spacetime.Comment: 20 pages, no figures - replaced with version to appear in Class.
Quant. Grav. - minor changes, added Conclusions sectio
Gauge fixing and equivariant cohomology
The supersymmetric model developed by Witten to study the equivariant
cohomology of a manifold with an isometric circle action is derived from the
BRST quantization of a simple classical model. The gauge-fixing process is
carefully analysed, and demonstrates that different choices of gauge-fixing
fermion can lead to different quantum theories.Comment: 18 pages LaTe
Quantum oscillator as 1D anyon
It is shown that in one spatial dimension the quantum oscillator is dual to
the charged particle situated in the field described by the superposition of
Coulomb and Calogero-Sutherland potentials.Comment: 9 pages, LaTe
Using conceptual metaphor and functional grammar to explore how language used in physics affects student learning
This paper introduces a theory about the role of language in learning
physics. The theory is developed in the context of physics students' and
physicists' talking and writing about the subject of quantum mechanics. We
found that physicists' language encodes different varieties of analogical
models through the use of grammar and conceptual metaphor. We hypothesize that
students categorize concepts into ontological categories based on the
grammatical structure of physicists' language. We also hypothesize that
students over-extend and misapply conceptual metaphors in physicists' speech
and writing. Using our theory, we will show how, in some cases, we can explain
student difficulties in quantum mechanics as difficulties with language.Comment: Accepted for publication in Phys. Rev. ST:PE
Conformal Quivers and Melting Molecules
Quiver quantum mechanics describes the low energy dynamics of a system of
wrapped D-branes. It captures several aspects of single and multicentered BPS
black hole geometries in four-dimensional supergravity such
as the presence of bound states and an exponential growth of microstates. The
Coulomb branch of an Abelian three node quiver is obtained by integrating out
the massive strings connecting the D-particles. It allows for a scaling regime
corresponding to a deep AdS throat on the gravity side. In this scaling
regime, the Coulomb branch is shown to be an invariant
multi-particle superconformal quantum mechanics. Finally, we integrate out the
strings at finite temperature---rather than in their ground state---and show
how the Coulomb branch `melts' into the Higgs branch at high enough
temperatures. For scaling solutions the melting occurs for arbitrarily small
temperatures, whereas bound states can be metastable and thus long lived.
Throughout the paper, we discuss how far the analogy between the quiver model
and the gravity picture, particularly within the AdS throat, can be taken.Comment: 49 pages, 16 figure
The cognitive integration of scientific instruments: Information, situated cognition, and scientific practice
Researchers in the biological and biomedical sciences, particularly those working in laboratories, use a variety of artifacts to help them perform their cognitive tasks. This paper analyses the relationship between researchers and cognitive artifacts in terms of integration. It first distinguishes different categories of cognitive artifacts used in biological practice on the basis of their informational properties. This results in a novel classification of scientific instruments, conducive to an analysis of the cognitive interactions between researchers and artifacts. It then uses a multidimensional framework in line with complementarity-based extended and distributed cognition theory to conceptualize how deeply instruments in different informational categories are integrated into the cognitive systems of their users. The paper concludes that the degree of integration depends on various factors, including the amount of informational malleability, the intensity and kind of information flow between agent and artifact, the trustworthiness of the information, the procedural and informational transparency, and the degree of individualisation
Scientific Discovery Through Fictionally Modelling Reality
How do scientific models represent in a way that enables us to discover new truths about reality and draw inferences about it? Contemporary accounts of scientific discovery answer this question by focusing on the cognitive mechanisms involved in the generation of new ideas and concepts in terms of a special sort of reasoning—or model-based reasoning—involving imagery. Alternatively, I argue that answering this question requires that we recognise the crucial role of the propositional imagination in the construction and development of models for the purpose of generating hypotheses that are plausible can- didates for truth. I propose simple fictionalism as a new account of models as Waltonian games of make-believe and suggest that models can lead to genuine scientific discovery when they are used as representations that denote real world phenomena and generate two main kinds of theoretical hypotheses, model-world comparisons and direct attributions
Superintegrable potentials on 3D Riemannian and Lorentzian spaces with non-constant curvature
A quantum sl(2,R) coalgebra is shown to underly the construction of a large
class of superintegrable potentials on 3D curved spaces, that include the
non-constant curvature analogues of the spherical, hyperbolic and (anti-)de
Sitter spaces. The connection and curvature tensors for these "deformed" spaces
are fully studied by working on two different phase spaces. The former directly
comes from a 3D symplectic realization of the deformed coalgebra, while the
latter is obtained through a map leading to a spherical-type phase space. In
this framework, the non-deformed limit is identified with the flat contraction
leading to the Euclidean and Minkowskian spaces/potentials. The resulting
Hamiltonians always admit, at least, three functionally independent constants
of motion coming from the coalgebra structure. Furthermore, the intrinsic
oscillator and Kepler potentials on such Riemannian and Lorentzian spaces of
non-constant curvature are identified, and several examples of them are
explicitly presented.Comment: 14 pages. Based in the contribution presented at the Group 27
conference, Yerevan, Armenia, August 13-19, 200
- …