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 $SU(n+1)$ group which commute with the supercharges of N=4 supersymmetric $\mathbb{CP}^n$ 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 $SU(n+1)$ 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 $\mathcal{N} = 2$ 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$_2$ throat on the gravity side. In this scaling regime, the Coulomb branch is shown to be an $SL(2,\mathbb{R})$ 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$_2$ 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