49,577 research outputs found
Metric space analysis of systems immersed in a magnetic field
Understanding the behavior of quantum systems subject to magnetic fields is
of fundamental importance and underpins quantum technologies. However, modeling
these systems is a complex task, because of many-body interactions and because
many-body approaches such as density functional theory get complicated by the
presence of a vector potential into the system Hamiltonian. We use the metric
space approach to quantum mechanics to study the effects of varying the
magnetic vector potential on quantum systems. The application of this technique
to model systems in the ground state provides insight into the fundamental
mapping at the core of current density functional theory, which relates the
many-body wavefunction, particle density and paramagnetic current density. We
show that the role of the paramagnetic current density in this relationship
becomes crucial when considering states with different magnetic quantum
numbers, . Additionally, varying the magnetic field uncovers a richer
complexity for the "band structure" present in ground state metric spaces, as
compared to previous studies varying scalar potentials. The robust nature of
the metric space approach is strengthened by demonstrating the gauge invariance
of the related metric for the paramagnetic current density. We go beyond ground
state properties and apply this approach to excited states. The results suggest
that, under specific conditions, a universal behavior may exist for the
relationships between the physical quantities defining the system
A fully 3-dimensional thermal model of a comet nucleus
A 3-D numerical model of comet nuclei is presented. An implicit numerical
scheme was developed for the thermal evolution of a spherical nucleus composed
of a mixture of ice and dust. The model was tested against analytical
solutions, simplified numerical solutions, and 1-D thermal evolution codes. The
3-D code was applied to comet 67P/Churyumov-Gerasimenko; surface temperature
maps and the internal thermal structure was obtained as function of depth,
longitude and hour angle. The effect of the spin axis tilt on the surface
temperature distribution was studied in detail. It was found that for small
tilt angles, relatively low temperatures may prevail on near-pole areas,
despite lateral heat conduction. A high-resolution run for a comet model of
67P/Churyumov-Gerasimenko with low tilt angle, allowing for crystallization of
amorphous ice, showed that the amorphous/crystalline ice boundary varies
significantly with depth as a function of cometary latitude.Comment: 19 pages, 10 figure
Procedural embodiment and magic in linear equations
How do students think about algebra? Here we consider a theoretical framework which builds from natural human functioning in terms of embodiment – perceiving the world, acting on it and reflecting on the effect of the actions – to shift to the use of symbolism to solve linear equations. In the main, the students involved in this study do not encapsulate algebraic expressions from process to object, they do not solve ‘evaluation equations’ such as by ‘undoing’ the operations on the left, they do not find such equations easier to solve than , and they do not use general principles of ‘do the same thing to both sides.’ Instead they build their own ways of working based on the embodied actions they perform on the symbols, mentally picking them up and moving them around, with the added ‘magic’ of rules such as ‘change sides, change signs.’ We consider the need for a theoretical framework that includes both embodiment and process-object encapsulation of symbolism and the need for communication of theoretical insights to address the practical problems of teachers and students
Darwin-Riemann problems in general relativity
A review is given of recent results about the computation of irrotational
Darwin-Riemann configurations in general relativity. Such configurations are
expected to represent fairly well the late stages of inspiralling binary
neutron stars.Comment: 20 pages, 11 PostScript figures, uses PTPTeX, to appear in the
Proceedings of Yukawa International Seminar 99 "Black Holes and Gravitational
Waves", edited by T. Nakamura & H. Kodama, Prog. Theor. Phys. Supp
Transport properties in resonant tunneling heterostructures
We use an adiabatic approximation in terms of instantaneous resonances to
study the steady-state and time-dependent transport properties of interacting
electrons in biased resonant tunneling heterostructures. This approach leads,
in a natural way, to a transport model of large applicability consisting of
reservoirs coupled to regions where the system is described by a nonlinear
Schr\"odinger equation. From the mathematical point of view, this work is
non-rigorous but may offer some fresh and interesting problems involving
semiclassical approximation, adiabatic theory, non-linear Schr\"odinger
equations and dynamical systems.Comment: 25 pages including 9 postscript figures; requires REVTeX 3.0, psfig;
uuencoded gz-compressed .tar file; preprint 1133 April 96 Ecole Polytechnique
to be published in J. Math. Phys. october 199
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