1,336 research outputs found
Aharonov-Bohm cages in the GaAlAs/GaAs system
Aharonov-Bohm oscillations have been observed in a lattice formed by a two
dimensional rhombus tiling. This observation is in good agreement with a recent
theoretical calculation of the energy spectrum of this so-called T3 lattice. We
have investigated the low temperature magnetotransport of the T3 lattice
realized in the GaAlAs/GaAs system. Using an additional electrostatic gate, we
have studied the influence of the channel number on the oscillations amplitude.
Finally, the role of the disorder on the strength of the localization is
theoretically discussed.Comment: 6 pages, 11 EPS figure
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When almost is not even close: Remarks on the approximability of HDTP
A growing number of researchers in Cognitive Science advocate the thesis that human cognitive capacities are constrained by computational tractability. If right, this thesis also can be expected to have far-reaching consequences for work in Artificial General Intelligence: Models and systems considered as basis for the development of general cognitive architectures with human-like performance would also have to comply with tractability constraints, making in-depth complexity theoretic analysis a necessary and important part of the standard research and development cycle already from a rather early stage. In this paper we present an application case study for such an analysis based on results from a parametrized complexity and approximation theoretic analysis of the Heuristic Driven Theory Projection (HDTP) analogy-making framework
Creation of effective magnetic fields in optical lattices: The Hofstadter butterfly for cold neutral atoms
We investigate the dynamics of neutral atoms in a 2D optical lattice which
traps two distinct internal states of the atoms in different columns. Two Raman
lasers are used to coherently transfer atoms from one internal state to the
other, thereby causing hopping between the different columns. By adjusting the
laser parameters appropriately we can induce a non vanishing phase of particles
moving along a closed path on the lattice. This phase is proportional to the
enclosed area and we thus simulate a magnetic flux through the lattice. This
setup is described by a Hamiltonian identical to the one for electrons on a
lattice subject to a magnetic field and thus allows us to study this equivalent
situation under very well defined controllable conditions. We consider the
limiting case of huge magnetic fields -- which is not experimentally accessible
for electrons in metals -- where a fractal band structure, the Hofstadter
butterfly, characterizes the system.Comment: 6 pages, RevTe
Future Missions to the Giant Planets that Can Advance Atmospheric Science Objectives:Space Science Reviews
Other papers in this special issue have discussed the diversity of planetary atmospheres and some of the key science questions for giant planet atmospheres to be addressed in the future. There are crucial measurements that can only be made by orbiters of giant planets and probes dropped into their atmospheres. To help the community be more effective developers of missions and users of data products, we summarize how NASA and ESA categorize their planetary space missions, and the restrictions and requirements placed on each category. We then discuss the atmospheric goals to be addressed by currently approved giant-planet missions as well as missions likely to be considered in the next few years, such as a joint NASA/ESA Ice Giant orbiter with atmospheric probe. Our focus is on interplanetary spacecraft, but we acknowledge the crucial role to be played by ground-based and near-Earth telescopes, as well as theoretical and laboratory work. © 2020, Springer Nature B.V
Computable functions, quantum measurements, and quantum dynamics
We construct quantum mechanical observables and unitary operators which, if
implemented in physical systems as measurements and dynamical evolutions, would
contradict the Church-Turing thesis which lies at the foundation of computer
science. We conclude that either the Church-Turing thesis needs revision, or
that only restricted classes of observables may be realized, in principle, as
measurements, and that only restricted classes of unitary operators may be
realized, in principle, as dynamics.Comment: 4 pages, REVTE
Hofstadter-type energy spectra in lateral superlattices defined by periodic magnetic and electrostatic fields
We calculate the energy spectrum of an electron moving in a two-dimensional
lattice which is defined by an electric potential and an applied perpendicular
magnetic field modulated by a periodic surface magnetization. The spatial
direction of this magnetization introduces complex phases into the Fourier
coefficients of the magnetic field. We investigate the effect of the relative
phases between electric and magnetic modulation on band width and internal
structure of the Landau levels.Comment: 5 LaTeX pages with one gif figure to appear in Phys. Rev.
A Tale of Two Fractals: The Hofstadter Butterfly and The Integral Apollonian Gaskets
This paper unveils a mapping between a quantum fractal that describes a
physical phenomena, and an abstract geometrical fractal. The quantum fractal is
the Hofstadter butterfly discovered in 1976 in an iconic condensed matter
problem of electrons moving in a two-dimensional lattice in a transverse
magnetic field. The geometric fractal is the integer Apollonian gasket
characterized in terms of a 300 BC problem of mutually tangent circles. Both of
these fractals are made up of integers. In the Hofstadter butterfly, these
integers encode the topological quantum numbers of quantum Hall conductivity.
In the Apollonian gaskets an infinite number of mutually tangent circles are
nested inside each other, where each circle has integer curvature. The mapping
between these two fractals reveals a hidden threefold symmetry embedded in the
kaleidoscopic images that describe the asymptotic scaling properties of the
butterfly. This paper also serves as a mini review of these fractals,
emphasizing their hierarchical aspects in terms of Farey fractions
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