1,249 research outputs found
Femto-Photography of Protons to Nuclei with Deeply Virtual Compton Scattering
Developments in deeply virtual Compton scattering allow the direct
measurements of scattering amplitudes for exchange of a highly virtual photon
with fine spatial resolution. Real-space images of the target can be obtained
from this information. Spatial resolution is determined by the momentum
transfer rather than the wavelength of the detected photon. Quantum photographs
of the proton, nuclei, and other elementary particles with resolution on the
scale of a fraction of a femtometer is feasible with existing experimental
technology.Comment: To be published in Physical Review D. Replaces previous version with
minor changes in presentatio
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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
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
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
On the Green's Function of the almost-Mathieu Operator
The square tight-binding model in a magnetic field leads to the
almost-Mathieu operator which, for rational fields, reduces to a
matrix depending on the components , of the wave vector in the
magnetic Brillouinzone. We calculate the corresponding Green's function without
explicit knowledge of eigenvalues and eigenfunctions and obtain analytical
expressions for the diagonal and the first off-diagonal elements; the results
which are consistent with the zero magnetic field case can be used to calculate
several quantities of physical interest (e. g. the density of states over the
entire spectrum, impurity levels in a magnetic field).Comment: 9 pages, 3 figures corrected some minor errors and typo
Quantum Hall Effect on the Hofstadter Butterfly
Motivated by recent experimental attempts to detect the Hofstadter butterfly,
we numerically calculate the Hall conductivity in a modulated two-dimensional
electron system with disorder in the quantum Hall regime. We identify the
critical energies where the states are extended for each of butterfly subbands,
and obtain the trajectory as a function of the disorder. Remarkably, we find
that when the modulation becomes anisotropic, the critical energy branches
accompanying a change of the Hall conductivity.Comment: 4 pages, 6 figure
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
Quantized Orbits and Resonant Transport
A tight binding representation of the kicked Harper model is used to obtain
an integrable semiclassical Hamiltonian consisting of degenerate "quantized"
orbits. New orbits appear when renormalized Harper parameters cross integer
multiples of . Commensurability relations between the orbit frequencies
are shown to correlate with the emergence of accelerator modes in the classical
phase space of the original kicked problem. The signature of this resonant
transport is seen in both classical and quantum behavior. An important feature
of our analysis is the emergence of a natural scaling relating classical and
quantum couplings which is necessary for establishing correspondence.Comment: REVTEX document - 8 pages + 3 postscript figures. Submitted to
Phys.Rev.Let
Spectral Density of the QCD Dirac Operator near Zero Virtuality
We investigate the spectral properties of a random matrix model, which in the
large limit, embodies the essentials of the QCD partition function at low
energy. The exact spectral density and its pair correlation function are
derived for an arbitrary number of flavors and zero topological charge. Their
microscopic limit provide the master formulae for sum rules for the inverse
powers of the eigenvalues of the QCD Dirac operator as recently discussed by
Leutwyler and Smilga.Comment: 9 pages + 1 figure, SUNY-NTG-93/
Effects of Electron Correlations on Hofstadter Spectrum
By allowing interactions between electrons, a new Harper's equation is
derived to examine the effects of electron correlations on the Hofstadter
energy spectra. It is shown that the structure of the Hofstadter butterfly ofr
the system of correlated electrons is modified only in the band gaps and the
band widths, but not in the characteristics of self-similarity and the Cantor
set.Comment: 13 pages, 5 Postscript figure
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