2,172 research outputs found
Constructive Field Theory and Applications: Perspectives and Open Problems
In this paper we review many interesting open problems in mathematical
physics which may be attacked with the help of tools from constructive field
theory. They could give work for future mathematical physicists trained with
the constructive methods well within the 21st century
Frequency Scaling of Microwave Conductivity in the Integer Quantum Hall Effect Minima
We measure the longitudinal conductivity at frequencies GHz over a range of temperatures K with particular emphasis on the Quantum Hall plateaus. We find that
scales linearly with frequency for a range of magnetic field
around the center of the plateaus, i.e. where . The width of this scaling region decreases with higher
temperature and vanishes by 1.2 K altogether. Comparison between localization
length determined from and DC measurements on the same
wafer show good agreement.Comment: latex 4 pages, 4 figure
Absence of Scaling in the Integer Quantum Hall Effect
We have studied the conductivity peak in the transition region between the
two lowest integer Quantum Hall states using transmission measurements of edge
magnetoplasmons. The width of the transition region is found to increase
linearly with frequency but remains finite when extrapolated to zero frequency
and temperature. Contrary to prevalent theoretical pictures, our data does not
show the scaling characteristics of critical phenomena.These results suggest
that a different mechanism governs the transition in our experiment.Comment: Minor changes and new references include
The numbers of chiral and achiral alkanes and monosubstituted alkanes
Whereas the theory for the enumeration of the optical isomers of the lakyl radicals and the alkanes has long been understood, this is not the case for the corresponding archiral isomers. We present for the first time recurrence formulae for counting the number of archiral isomers of the alkyl radicals and the alkanes. For chiral and archiral alkanes and monosubstituted alkanes, numerical results up to C14 are tabulated.After presenting the history of the problem and the necessary definitions, we proceed to derive functional equations on the various generating functions, which readily yield the more explicit recurrence formulae usefule for numerical calculations. In the process, we first re-derive Polya's expression for planted steric trees using his classical enumeration theorem. This result is then extended to the enumeration of free steric trees using the now standard tree-counting method due to Otter and known as a dissimilarity characteristic equation.By definition, a steric tree is a quartic tree (all points having degree 1 or 4) in which the four neighbors of every carbon point are given a tetrahedral configuration. Building on the methods of the first two authors for counting chiral and archiral trees in the plane, we obtain the formula for counting achiral steric trees, thus setting a problem first enunciated by van't Hoff and Le Bel in 1874.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/21904/1/0000311.pd
Strong, Ultra-narrow Peaks of Longitudinal and Hall Resistances in the Regime of Breakdown of the Quantum Hall Effect
With unusually slow and high-resolution sweeps of magnetic field, strong,
ultra-narrow (width down to ) resistance peaks are observed in
the regime of breakdown of the quantum Hall effect. The peaks are dependent on
the directions and even the history of magnetic field sweeps, indicating the
involvement of a very slow physical process. Such a process and the sharp peaks
are, however, not predicted by existing theories. We also find a clear
connection between the resistance peaks and nuclear spin polarization.Comment: 5 pages with 3 figures. To appear in PR
Optimizing Multi-Photon Fluorescence Microscopy Light Collection from Living Tissue by Non-Contact Total Emission Detection (TEDII)
Farrando Sicilia, Jordi; Fuente Fuente, Carlo
Sparse Kneser graphs are Hamiltonian
For integers k≥1 and n≥2k+1, the Kneser graph K(n,k) is the graph whose vertices are the k-element subsets of {1,…,n} and whose edges connect pairs of subsets that are disjoint. The Kneser graphs of the form K(2k+1,k) are also known as the odd graphs. We settle an old problem due to Meredith, Lloyd, and Biggs from the 1970s, proving that for every k≥3, the odd graph K(2k+1,k) has a Hamilton cycle. This and a known conditional result due to Johnson imply that all Kneser graphs of the form K(2k+2a,k) with k≥3 and a≥0 have a Hamilton cycle. We also prove that K(2k+1,k) has at least 22k−6 distinct Hamilton cycles for k≥6. Our proofs are based on a reduction of the Hamiltonicity problem in the odd graph to the problem of finding a spanning tree in a suitably defined hypergraph on Dyck words
Optimizing Multi-Photon Fluorescence Microscopy Light Collection from Living Tissue by Non-Contact Total Emission Detection (TEDII)
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