23,329 research outputs found
Techniques for achieving magnetic cleanliness on deep-space missions
Techniques for obtaining magnetic cleanliness on deep space missions to allow interplanetary magnetic field mappin
Probing the Melting of a Two-dimensional Quantum Wigner Crystal via its Screening Efficiency
One of the most fundamental and yet elusive collective phases of an
interacting electron system is the quantum Wigner crystal (WC), an ordered
array of electrons expected to form when the electrons' Coulomb repulsion
energy eclipses their kinetic (Fermi) energy. In low-disorder, two-dimensional
(2D) electron systems, the quantum WC is known to be favored at very low
temperatures () and small Landau level filling factors (), near the
termination of the fractional quantum Hall states. This WC phase exhibits an
insulating behavior, reflecting its pinning by the small but finite disorder
potential. An experimental determination of a vs phase diagram for
the melting of the WC, however, has proved to be challenging. Here we use
capacitance measurements to probe the 2D WC through its effective screening as
a function of and . We find that, as expected, the screening
efficiency of the pinned WC is very poor at very low and improves at higher
once the WC melts. Surprisingly, however, rather than monotonically
changing with increasing , the screening efficiency shows a well-defined
maximum at a which is close to the previously-reported melting temperature
of the WC. Our experimental results suggest a new method to map out a vs
phase diagram of the magnetic-field-induced WC precisely.Comment: The formal version is published on Phys. Rev. Lett. 122, 116601
(2019
Intersection Graph of a Module
Let be a left -module where is a (not necessarily commutative)
ring with unit. The intersection graph \cG(V) of proper -submodules of
is an undirected graph without loops and multiple edges defined as follows: the
vertex set is the set of all proper -submodules of and there is an edge
between two distinct vertices and if and only if We
study these graphs to relate the combinatorial properties of \cG(V) to the
algebraic properties of the -module We study connectedness, domination,
finiteness, coloring, and planarity for \cG (V). For instance, we find the
domination number of \cG (V). We also find the chromatic number of \cG(V)
in some cases. Furthermore, we study cycles in \cG(V), and complete subgraphs
in \cG (V) determining the structure of for which \cG(V) is planar
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