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 ($T$) and small Landau level filling factors ($\nu$), 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 $T$ vs $\nu$ 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 $T$ and $\nu$. We find that, as expected, the screening efficiency of the pinned WC is very poor at very low $T$ and improves at higher $T$ once the WC melts. Surprisingly, however, rather than monotonically changing with increasing $T$, the screening efficiency shows a well-defined maximum at a $T$ which is close to the previously-reported melting temperature of the WC. Our experimental results suggest a new method to map out a $T$ vs $\nu$ 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 $V$ be a left $R$-module where $R$ is a (not necessarily commutative) ring with unit. The intersection graph \cG(V) of proper $R$-submodules of $V$ is an undirected graph without loops and multiple edges defined as follows: the vertex set is the set of all proper $R$-submodules of $V,$ and there is an edge between two distinct vertices $U$ and $W$ if and only if $U\cap W\neq 0.$ We study these graphs to relate the combinatorial properties of \cG(V) to the algebraic properties of the $R$-module $V.$ 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 $V$ for which \cG(V) is planar