Brane structures in microlocal sheaf theory

Let $L$ be an exact Lagrangian submanifold of a cotangent bundle $T^* M$, asymptotic to a Legendrian submanifold $\Lambda \subset T^{\infty} M$. We study a locally constant sheaf of $\infty$-categories on $L$, called the sheaf of brane structures or $\mathrm{Brane}_L$. Its fiber is the $\infty$-category of spectra, and we construct a Hamiltonian invariant, fully faithful functor from $\Gamma(L,\mathrm{Brane}_L)$ to the $\infty$-category of sheaves of spectra on $M$ with singular support in $\Lambda$.Comment: 35 pages, 13 figure

Measurement of single electron spin with sub-micron Hall magnetometer

Submicron Hall magnetometry has been demonstrated as an efficient technique to probe extremely weak magnetic fields. In this letter, we analyze the possibility of employing it to detect single electron spin. Signal strength and readout time are estimated and discussed with respect to a number of practical issues.Comment: 4 pages, 2 figur

The signatures of the new particles h2h_2 and ZμτZ_{\mu\tau} at e-p colliders in the U(1)Lμ−LτU(1)_{L_\mu-L_\tau} model

Considering the superior performances of the future e-p colliders, LHeC and FCC-eh, we discuss the feasibility of detecting the extra neutral scalar $h_{2}$ and the light gauge boson $Z^{}_{\mu\tau}$, which are predicted by the ${U(1)}_{L^{}_{\mu} - L^{}_{\tau}}$ model. Taking into account the experimental constraints on the relevant free parameters, we consider all possible production channels of $h_{2}$ and $Z^{}_{\mu\tau}$ at e-p colliders and further investigate their observability through the optimal channels in the case of the beam polarization P($e^{-}$)= -0.8. We find that the signal significance above 5$\sigma$ of $h_{2}$ as well as $Z^{}_{\mu\tau}$ detecting can be achieved via $e^{-}p\to{e^{-}jh_{2}(\to{Z_{\mu\tau}Z_{\mu\tau}})}\to~e^{-}j+/\!\!\!\!{E}^{}_{T}$ process and a 5$\sigma$ sensitivity of $Z^{}_{\mu\tau}$ detecting can be gained via $e^{-}p\to{e^{-}jh_{1}(\to{Z^{}_{\mu\tau}Z^{}_{\mu\tau}})\to}~e^{-}j+/\!\!\!\!{E}^{}_{T}$ process at e-p colliders with appropriate parameter values and a designed integrated luminosity. However, the signals of $h_{2}$ decays into pair of SM particles are difficult to be detected.Comment: 22 pages, 9 figures, references added and typos are correcte

Finite 33-connected homogeneous graphs

A finite graph \G is said to be {\em $(G,3)$-$($connected$)$ homogeneous} if every isomorphism between any two isomorphic (connected) subgraphs of order at most $3$ extends to an automorphism $g\in G$ of the graph, where $G$ is a group of automorphisms of the graph. In 1985, Cameron and Macpherson determined all finite $(G, 3)$-homogeneous graphs. In this paper, we develop a method for characterising $(G,3)$-connected homogeneous graphs. It is shown that for a finite $(G,3)$-connected homogeneous graph \G=(V, E), either G_v^{\G(v)} is $2$--transitive or G_v^{\G(v)} is of rank $3$ and \G has girth $3$, and that the class of finite $(G,3)$-connected homogeneous graphs is closed under taking normal quotients. This leads us to study graphs where $G$ is quasiprimitive on $V$. We determine the possible quasiprimitive types for $G$ in this case and give new constructions of examples for some possible types