Ultra-low-frequency electromagnetic waves as signals and special counterparts of gravitational waves (from binary mergers) having tensorial and possible nontensorial polarizations

Gravitational waves (GWs, from binary merger) interacting with super-strong magnetic fields of the neutron star (in the same binary system), would lead to perturbed electromagnetic waves [EMWs, in the same frequencies of these GWs, partially in the ultra-low-frequency (ULF) band for the EMWs]. Such perturbed ULF-EMWs are not only the signals, but also a new type of special EM counterparts of the GWs. Here, generation of the perturbed ULF-EMWs is investigated for the first time, and the strengths of their magnetic components are estimated to be around 10^{-12}Tesla to 10^{-17}Tesla (in fISCO) at the Earth for various cases [not including the influence of interstellar medium (ISM)].The components with higher frequencies of the ULF-EMWs (e.g., especially produced by the GWs of the post-merger stage) above 1.8kHz (typical plasma frequency around solar system in the Milky way), could propagate through the ISM from the source until the Earth, and the perturbed ULF-EMWs will be reprocessed before they arrived at the Earth due to the ISM. Also, the waveforms of the perturbed ULF-EMWs will be modified into shapes different but related to the waveforms of the GWs, by the amplification process during the binary mergers which could amplify the magnetic fields into 10^{12}Tesla or even higher. Specific connection relationships between the polarizations of the perturbed ULF-EMWs and the polarizations (tensorial and possible nontensorial) of the GWs of binary mergers, are also addressed here. Characteristic properties of the perturbed ULF-EMWs (which would bring us some different new information of fundamental properties of the gravity and Universe) will be very helpful for extracting the signals from background noise for possible observations in the future.Comment: 16 pages, 6 figure

Counting Multiplicities in a Hypersurface over a Number Field

We fix a counting function of multiplicities of algebraic points in a projective hypersurface over a number field, and take the sum over all algebraic points of bounded height and fixed degree. An upper bound for the sum with respect to this counting function will be given in terms of the degree of the hypersurface, the dimension of the singular locus, the upper bounds of height, and the degree of the field of definition.Comment: 23 page

A twisted ∂ˉf\bar{\partial}_f-Neumann problem and Toeplitz nn-tuples from singularity theory

A twisted $\bar{\partial}_f$-Neumann problem associated to a singularity $(\mathscr{O}_n,f)$ is established. By constructing the connection to the Koszul complex for toeplitz $n$-tuples $(f_1,\cdots,f_n)$ on Bergman spaces $B^0(D)$, we can solve this $\bar{\partial}_f$-Neumann problem. Moreover, we can compute the cohomology of the $L^2$ holomorphic Koszul complex $(B^*(D),\partial f\wedge)$ explicitlyComment: 20 page

On the L2-Hodge theory of Landau-Ginzburg models

Let X be a non-compact Calabi-Yau manifold and f be a holomorphic function on X with compact critical locus. We introduce the notion of f-twisted Sobolev spaces for the pair (X,f) and prove the corresponding Hodge-to-de Rham degeneration property via L2-Hodge theoretical methods when f satisfies an asymptotic condition of strongly ellipticity. This leads to a Frobenius manifold via the Barannikov-Kontsevich construction, unifying the Landau-Ginzburg and Calabi-Yau geometry. Our construction can be viewed as a generalization of K.Saito's higher residue and primitive form theory for isolated singularities. As an application, we construct Frobenius manifolds for orbifold Landau-Ginzburg B-models which admit crepant resolutions.Comment: 41 pages, comments are welcom

Stability of Steady Solutions to Reaction-Hyperbolic Systems for Axonal Transport

This paper is concerned with the stability of steady solutions to initial-boundary-value problems of reaction-hyperbolic systems for axonal transport. Under proper structural assumptions, we clarify the relaxation structure of the reaction-hyperbolic systems and show the time-asymptotic stability of steady solutions or relaxation boundary-layers

Improving spin-based noise sensing by adaptive measurements

Localized spins in the solid state are attracting widespread attention as highly sensitive quantum sensors with nanoscale spatial resolution and fascinating applications. Recently, adaptive measurements were used to improve the dynamic range for spin-based sensing of deterministic Hamiltonian parameters. Here we explore a very different direction -- spin-based adaptive sensing of random noises. First, we identify distinguishing features for the sensing of magnetic noises compared with the estimation of deterministic magnetic fields, such as the different dependences on the spin decoherence, the different optimal measurement schemes, the absence of the modulo-2\pi phase ambiguity, and the crucial role of adaptive measurement. Second, we perform numerical simulations that demonstrate significant speed up of the characterization of the spin decoherence time via adaptive measurements. This paves the way towards adaptive noise sensing and coherence protection.Comment: 13 pages, 7 figure

Simulating the Chiral Magnetic Wave in a Box System

The chiral magnetic wave from the interplay between the chiral magnetic effect and the chiral separation effect is simulated in a box system with the periodic boundary condition based on the chiral kinetic equations of motion. Simulation results are compared with available limits from theoretical derivations, and effects of the temperature, the magnetic field, and the specific shear viscosity on the key properties of the chiral magnetic wave are discussed. Our study serves as a baseline for further simulations of chiral anomalies in relativistic heavy-ion collisions.Comment: 7 pages, 5 figure

Strange Quark Stars as Probe of Dark Matter

We demonstrate that the observation of old strange quark stars (SQSs) can set important limits on the scattering cross sections $\sigma_q$ between the light quarks and the non-interacting scalar dark matter (DM). By analyzing a set of 1403 of solitary pulsarlike compact stars in the Milky Way, we find the old solitary pulsar PSR J1801-0857D can set the most stringent upper limits on $\sigma_q$ or the DM-proton scattering cross sections $\sigma_p$. By converting $\sigma_q$ into $\sigma_p$ based on effective operator analyses, we show the resulting $\sigma_p$ limit by assuming PSR J1801-0857D to be a SQS could be comparable with that of the current direct detection experiments but much weaker (by several orders of magnitude) than that obtained by assuming PSR J1801-0857D to be a neutron star (NS), which requires an extremely small $\sigma_p$ far beyond the limits of direct detection experiments. Our findings imply that the old pulsars are favored to be SQSs rather than NSs if the scalar DM were observed by future terrestrial experiments.Comment: 6 pages, 4 figures. Some results updated and discussions added. Accepted version to appear in Ap

Effects of the U-boson on the inner edge of neutron star crusts

We explore effects of the light vector $U$-boson, which is weakly coupled to nucleons, on the transition density $\rho_{t}$ and pressure $P_{t}$ at the inner edge separating the liquid core from the solid crust of neutron stars. Three methods, i.e., the thermodynamical approach, the curvature matrix approach and the Vlasov equation approach are used to determine the transition density $\rho_{t}$ with the Skyrme effective nucleon-nucleon interactions. We find that the $\rho_{t}$ and $P_{t}$ depend on not only the ratio of coupling strength to mass squared of the $U$-boson $g^{2}/\mu ^{2}$ but also its mass $\mu$ due to the finite range interaction from the $U$-boson exchange. In particular, our results indicate that the $\rho_{t}$ and $P_{t}$ are sensitive to both $g^{2}/\mu ^{2}$ and $\mu$ if the $U$-boson mass $\mu$ is larger than about 2 MeV. Furthermore, we show that both $g^{2}/\mu ^{2}$ and $\mu$ can have significant influence on the mass-radius relation and the crustal fraction of total moment of inertia of neutron stars. In addition, we study the exchange term contribution of the $U$-boson based on the density matrix expansion method, and demonstrate that the exchange term effects on the nuclear matter equation of state as well as the $\rho_{t}$ and $P_{t}$ are generally negligible.Comment: 16 pages, 8 figures. Fig. 1 and Fig. 4 revised, typos fixed. Published version in PR

Weak entropy solutions of nonlinear reaction-hyperbolic systems for axonal transport

This paper is concerned with a class of nonlinear reaction-hyperbolic systems as models for axonal transport in neuroscience. We show the global existence of entropy-satisfying BV-solutions to the initial-value problems by using hyperbolic-type methods. Moreover, we rigorously justify the limit as the biochemical processes are much faster than the transport ones