Topological Strings and Quantum Spectral Problems

We consider certain quantum spectral problems appearing in the study of local Calabi-Yau geometries. The quantum spectrum can be computed by the Bohr-Sommerfeld quantization condition for a period integral. For the case of small Planck constant, the periods are computed perturbatively by deformation of the Omega background parameters in the Nekrasov-Shatashvili limit. We compare the calculations with the results from the standard perturbation theory for the quantum Hamiltonian. There have been proposals in the literature for the non-perturbative contributions based on singularity cancellation with the perturbative contributions. We compute the quantum spectrum numerically with some high precisions for many cases of Planck constant. We find that there are also some higher order non-singular non-perturbative contributions, which are not captured by the singularity cancellation mechanism. We fix the first few orders formulas of such corrections for some well known local Calabi-Yau models.Comment: 47 pages, 3 figures. v2: journal version, typos correcte

Giant negative magnetoresistance induced by the chiral anomaly in individual Cd3As2 nanowires

Cd3As2 is a newly booming Dirac semimetal with linear dispersion along all three momentum directions and can be viewed as 3D analog of graphene. As breaking of either time reversal symmetry or spatial inversion symmetry, the Dirac semimetal is believed to transform into Weyl semimetal with exotic chiral anomaly effect, while the experimental evidence of the chiral anomaly is still missing in Cd3As2. Here we report the magneto-transport properties of individual Cd3As2 nanowires. Large negative magnetoresistance (MR) with magnitude of -63% at 60 K and -11% at 300 K are observed when the magnetic field is parallel with the electric field direction, giving the evidence of the chiral magnetic effect in Cd3As2 nanowires. In addition, the critical magnetic field BC, where there is an extremum of the negative MR, increases with increasing temperature. As the first observation of chiral anomaly induced negative MR in Cd3As2 nanowires, it may offer valuable insights for low dimensional physics in Dirac semimetals.Comment: 4 figure

Iterative Schemes by a New Generalized Resolvent for a Monotone Mapping and a Relatively Weak Nonexpansive Mapping

We introduce a new generalized resolvent in a Banach space and discuss some of its properties. Using these properties, we obtain an iterative scheme for finding a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping. Furthermore, strong convergence of the scheme to a point which is a fixed point of relatively weak nonexpansive mapping and a zero of monotone mapping is proved

Ballistic Thermal Rectification in Asymmetric Three-Terminal Mesoscopic Dielectric Systems

By coupling the asymmetric three-terminal mesoscopic dielectric system with a temperature probe, at low temperature, the ballistic heat flux flow through the other two asymmetric terminals in the nonlinear response regime is studied based on the Landauer formulation of transport theory. The thermal rectification is attained at the quantum regime. It is a purely quantum effect and is determined by the dependence of the ratio $\tau_{RC}(\omega)/\tau_{RL}(\omega)$ on $\omega$, the phonon's frequency. Where $\tau_{RC}(\omega)$ and $\tau_{RL}(\omega)$ are respectively the transmission coefficients from two asymmetric terminals to the temperature probe, which are determined by the inelastic scattering of ballistic phonons in the temperature probe. Our results are confirmed by extensive numerical simulations.Comment: 10 pages, 4 figure

Varstrometry Selected Radio-Loud Candidates of Dual and Off-Nucleus Quasars at Sub-kpc Scales

Dual super massive black holes at sub-kpc to kpc scales, the product of galaxy mergers, are progenitors of eventually coalescing binary SMBHs. If both or one of the dual SMBHs are accreting, they may appear as dual AGNs or off-nucleus AGNs. Studying such systems is essential to learn the dynamical evolution of binary SMBHs as well as the process of galaxy merging. Recently a novel astrometry-based method named varstrometry has been put forward to search for dual SMBHs at high redshift, as the unsynchronized flux variability of dual AGNs (or off-nucleus AGNs) will cause astrometric jitters detectable by Gaia without spatially resolving them. Based on Gaia varstrometry we select a rare sample of 5 radio loud quasars with clear Gaia astrometric jitters. With e-MERLIN observations we have revealed a single compact radio source for each of them. Remarkably all but one exhibit clear Gaia-radio offsets of ~ 9 -- 60 mas. The observed Gaia jitters appear consistent with the expected values. These detected Gaia-radio offsets suggest these candidate dual SMBHs may have projected separations as small as ~ 0.01 -- 0.1'' (~ 0.1 kpc, depending on the optical flux ratio of two SMBHs). Meanwhile, this work highlights the remarkably high efficiency of Gaia varstrometry selection of jittering sources.Comment: 6 pages, 5 figures, 1 table; accepted for publication in MNRAS Letter