Fano Resonance Induced Anomalous Collective Hotspots in Metallic Nanoparticle Dimer Chains

Hotspots with strong near fields due to localized surface plasmons (LSPs) in metallic nanostructures have various applications, such as surface enhanced Raman scattering (SERS). The long range Coulomb coupling between LSPs in periodic metallic nanostructures may lead to interesting collective effects. In this paper, we investigate the combination effects of the local field enhancement and collective plasmon resonances in one dimensional metallic nanoparticle dimer chains. It is found that the strong near field in the gap and the far field interactions among the metallic nanoparticles lead to anomalous collective hotspots with dual enhancement of the electromagnetic field. In particular, the interference between the incident field and the induced internal field leads to Fano-type effect with Wood anomaly related destructive interference and the strong resonance with an extremely narrow width. Our systematic study shows that the correlation between the local structure and the global structure has important impact on the collective spots, which leads to an optimal orientation of the dimer (about 60{\deg} with respect to the chain direction) for the largest gap field enhancement with the incident field polarization parallel to the long axis of the dimer.Comment: 14 pages, 7 figure

Relative volume comparison of Ricci Flow and its applications

In this paper, we derive a relative volume comparison estimate along Ricci flow and apply it to studying the Gromov-Hausdorff convergence of K\"ahler-Ricci flow on a minimal manifold. This new estimate generalizes Perelman's no local collapsing estimate and can be regarded as an analogue of the Bishop-Gromov volume comparison for Ricci flow.Comment: 28 pages; minor change in the proof of Lemma 3.

Degeneration of K\"ahler-Ricci solitons

Let $(Y, d)$ be a Gromov-Hausdorff limit of $n$-dimensional closed shrinking K\"ahler-Ricci solitons with uniformly bounded volumes and Futaki invariants. We prove that off a closed subset of codimension at least 4, Y is a smooth manifold satisfying a shrinking K\"ahler-Ricci soliton equation. A similar convergence result for K\"ahler-Ricci flow of positive first Chern class is also obtained.Comment: 24 page

Ward Identity Implies Recursion Relation at Tree and Loop Level

In this article, we use Ward identity to calculate tree and one loop level off shell amplitudes in pure Yang-Mills theory with a pair of external lines complexified. We explicitly prove Ward identity at tree and one loop level using Feynman rules, and then give recursion relations for the off shell amplitudes. We find that the cancellation details in the proof of Ward identity simplifies our derivation of the recursion relations. Then we calculate three and four point one loop off shell amplitudes as examples of our method.Comment: 23 pages, 10 figure

Exploring the Υ(4S,5S,6S)→hb(1P)η\Upsilon(4S,5S,6S) \to h_b(1P)\eta hidden-bottom hadronic transitions

Recently, Belle Collaboration has reported the measurement of the spin-flipping transition $\Upsilon(4S) \to h_b(1P)\eta$ with an unexpectedly large branching ratio: $\mathcal{B}(\Upsilon(4S) \to h_b(1P)\eta) =(2.18\pm 0.11\pm 0.18)\times 10^{-3}$. Such a large branching fraction contradicts with the anticipated suppression for the spin flip. In this work, we examine the effects induced by intermediate bottomed meson loops and point out that these effects are significantly important. Using the effective Lagrangian approach (ELA), we find the experimental data on $\Upsilon(4S) \to h_b(1P)\eta$ can be accommodated with the reasonable inputs. We then explore the decays $\Upsilon(5S,6S)\to h_b(1P)\eta$ and find that these two channels also have sizable branching fractions. We also calculate these these processes in the framework of nonrelativistic effective field theory (NREFT). For the decays $\Upsilon(4S) \to h_b(1P) \eta$, the NREFT results are at the same order of magnitude but smaller than the ELA results by a factor of $2$ to $5$. For the decays $\Upsilon(5S, 6S) \to h_b(1P) \eta$ the NREFT results are smaller than the ELA results by approximately one order of magnitude. We suggest future experiment Belle-II to search for the $\Upsilon(5S, 6S)\to h_b(1P) \eta$ decays which will be helpful to understand the transition mechanism.Comment: 11 pages, 3 figure

Physical Unclonable Function-based Key Sharing for IoT Security

In many Industry Internet of Things (IIoT) applications, resources like CPU, memory, and battery power are limited and cannot afford the classic cryptographic security solutions. Silicon Physical Unclonable Function (PUF) is a lightweight security primitive that exploits manufacturing variations during the chip fabrication process for key generation and/or device authentication. However, traditional weak PUFs such as Ring Oscillator (RO) PUF generate chip-unique key for each device, which restricts their application in security protocols where the same key is required to be shared in resource-constrained devices. In order to address this issue, we propose a PUF-based key sharing method for the first time. The basic idea is to implement one-to-one input-output mapping with Lookup Table (LUT)-based interstage crossing structures in each level of inverters of RO PUF. Individual customization on configuration bits of interstage crossing structure and different RO selections with challenges bring high flexibility. Therefore, with the flexible configuration of interstage crossing structures and challenges, CRO PUF can generate the same shared key for resource-constrained devices, which enables a new application for lightweight key sharing protocols.Comment: 9 pages, 8 figure

Sensitivity Analysis of an Inverse Problem for the Wave Equation with Caustics

The paper investigates the sensitivity of the inverse problem of recovering the velocity field in a bounded domain from the boundary dynamic Dirichlet-to-Neumann map (DDtN) for the wave equation. Three main results are obtained: (1) assuming that two velocity fields are non-trapping and are equal to a constant near the boundary, it is shown that the two induced scattering relations must be identical if their corresponding DDtN maps are sufficiently close; (2) a geodesic X-ray transform operator with matrix-valued weight is introduced by linearizing the operator which associates each velocity field with its induced Hamiltonian flow. A selected set of geodesics whose conormal bundle can cover the cotangent space at an interior point is used to recover the singularity of the X-ray transformed function at the point; a local stability estimate is established for this case. Although fold caustics are allowed along these geodesics, it is required that these caustics contribute to a smoother term in the transform than the point itself. The existence of such a set of geodesics is guaranteed under some natural assumptions in dimension greater than or equal to three by the classification result on caustics and regularity theory of Fourier Integral Operators. The interior point with the above required set of geodesics is called "fold-regular"; (3) assuming that a background velocity field with every interior point fold-regular is fixed and another velocity field is sufficiently close to it and satisfies a certain orthogonality condition, it is shown that if the two corresponding DDtN maps are sufficiently close then they must be equal.Comment: 32 page

Convergence of K\"ahler-Ricci flow on lower dimensional algebraic manifolds of general type

In this paper, we prove that the $L^4$-norm of Ricci curvature is uniformly bounded along a K\"ahler-Ricci flow on any minimal algebraic manifold. As an application, we show that on any minimal algebraic manifold $M$ of general type and with dimension $n\le 3$, any solution of the normalized K\"ahler-Ricci flow converges to the unique singular K\"ahler-Einstein metric on the canonical model of $M$ in the Cheeger-Gromov topology

Regularity of K\"ahler-Ricci flow

In this short note we announce a regularity theorem for K\"ahler-Ricci flow on a compact Fano manifold (K\"ahler manifold with positive first Chern class) and its application to the limiting behavior of K\"ahler-Ricci flow on Fano 3-manifolds. Moreover, we also present a partial $C^0$ estimate to the K\"ahler-Ricci flow under the regularity assumption, which extends previous works on K\"ahler-Einstein metrics and shrinking K\"ahler-Ricci solitons (cf. \cite{Ti90}, \cite{DoSu12}, \cite{Ti12}, \cite{PSS12}). The detailed proof will appear in \cite{TiZh13}

Stability for the lens rigidity problem

Let $g$ be a Riemannian metric for $\mathbf{R}^d$ ($d\geq 3$) which differs from the Euclidean metric only in a smooth and strictly convex bounded domain $M$. The lens rigidity problem is concerned with recovering the metric $g$ inside $M$ from the corresponding lens relation on the boundary $\partial M$. In this paper, the stability of the lens rigidity problem is investigated for metrics which are a priori close to a given non-trapping metric satisfying "strong fold-regular" condition. A metric $g$ is called strong fold-regular if for each point $x\in M$, there exists a set of geodesics passing through $x$ whose conormal bundle covers $T^*_{x}M$. Moreover, these geodesics contain either no conjugate points or only fold conjugate points with a non-degeneracy condition. Examples of strong fold-regular metrics are constructed and are expected to be generic. Our main result gives the first stability result for the lens rigidity problem in the case of anisotropic metrics which allow conjugate points. The approach is based on the study of the linearized inverse problem of recovering a metric from its induced geodesic flow, which is a weighted geodesic X-ray transform problem for symmetric 2-tensor fields. A key ingredient is to show that the kernel of the X-ray transform on symmetric solenoidal 2-tensor fields is of finite dimension. It remains open whether the kernel space is trivial or not.Comment: A minor modification compared to the previous version to take into account the update of the reference