Ranking and Selection under Input Uncertainty: Fixed Confidence and Fixed Budget

In stochastic simulation, input uncertainty (IU) is caused by the error in estimating the input distributions using finite real-world data. When it comes to simulation-based Ranking and Selection (R&S), ignoring IU could lead to the failure of many existing selection procedures. In this paper, we study R&S under IU by allowing the possibility of acquiring additional data. Two classical R&S formulations are extended to account for IU: (i) for fixed confidence, we consider when data arrive sequentially so that IU can be reduced over time; (ii) for fixed budget, a joint budget is assumed to be available for both collecting input data and running simulations. New procedures are proposed for each formulation using the frameworks of Sequential Elimination and Optimal Computing Budget Allocation, with theoretical guarantees provided accordingly (e.g., upper bound on the expected running time and finite-sample bound on the probability of false selection). Numerical results demonstrate the effectiveness of our procedures through a multi-stage production-inventory problem

Tunable Intrinsic Plasmons due to Band Inversion in Topological Materials

The band inversion has led to rich physical effects in both topological insulators and topological semimetals. It has been found that the inverted band structure with the Mexican-hat dispersion could enhance the interband correlation leading to a strong intrinsic plasmon excitation. Its frequency ranges from several $\mathrm{meV}$ to tens of $\mathrm{meV}$ and can be effectively tuned by the external fields. The electron-hole asymmetric term splits the peak of the plasmon excitation into double peaks. The fate and properties of this plasmon excitation can also act as a probe to characterize the topological phases even in the lightly doped systems. We numerically demonstrate the impact of the band inversion on plasmon excitations in magnetically doped thin films of three-dimensional strong topological insulators, V- or Cr-doped (Bi, Sb)$_2$Te$_3$, which support the quantum anomalous Hall states. Our work thus sheds some new light on the potential applications of topological materials in plasmonics.Comment: 6 pages, 5 figures, Accepted in PR

Physical limits to sensing material properties

Constitutive relations describe how materials respond to external stimuli such as forces. All materials respond heterogeneously at small scales, which limits what a localized sensor can discern about the global constitution of a material. In this paper, we quantify the limits of such constitutional sensing by determining the optimal measurement protocols for sensors embedded in disordered media. For an elastic medium, we find that the least fractional uncertainty with which a sensor can determine a material constant $\lambda_0$ is approximately \begin{equation*} \frac{\delta \lambda_0}{\lambda_0 } \sim \left( \frac{\Delta_{\lambda} }{ \lambda_0^2} \right)^{1/2} \left( \frac{ d }{ a } \right)^{D/2} \left( \frac{ \xi }{ a } \right)^{D/2} \end{equation*} for $a \gg d \gg \xi$, $\lambda_0 \gg \Delta_{\lambda}^{1/2}$, and $D>1$, where $a$ is the size of the sensor, $d$ is its spatial resolution, $\xi$ is the correlation length of fluctuations in the material constant, $\Delta_{\lambda}$ is the local variability of the material constant, and $D$ is the dimension of the medium. Our results reveal how one can construct microscopic devices capable of sensing near these physical limits, e.g. for medical diagnostics. We show how our theoretical framework can be applied to an experimental system by estimating a bound on the precision of cellular mechanosensing in a biopolymer network.Comment: 33 pages, 3 figure

Berry phase modification to the energy spectrum of excitons

By quantizing the semiclassical motion of excitons, we show that the Berry curvature can cause an energy splitting between exciton states with opposite angular momentum. This splitting is determined by the Berry curvature flux through the $\bm k$-space area spanned by the relative motion of the electron-hole pair in the exciton wave function. Using the gapped two-dimensional Dirac equation as a model, we show that this splitting can be understood as an effective spin-orbit coupling effect. In addition, there is also an energy shift caused by other "relativistic" terms. Our result reveals the limitation of the venerable hydrogenic model of excitons, and highlights the importance of the Berry curvature in the effective mass approximation.Comment: 4.5 pages, 2 figures, reference updated and minor change