arXiv subjects

Chih-Hao Chang

Publications and source records attributed to Chih-Hao Chang.

7 recordsLinked to original sources

arXiv2026

Gravitational Sommerfeld Effects: Formalism, Renormalization, and Perturbation to $O(G^{10})$

In the effective field theory (EFT) description of binary inspirals, the radiated gravitational waveform receives universal corrections from the curved background, the so-called ``tail effects'', that resum into the so-called ``Sommerfeld factor''. We develop a systematic framework for computing this gravitational Sommerfeld factor for scalar perturbations with the presence of tidal effects on the system. Using the worldline EFT, we recast the diagrammatic resummation as a solution to the $d$-dimensional wave equation with a localized source, and derive a closed-form expression for the Sommerfeld factor in terms of the EFT connection matrix. We prove that the phase of the Sommerfeld factor is exactly the same as elastic Compton scattering phase shift when there is no tidal dissipation. By combining the renormalization techniques in EFT with the Mano--Suzuki--Takasugi method in black hole perturbation theory, we analytically solve the Sommerfeld factor for both the magnitude and phase to $O(G^{10})$ for the $\ell = 0, 1, 2$ partial waves. We further establish a new renormalization group equation for the radiative multipole moments, whose exact solution yields an improved resummation of the waveform beyond the universal tail logarithms. These high-precision data and exact relations pave the way for future waveform resummation.

hep-th↗

arXiv2026

Single-exposure holographic 3D printing via inverse-designed phase masks

Additive manufacturing using light is commonly constrained by serial voxel-by-voxel or layer-by-layer processing, which fundamentally limits fabrication speed and scalability. Here, we introduce a single-exposure holographic three-dimensional (3D) printing approach that synthesizes an entire volumetric dose distribution optically in one step. The method combines inverse-designed microstructured phase masks with photopolymer resins engineered for controlled optical absorption. By precisely tailoring the phase-mask topography, we generate arbitrary 3D light-intensity distributions within the resin, including intentionally encoded dark regions that define hollow internal features. Simultaneously, the resin formulation is designed to balance optical penetration with sufficient local energy deposition to achieve high-fidelity polymerization throughout the volume. Using this approach, millimeter-scale architectures comprising more than $10^{6}$ addressable voxels are fabricated in a single 7.5~s exposure, corresponding to a volumetric throughput of $\sim$1~mm$^{3}$/s ($>10^{5}$~voxels/s). The demonstrated performance is presently limited by resin kinetics and illumination geometry rather than by the phase-mask framework itself. Because the volumetric information capacity scales with the space--bandwidth product of the phase mask, this approach provides a clear pathway toward substantially higher throughput, enabling scalable fabrication of micro-optical components, biomedical scaffolds, and other precision-engineered mesoscale systems.

physics.optics↗

arXiv2025

Towards Hamiltonian Formalism for String Field Theory and Nonlocality

String field theories exhibit exponential suppression of interactions among the component fields at high energies due to infinite-derivative factors such as $e^{\ell^2 \Box / 2}$ in the vertices. This nonlocality has hindered the development of a consistent Hamiltonian formalism, leading some to question whether such a formalism is even viable. To address this challenge, we introduce a toy model inspired by string field theory and construct its Hamiltonian formalism by demanding that it reproduce all correlation functions derived from the path-integral formalism. Within this framework, we demonstrate for this toy model that physical-state constraints can be imposed to eliminate negative-norm states, while zero-norm states decouple from the physical state space. This approach provides a novel perspective on the nonlocality inherent in string field theories.

hep-th↗

arXiv2024

Fabrication of Hierarchical Sapphire Nanostructures using Ultrafast Laser Induced Morphology Change

Sapphire is an attractive material in photonic, optoelectronic, and transparent ceramic applications that stand to benefit from surface functionalization effects stemming from micro/nanostructures. Here we investigate the use of ultrafast lasers for fabricating nanostructures in sapphire by exploring the relationship between irradiation parameters, morphology change, and selective etching. In this approach an ultrafast laser pulse is focused on the sapphire substrate to change the crystalline morphology to amorphous or polycrystalline, which is characterized by examining different vibrational modes using Raman spectroscopy. The irradiated regions are then removed using a subsequent wet etch in hydrofluoric acid. Laser confocal measurements conducted before and after the etching process quantify the degree of selective etching. The results indicate that a threshold laser pulse intensity is required for selective etching to occur. This process can be used to fabricate hierarchical sapphire nanostructures over large areas with enhanced hydrophobicity, which exhibits an apparent contact angle of 140 degrees and a high roll-off angle that are characteristic of the rose petal effect. Additionally, the fabricated structures have high broadband diffuse transmittance of up to 81.8% with low loss, which can find applications in optical diffusers. Our findings provide new insights into the interplay between the light-matter interactions, where Raman shifts associated with different vibrational modes can be used as a predictive measure of selective etching. These results advance the development of sapphire nanostructure fabrication, which can find applications in infrared optics, protective windows, and consumer electronics.

cond-mat.mtrl-sci↗

arXiv2021

Inference of Random Effects for Linear Mixed-Effects Models with a Fixed Number of Clusters

We consider a linear mixed-effects model with a clustered structure, where the parameters are estimated using maximum likelihood (ML) based on possibly unbalanced data. Inference with this model is typically done based on asymptotic theory, assuming that the number of clusters tends to infinity with the sample size. However, when the number of clusters is fixed, classical asymptotic theory developed under a divergent number of clusters is no longer valid and can lead to erroneous conclusions. In this paper, we establish the asymptotic properties of the ML estimators of random-effects parameters under a general setting, which can be applied to conduct valid statistical inference with fixed numbers of clusters. Our asymptotic theorems allow both fixed effects and random effects to be misspecified, and the dimensions of both effects to go to infinity with the sample size.

math.ST↗

arXiv2016

Mixed domain asymptotics for a stochastic process model with time trend and measurement error

We consider a stochastic process model with time trend and measurement error. We establish consistency and derive the limiting distributions of the maximum likelihood (ML) estimators of the covariance function parameters under a general asymptotic framework, including both the fixed domain and the increasing domain frameworks, even when the time trend model is misspecified or its complexity increases with the sample size. In particular, the convergence rates of the ML estimators are thoroughly characterized in terms of the growing rate of the domain and the degree of model misspecification/complexity.

math.ST↗

arXiv2014

Asymptotic theory of generalized information criterion for geostatistical regression model selection

Information criteria, such as Akaike's information criterion and Bayesian information criterion are often applied in model selection. However, their asymptotic behaviors for selecting geostatistical regression models have not been well studied, particularly under the fixed domain asymptotic framework with more and more data observed in a bounded fixed region. In this article, we study the generalized information criterion (GIC) for selecting geostatistical regression models under a more general mixed domain asymptotic framework. Via uniform convergence developments of some statistics, we establish the selection consistency and the asymptotic loss efficiency of GIC under some regularity conditions, regardless of whether the covariance model is correctly or wrongly specified. We further provide specific examples with different types of explanatory variables that satisfy the conditions. For example, in some situations, GIC is selection consistent, even when some spatial covariance parameters cannot be estimated consistently. On the other hand, GIC fails to select the true polynomial order consistently under the fixed domain asymptotic framework. Moreover, the growth rate of the domain and the degree of smoothness of candidate regressors in space are shown to play key roles for model selection.

math.ST↗