B.Sc. Physics undergraduate at Xiamen University Malaysia working across mathematical physics, geometry, spectral methods, and quantum foundations. Current projects use eigenvalue localisation, symplectic dynamics, differential geometry, singular perturbation theory, and validation-first numerics.
Technical papers and source repositories for current and past projects.
Independent work · unpublished draft
A preliminary application of Gershgorin discs and Brauer Cassini ovals to eigenvalue localisation for a structured Weyl matrix in the Newman–Penrose formalism.
Read the explanation → #spectral theory#general relativity#structured matrices
Exact kernel overlap, holonomy response, and non-negative synthesis
A complete fixed-sphere research note deriving the exact orientation response of an anisotropic removal kernel, its weak-anisotropy expansion, and a finite non-negative fitting benchmark.
Read the explanation → Read the PDF ↗ Repository ↗ #differential geometry#holonomy#geometric control
Ongoing undergraduate research · supervised by Prof. Tomasz Paterek
A Gaussian-state study of whether local control can enable unconditional gravity-mediated entanglement, using symplectic covariance dynamics, logarithmic negativity, and Riccati methods.
Read the explanation → Read the PDF ↗ Repository ↗ #symplectic dynamics#Floquet theory#quantum information
Self-study note
A literature-based comparison of real, complex, and quaternionic Hilbert-space formulations, aimed at isolating the composition and locality assumptions used by standard quantum theory.
Read the explanation → Read the PDF ↗ Repository ↗ #quantum foundations#division algebras#composition rules
PHY204 term paper · with Xu Ya-Xuan · AI assistance disclosed
A singular-perturbation reading of radiation reaction: τ₀ multiplies the highest derivative, so the τ₀ → 0 limit changes the differential order rather than providing a regular perturbative correction.
Read the explanation → Read the PDF ↗ Repository ↗ #singular perturbations#electrodynamics#numerical methods
Phase-space quantum mechanics and semiclassical limits
A self-contained pedagogical monograph on quantum mechanics formulated in phase space, from the Weyl–Wigner correspondence to the Moyal ⋆-product and the emergence of classical Poisson dynamics as ħ → 0.
Read the explanation → Read the PDF ↗ Repository ↗ #phase space#deformation quantization#semiclassical
Angular momentum algebra and representation theory
A rigorous algebraic treatment of angular momentum in quantum mechanics, built on the 𝔰𝔬(3) and 𝔰𝔲(2) structure, ladder operators, and representation theory, then applied to the hydrogen atom without heuristic shortcuts.
Read the explanation → Read the PDF ↗ Repository ↗ #angular momentum#representation theory#hydrogen atom
Discrete- and continuous-time quantum walks, with numerics
A systematic survey of discrete- and continuous-time quantum walks from a mathematical and physical perspective, contrasting classical diffusion (σ ∝ √t) with quantum ballistic spreading (σ ∝ t), with numerical simulations in Python.
Read the explanation → Read the PDF ↗ Repository ↗ #quantum walks#quantum algorithms#numerics
Eigenvalue localisation (Gershgorin and Cassini) · symplectic and covariance-matrix methods · Floquet theory · Hamilton–Jacobi and Madelung formulations · principal and frame bundles · holonomy · Lie groups · spherical harmonics · singular perturbation theory · real and quaternionic Hilbert spaces.
朋友問我，一顆球形棒棒糖能不能只靠舔變成地球。最佳策略其實只有一行；而我在找到它之前，罰錯了一個星期。