arXiv subjects

Hua-Yu Bai

Publications and source records attributed to Hua-Yu Bai.

3 recordsLinked to original sources

arXiv2026

Generating function for Hermitian and non-Hermitian models

It is well known that Hermitian and non-Hermitian models exhibit distinct physics and require different theoretical tools. In this work, we propose a unified generating-function framework for both classes with generic boundary conditions and local impurities. Within this framework, any finite lattice model can be mapped to a generating function of the form G(z)=P(z)/Q(z), where Q(z) and P(z) denote the bulk recurrence relation and boundary terms or impurities, respectively. The problem of solving for eigenstates reduces to a simple criterion based on the cancellation of zeros of Q(z) and P(z). Applying this method to the Hatano-Nelson (HN) model, we show how boundary conditions and impurities determine the location of the zeros, thereby demonstrating the boundary sensitivity of non-Hermitian systems. We further investigate topological edge states in the non-Hermitian Su-Schrieffer-Heeger (SSH) model and identify its topological phase transition. Inspired by generating-function techniques widely used in discrete mathematics, particularly in the study of the Fibonacci sequence, our results establish a direct connection between non-Hermitian physics and recurrence relations, providing a new perspective for analyzing non-Hermitian systems and exploring their connections with discrete mathematical structures.

quant-ph↗

arXiv2025

Skin mode tunability and self-healing effect in photonic Floquet lattices

Non-Hermitian systems host exotic phenomena absent in their Hermitian counterparts, including the recently predicted self-healing effect (SHE) of non-Hermitian skin modes. To date, the SHE of skin modes in non-Hermitian systems has not been observed experimentally. Here we propose a feasible scheme to realize SHE in photonic Floquet lattices by exploiting skin mode tunability (SMT), a mechanism in which the spectrum of skin modes localized at one boundary can be tuned via a potential applied at the opposite boundary. Such tunability arises from the non-Hermitian biorthogonality of the eigenstates. We demonstrate that a certain skin mode is exceptionally sensitive to remote-boundary potentials in an array of $100$ coupled helical waveguides, allowing broad-range spectral control and the generation of SHE with experimentally accessible parameters. Our results establish a general framework for engineering skin modes via local perturbations, thereby expanding the toolbox for non-Hermitian wave control.

physics.optics↗

arXiv2025

Reentrant phase transition in quasiperiodic photonic waveguides

Anderson transition in quasiperiodic potentials and the associated mobility edges have been a central focus in quantum simulation across multidisciplinary physical platforms. While these transitions have been experimentally observed in ultracold atoms, acoustic systems, optical waveguides, and superconducting junctions, their interplay between quasiperiodic potential and long-range hopping remains unexplored experimentally. In this work, we report the observation of localization-delocalization transition induced by the hopping between the next-nearest neighboring sites using quasiperiodic photonic waveguides. Our findings demonstrate that increasing the next-nearest hopping strength induces a reentrant phase transition, where the system transitions from an initially extended phase into a localized phase before eventually returning to an extended phase. This remarkable interplay between hopping and quasiperiodic potential in the lattice models provides crucial insights into the mechanism of Anderson transition. Furthermore, our numerical simulation reveals that this phase transition exhibits a critical exponent of $ν\simeq 1/3$, which is experimentally observable for system sizes $L\sim10^3$ - $10^4$. These results establish a framework for direct observation of the Anderson transition and precise determination of its critical exponents, which can significantly advance our understanding of localization physics in quasiperiodic systems.

cond-mat.mes-hall↗