arXiv subjects

Jianlong Liu

Publications and source records attributed to Jianlong Liu.

7 recordsLinked to original sources

arXiv2026

Covers of Tiling Spaces

We study the ways that one tiling space can be a finite regular cover of another. We classify all of the finite regular covers of a tiling space via its structure as an inverse limit space. If the tiling space $\Omega$ can be written as an inverse limit $\varprojlim \Gamma_n$, then the \'etale fundamental group of $\Omega$, which is defined via a limit of covers, is isomorphic to the inverse limit $\hat \pi_1(\Omega) := \varprojlim \hat \pi_1(\Gamma_n)$ of the profinite completions of the fundamental groups $\pi_1(\Gamma_n)$. This isomorphism allows us to construct all covers of tiling spaces and to use those covers to distinguish spaces that have identical cohomology groups.

math.AT↗

arXiv2025

New results on tilings via cup products and Chern characters on tiling spaces

We study the cohomology rings of tiling spaces $Ω$ given by cubical substitutions. While there have been many calculations before of cohomology groups of such tiling spaces, the innovation here is that we use computer-assisted methods to compute the cup-product structure. This leads to examples of substitution tilings with isomorphic cohomology groups but different cohomology rings. Part of the interest in studying the cup product comes from Bellissard's gap-labeling conjecture, which is known to hold in dimensions $\le 3$, but where a proof is known in dimensions $\ge 4$ only when the Chern character from $K^0(Ω)$ to $H^*(Ω,\mathbb{Q})$ lands in $H^*(Ω,\mathbb{Z})$. Computation of the cup product on cohomology often makes it possible to compute the Chern character. We introduce a natural generalization of the gap-labeling conjecture, called the equivariant gap-labeling conjecture, which applies to tilings with a finite symmetry group. Again this holds in dimensions $\le 3$, but we are able to show that it fails in general in dimensions $\ge 4$. This, plus some of our cup product calculations, makes it plausible that the gap-labeling conjecture might fail in high dimensions.

math.DS↗

arXiv2024

Research on the identification of the two-phase flow pattern of gas-liquid in a vertical rising tube based on BP neural networks

Research on the identification of the two-phase flow pattern of gas-liquid in a vertical rising pipe is of great significance for improving the production capacity and production efficiency of the petrochemical industry. In order to address the problem of the accuracy of the identification of the two-phase flow pattern of gas-liquid, this paper proposes a method for identifying the two-phase flow pattern of gas-liquid in a vertical rising pipe based on BP neural networks. In the study, the Fluent software was used to numerically simulate different two-phase flow velocities. The pipes were all constructed as vertical rising pipes with an inner diameter of 20 mm and a length of 2000 mm. Three flow pattern cloud diagrams and their related data were obtained for bubble flow, elastic flow, and annular flow. The gas content of the three flow types was used to collect data to form a database. The BP neural network was used to classify and identify the three flow patterns, but the result was only 90.73%. We again used the Adam algorithm to optimise the BP neural network and regularise it, and the flow pattern recognition result reached 96.68%, which was a better recognition

physics.flu-dyn↗

arXiv2023

$K$-theory of two-dimensional substitution tiling spaces from $AF$-algebras

Given a two-dimensional substitution tiling space, we show that, under some reasonable assumptions, the $K$-theory of the groupoid $C^\ast$-algebra of its unstable groupoid can be explicitly reconstructed from the $K$-theory of the $AF$-algebras of the substitution rule and its analogue on the $1$-skeleton. We prove this by generalizing the calculations done for the chair tiling in [JS16] using relative $K$-theory and excision, and packaging the result into an exact sequence purely in topology. From this exact sequence, it appears that one cannot use only ordinary $K$-theory to compute using the dimension-filtration on the unstable groupoid. Several examples are computed using Sage and the results are compiled in a table.

math.OA↗

arXiv2019

Near-term performance of quantum repeaters with imperfect ensemble-based quantum memories

We study the feasibility of meaningful proof-of-principle demonstrations of several quantum repeater protocols with photon (single-photon and photon-pair) sources and atomic-ensemble based quantum memories. We take into account non-unit memory efficiencies that decay exponentially with time, which complicates the calculation of repeater rates. We discuss implementations based on quantum dots, parametric down-conversion, rare-earth-ion doped crystals, and Rydberg atoms. Our results provide guidance for the near-term implementation of long-distance quantum repeater demonstrations, suggesting that such demonstrations are within reach of current technology.

quant-ph↗

arXiv2019

Polarization diversity close to the optical bound states in the continuum

Bound states in the continuum (BICs) realized in two-dimensional (2D) photonic crystal slabs (PhCSs) have attracted considerable attentions, owing to the advantages in the fabrications and on-chip applications. The polarization vortex centered at BICs in the momentum space displayed by the linear polarization vectors of far-field radiation is a striking property of BICs. Here, by constructing BICs at K point in photonic graphenes, we theoretically demonstrate that the far-field polarization states close to BICs can exhibit remarkable polarization diversity. Interestingly, C-points (circular polarizations) close to BIC at K point are observed. Thus, we propose that, along a closed loop enclosing BICs in the momentum space, the trajectory of the far-field polarization states on the shell of the Poincare sphere could provide a general and straightforward means to characterize the topological natures of BICs. The topological charge carried by the BIC can be defined by the half of the winding number of the trajectory around the S3 axis, which is an integer and half integer for the non-degenerate and double-degenerate BICs at K point, respectively. Our findings could open a gateway towards the applications of BICs in lasers with full polarizations and the generation and manipulation of vector beams of light.

physics.optics↗

arXiv2016

Pseudospin induced chirality with Staggered Optical Graphene

Pseudospin plays a very important role in understanding various interesting physical phenomena associated with 2D materials such as graphene. It has been proposed that pseudospin is directly related to angular momentum, and it was recently experimentally demonstrated that orbit angular momentum is an intrinsic property of pseudospin in a photonic honeycomb lattice. However, in photonics, the interaction between spin and pseudospin for light has never been investigated. In this Letter, we propose that, in an optical analogue of staggered graphene, i.e. a photonic honeycomb lattice waveguide with in-plane inversion symmetry breaking, the pseudospin mode can strongly couple to the spin of an optical beam incident along certain directions. The spin-pseudospin coupling, caused by the spin-orbit conversion in the scattering process, induces a strong optical chiral effect for the transmitted optical beam. Spin-pseudospin coupling of light opens door to the design of pseudospin-mediated spin or valley selective photonic devices.

physics.optics↗