arXiv subjects

Zhimin Liu

Publications and source records attributed to Zhimin Liu.

6 recordsLinked to original sources

arXiv2024

Quantum state tracking and control of a single molecular ion in a thermal environment

Understanding molecular state evolution is central to many disciplines, including molecular dynamics, precision measurement, and molecule-based quantum technology. Details of the evolution are obscured when observing a statistical ensemble of molecules. Here, we reported real-time observations of thermal radiation-driven transitions between individual states ("jumps") of a single molecule. We reversed these "jumps" through microwave-driven transitions, resulting in a twentyfold improvement in the time the molecule dwells in a chosen state. The measured transition rates showed anisotropy in the thermal environment, pointing to the possibility of using single molecules as in-situ probes for the strengths of ambient fields. Our approaches for state detection and manipulation could apply to a wide range of species, facilitating their uses in fields including quantum science, molecular physics, and ion-neutral chemistry.

physics.atom-ph↗

arXiv2022

Weak Hopf Algebras, Smash Products and Applications to Adjoint-Stable Algebras

For a semisimple quasi-triangular Hopf algebra $\left( H,R\right) $ over a field $k$ of characteristic zero, and a strongly separable quantum commutative $H$-module algebra $A$ over which the Drinfeld element of $H$ acts trivially, we show that $A\#H$ is a weak Hopf algebra, and it can be embedded into a weak Hopf algebra $\operatorname{End}A^{\ast}\otimes H$. With these structure, $_{A\#H}\operatorname{Mod}$ is the monoidal category introduced by Cohen and Westreich, and $_{\operatorname{End}A^{\ast}\otimes H}\mathcal{M}$ is tensor equivalent to $_{H}\mathcal{M}$. If $A$ is in the M{ü}ger center of $_{H}{\mathcal{M}}$, then the embedding is a quasi-triangular weak Hopf algebra morphism. This explains the presence of a subgroup inclusion in the characterization of irreducible Yetter-Drinfeld modules for a finite group algebra.

math.QA↗

arXiv2022

Structures of Adjoint-Stable Algebras over Factorizable Hopf Algebras

For a quasi-triangular Hopf algebra $\left( H,R\right) $, there is a notion of transmuted braided group $H_{R}$ of $H$ introduced by Majid. The transmuted braided group $H_{R}$ is a Hopf algebra in the braided category $_{H}\mathcal{M}$. The $R$-adjoint-stable algebra associated with any simple left $H_{R}$-comodule is defined by the authors, and is used to characterize the structure of all irreducible Yetter-Drinfeld modules in ${}_{H}^{H} \mathcal{YD}$. In this note, we prove for a semisimple factorizable Hopf algebra $ \left( H,R\right) $ that any simple subcoalgebra of $H_R$ is $H$-stable and the $R$-adjoint-stable algebra for any simple left $H_R$-comodule is anti-isomorphic to $H$. As an application, we characterize all irreducible Yetter-Drinfeld modules.

math.RA↗

arXiv2021

Centers of Braided Tensor Categories

Let $\mathcal{C}$ be a finite braided multitensor category. Let $B$ be Majid's automorphism braided group of $\mathcal{C}$, then $B$ is a cocommutative Hopf algebra in $\mathcal{C}$. We show that the center of $\mathcal{C}$ is isomorphic to the category of left $B$-comodules in $\mathcal{C}$, and the decomposition of $B$ into a direct sum of indecomposable $\mathcal{C}$-subcoalgebras leads to a decomposition of $B$-$\operatorname*{Comod}_{\mathcal{C}}$ into a direct sum of indecomposable $\mathcal{C}$-module subcategories. As an application, we present an explicit characterization of the structure of irreducible Yetter-Drinfeld modules over semisimple quasi-triangular weak Hopf algebras. Our results generalize those results on finite groups and on quasi-triangular Hopf algebras.

math.QA↗

arXiv2020

Isotropic or anisotropic screening in black phosphorous: can doping tip the balance?

Black phosphorus (BP), a layered van der Waals (vdW) crystal, has unique in-plane band anisotropy and many resulting anisotropy properties such as the effective mass, electron mobility, optical absorption, thermal conductivity and plasmonic dispersion. However, whether anisotropic or isotropic charge screening exist in BP remains a controversial issue. Based on first-principles calculations, we study the screening properties in both of single-layer and bulk BP, especially concerning the role of doping. Without charge doping, the single-layer and bulk-phase BP show slight anisotropic screening. Electron and hole doping can increase the charge screening of BP and significantly change the relative static dielectric tensor elements along two different in-plane directions. We further study the charge density change induced by potassium (K) adatom near the BP surface, under different levels of charge doping. The calculated two-dimensional (2D) charge redistribution patterns also confirm that doping can greatly affect the screening feature and tip the balance between isotropic and anisotropic screening. We corroborate that screening in BP exhibit slight intrinsic anisotropy and doping has significant influence on its screening property.

cond-mat.mtrl-sci↗

arXiv2019

On the Structure of Irreducible Yetter-Drinfeld Modules over Quasi-Triangular Hopf Algebras

Let $\left( H,R\right) $ be a finite dimensional semisimple and cosemisimple quasi-triangular Hopf algebra over a field $k$. In this paper, we give the structure of irreducible objects of the Yetter-Drinfeld module category ${} {}_{H}^{H}\mathcal{YD}.$ Let $H_{R}$ be the Majid's transmuted braided group of $\left( H,R\right) ,$ we show that $H_{R}$ is cosemisimple. As a coalgebra, let $H_{R}=D_{1}\oplus\cdots\oplus D_{r}$ be the sum of minimal $H$-adjoint-stable subcoalgebras. For each $i$ $\left( 1\leq i\leq r\right) $, we choose a minimal left coideal $W_{i}$ of $D_{i}$, and we can define the $R$-adjoint-stable algebra $N_{W_{i}}$ of $W_{i}$. Using Ostrik's theorem on characterizing module categories over monoidal categories, we prove that $V\in{}_{H}^{H}\mathcal{YD}$ is irreducible if and only if there exists an $i$ $\left( 1\leq i\leq r\right) $ and an irreducible right $N_{W_{i}}$-module $U_{i}$, such that $V\cong U_{i}\otimes_{N_{W_{i}}}\left( H\otimes W_{i}\right) $. Our structure theorem generalizes the results of Dijkgraaf-Pasquier-Roche and Gould on Yetter-Drinfeld modules over finite group algebras. If $k$ is an algebraically closed field of characteristic, we stress that the $R$-adjoint-stable algebra $N_{W_{i}}$ is an algebra over which the dimension of each irreducible right module divides its dimension.

math.RA↗